AI Data Water

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  Apache Parquet

  Apache Parquet is a free and open-source column-oriented data storage format in the Apache Hadoop ecosystem inspired by Google Dremel interactive ad-hoc query system for analysis of read-only nested data. It is similar to RCFile and ORC, the other columnar-storage file formats in Hadoop, and is compatible with most of the data processing frameworks around Hadoop. It provides data compression and encoding schemes with enhanced performance to handle complex data in bulk. == History == The open-source project to build Apache Parquet began as a joint effort between Twitter and Cloudera using the record shredding and assembly algorithm as described in Google's Dremel. Parquet was designed as an improvement on the Trevni columnar storage format created by Doug Cutting, the creator of Hadoop. The name 'parquet' (lit. 'small compartment') refers to a style of decorative flooring and was chosen to "evoke the bottom layer of a database with an interesting layout". The first version, Apache Parquet 1.0, was released in July 2013. Since April 27, 2015, Apache Parquet has been a top-level Apache Software Foundation (ASF)-sponsored project. == Features == Apache Parquet is implemented using the record-shredding and assembly algorithm, which accommodates the complex data structures that can be used to store data. The values in each column are stored in contiguous memory locations, providing the following benefits: Column-wise compression is efficient in storage space Encoding and compression techniques specific to the type of data in each column can be used Queries that fetch specific column values need not read the entire row, thus improving performance Apache Parquet is implemented using the Apache Thrift framework, which increases its flexibility; it can work with a number of programming languages like C++, Java, Python, PHP, etc. As of August 2015, Parquet supports the big-data-processing frameworks including Apache Hive, Apache Drill, Apache Impala, Apache Crunch, Apache Pig, Cascading, Presto and Apache Spark. It is one of the external data formats used by the pandas Python data manipulation and analysis library. == Compression and encoding == In Parquet, compression is performed column by column, which enables different encoding schemes to be used for text and integer data. This strategy also keeps the door open for newer and better encoding schemes to be implemented as they are invented. Parquet supports various compression formats: snappy, gzip, LZO, brotli, zstd, and LZ4. === Dictionary encoding === Parquet has an automatic dictionary encoding enabled dynamically for data with a small number of unique values (i.e. below 105) that enables significant compression and boosts processing speed. === Bit packing === Storage of integers is usually done with dedicated 32 or 64 bits per integer. For small integers, packing multiple integers into the same space makes storage more efficient. === Run-length encoding (RLE) === To optimize storage of multiple occurrences of the same value, run-length encoding is used, which is where a single value is stored once along with the number of occurrences. Parquet implements a hybrid of bit packing and RLE, in which the encoding switches based on which produces the best compression results. This strategy works well for certain types of integer data and combines well with dictionary encoding. == Cloud Storage and Data Lakes == Parquet is widely used as the underlying file format in modern cloud-based data lake architectures. Cloud storage systems such as Amazon S3, Azure Data Lake Storage, and Google Cloud Storage commonly store data in Parquet format due to its efficient columnar representation and retrieval capabilities. Data lakehouse frameworks—including Apache Iceberg, Delta Lake, and Apache Hudi —build an additional metadata layer on top of Parquet files to support features such as schema evolution, time-travel queries, and ACID-compliant transactions. In these architectures, Parquet files serve as the immutable storage layer while the table formats manage data versioning and transactional integrity. == Comparison == Apache Parquet is comparable to RCFile and Optimized Row Columnar (ORC) file formats — all three fall under the category of columnar data storage within the Hadoop ecosystem. They all have better compression and encoding with improved read performance at the cost of slower writes. In addition to these features, Apache Parquet supports limited schema evolution, i.e., the schema can be modified according to the changes in the data. It also provides the ability to add new columns and merge schemas that do not conflict. Apache Arrow is designed as an in-memory complement to on-disk columnar formats like Parquet and ORC. The Arrow and Parquet projects include libraries that allow for reading and writing between the two formats. == Implementations == Known implementations of Parquet include:

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  Autoencoder

  An autoencoder is a type of artificial neural network used to learn efficient codings of unlabeled data (unsupervised learning). An autoencoder learns two functions: an encoding function that transforms the input data, and a decoding function that recreates the input data from the encoded representation. The autoencoder learns an efficient representation (encoding) for a set of data, typically for dimensionality reduction, to generate lower-dimensional embeddings for subsequent use by other machine learning algorithms. Variants exist which aim to make the learned representations assume useful properties. Examples are regularized autoencoders (sparse, denoising and contractive autoencoders), which are effective in learning representations for subsequent classification tasks, and variational autoencoders, which can be used as generative models. Autoencoders are applied to many problems, including facial recognition, feature detection, anomaly detection, and learning the meaning of words. In terms of data synthesis, autoencoders can also be used to randomly generate new data that is similar to the input (training) data. == Mathematical principles == === Definition === An autoencoder is defined by the following components: Two sets: the space of encoded messages Z {\displaystyle {\mathcal {Z}}} ; the space of decoded messages X {\displaystyle {\mathcal {X}}} . Typically X {\displaystyle {\mathcal {X}}} and Z {\displaystyle {\mathcal {Z}}} are Euclidean spaces, that is, X = R m , Z = R n {\displaystyle {\mathcal {X}}=\mathbb {R} ^{m},{\mathcal {Z}}=\mathbb {R} ^{n}} with m > n . {\displaystyle m>n.} Two parametrized families of functions: the encoder family E ϕ : X → Z {\displaystyle E_{\phi }:{\mathcal {X}}\rightarrow {\mathcal {Z}}} , parametrized by ϕ {\displaystyle \phi } ; the decoder family D θ : Z → X {\displaystyle D_{\theta }:{\mathcal {Z}}\rightarrow {\mathcal {X}}} , parametrized by θ {\displaystyle \theta } .For any x ∈ X {\displaystyle x\in {\mathcal {X}}} , we usually write z = E ϕ ( x ) {\displaystyle z=E_{\phi }(x)} , and refer to it as the code, the latent variable, latent representation, latent vector, etc. Conversely, for any z ∈ Z {\displaystyle z\in {\mathcal {Z}}} , we usually write x ′ = D θ ( z ) {\displaystyle x'=D_{\theta }(z)} , and refer to it as the (decoded) message. Usually, both the encoder and the decoder are defined as multilayer perceptrons (MLPs). For example, a one-layer-MLP encoder E ϕ {\displaystyle E_{\phi }} is: E ϕ ( x ) = σ ( W x + b ) {\displaystyle E_{\phi }(\mathbf {x} )=\sigma (Wx+b)} where σ {\displaystyle \sigma } is an element-wise activation function, W {\displaystyle W} is a "weight" matrix, and b {\displaystyle b} is a "bias" vector. === Training an autoencoder === An autoencoder, by itself, is simply a tuple of two functions. To judge its quality, we need a task. A task is defined by a reference probability distribution μ r e f {\displaystyle \mu _{ref}} over X {\displaystyle {\mathcal {X}}} , and a "reconstruction quality" function d : X × X → [ 0 , ∞ ] {\displaystyle d:{\mathcal {X}}\times {\mathcal {X}}\to [0,\infty ]} , such that d ( x , x ′ ) {\displaystyle d(x,x')} measures how much x ′ {\displaystyle x'} differs from x {\displaystyle x} . With those, we can define the loss function for the autoencoder as L ( θ , ϕ ) := E x ∼ μ r e f [ d ( x , D θ ( E ϕ ( x ) ) ) ] {\displaystyle L(\theta ,\phi ):=\mathbb {\mathbb {E} } _{x\sim \mu _{ref}}[d(x,D_{\theta }(E_{\phi }(x)))]} The optimal autoencoder for the given task ( μ r e f , d ) {\displaystyle (\mu _{ref},d)} is then arg ⁡ min θ , ϕ L ( θ , ϕ ) {\displaystyle \arg \min _{\theta ,\phi }L(\theta ,\phi )} . The search for the optimal autoencoder can be accomplished by any mathematical optimization technique, but usually by gradient descent. This search process is referred to as "training the autoencoder". In most situations, the reference distribution is just the empirical distribution given by a dataset { x 1 , . . . , x N } ⊂ X {\displaystyle \{x_{1},...,x_{N}\}\subset {\mathcal {X}}} , so that μ r e f = 1 N ∑ i = 1 N δ x i {\displaystyle \mu _{ref}={\frac {1}{N}}\sum _{i=1}^{N}\delta _{x_{i}}} where δ x i {\displaystyle \delta _{x_{i}}} is the Dirac measure, the quality function is just L 2 {\displaystyle L^{2}} loss: d ( x , x ′ ) = ‖ x − x ′ ‖ 2 2 {\displaystyle d(x,x')=\|x-x'\|_{2}^{2}} , and ‖ ⋅ ‖ 2 {\displaystyle \|\cdot \|_{2}} is the Euclidean norm. Then the problem of searching for the optimal autoencoder is just a least-squares optimization: min θ , ϕ L ( θ , ϕ ) , where L ( θ , ϕ ) = 1 N ∑ i = 1 N ‖ x i − D θ ( E ϕ ( x i ) ) ‖ 2 2 {\displaystyle \min _{\theta ,\phi }L(\theta ,\phi ),\qquad {\text{where }}L(\theta ,\phi )={\frac {1}{N}}\sum _{i=1}^{N}\|x_{i}-D_{\theta }(E_{\phi }(x_{i}))\|_{2}^{2}} === Interpretation === An autoencoder has two main parts: an encoder that maps the message to a code, and a decoder that reconstructs the message from the code. An optimal autoencoder would perform as close to perfect reconstruction as possible, with "close to perfect" defined by the reconstruction quality function d {\displaystyle d} . The simplest way to perform the copying task perfectly would be to duplicate the signal. To suppress this behavior, the code space Z {\displaystyle {\mathcal {Z}}} usually has fewer dimensions than the message space X {\displaystyle {\mathcal {X}}} . Such an autoencoder is called undercomplete. It can be interpreted as compressing the message, or reducing its dimensionality. At the limit of an ideal undercomplete autoencoder, every possible code z {\displaystyle z} in the code space is used to encode a message x {\displaystyle x} that really appears in the distribution μ r e f {\displaystyle \mu _{ref}} , and the decoder is also perfect: D θ ( E ϕ ( x ) ) = x {\displaystyle D_{\theta }(E_{\phi }(x))=x} . This ideal autoencoder can then be used to generate messages indistinguishable from real messages, by feeding its decoder arbitrary code z {\displaystyle z} and obtaining D θ ( z ) {\displaystyle D_{\theta }(z)} , which is a message that really appears in the distribution μ r e f {\displaystyle \mu _{ref}} . If the code space Z {\displaystyle {\mathcal {Z}}} has dimension larger than (overcomplete), or equal to, the message space X {\displaystyle {\mathcal {X}}} , or the hidden units are given enough capacity, an autoencoder can learn the identity function and become useless. However, experimental results found that overcomplete autoencoders might still learn useful features. In the ideal setting, the code dimension and the model capacity could be set on the basis of the complexity of the data distribution to be modeled. A standard way to do so is to add modifications to the basic autoencoder, to be detailed below. == Variations == === Variational autoencoder (VAE) === Variational autoencoders (VAEs) belong to the families of variational Bayesian methods. Despite the architectural similarities with basic autoencoders, VAEs are architected with different goals and have a different mathematical formulation. The latent space is, in this case, composed of a mixture of distributions instead of fixed vectors. Given an input dataset x {\displaystyle x} characterized by an unknown probability function P ( x ) {\displaystyle P(x)} and a multivariate latent encoding vector z {\displaystyle z} , the objective is to model the data as a distribution p θ ( x ) {\displaystyle p_{\theta }(x)} , with θ {\displaystyle \theta } defined as the set of the network parameters so that p θ ( x ) = ∫ z p θ ( x , z ) d z {\displaystyle p_{\theta }(x)=\int _{z}p_{\theta }(x,z)dz} . === Sparse autoencoder (SAE) === Inspired by the sparse coding hypothesis in neuroscience, sparse autoencoders (SAE) are variants of autoencoders, such that the codes E ϕ ( x ) {\displaystyle E_{\phi }(x)} for messages tend to be sparse codes, that is, E ϕ ( x ) {\displaystyle E_{\phi }(x)} is close to zero in most entries. Sparse autoencoders may include more (rather than fewer) hidden units than inputs, but only a small number of the hidden units are allowed to be active at the same time. Encouraging sparsity improves performance on classification tasks. There are two main ways to enforce sparsity. One way is to simply clamp all but the highest-k activations of the latent code to zero. This is the k-sparse autoencoder. The k-sparse autoencoder inserts the following "k-sparse function" in the latent layer of a standard autoencoder: f k ( x 1 , . . . , x n ) = ( x 1 b 1 , . . . , x n b n ) {\displaystyle f_{k}(x_{1},...,x_{n})=(x_{1}b_{1},...,x_{n}b_{n})} where b i = 1 {\displaystyle b_{i}=1} if | x i | {\displaystyle |x_{i}|} ranks in the top k, and 0 otherwise. Backpropagating through f k {\displaystyle f_{k}} is simple: set gradient to 0 for b i = 0 {\displaystyle b_{i}=0} entries, and keep gradient for b i = 1 {\displaystyle b_{i}=1} entries. This is essentially a generalized ReLU function. The other way is a relaxed version of the k-

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  Detrended correspondence analysis

  Detrended correspondence analysis (DCA) is a multivariate statistical technique widely used by ecologists to find the main factors or gradients in large, species-rich but usually sparse data matrices that typify ecological community data. DCA is frequently used to suppress artifacts inherent in most other multivariate analyses when applied to gradient data. == History == DCA was created in 1979 by Mark Hill of the United Kingdom's Institute for Terrestrial Ecology (now merged into Centre for Ecology and Hydrology) and implemented in FORTRAN code package called DECORANA (Detrended Correspondence Analysis), a correspondence analysis method. DCA is sometimes erroneously referred to as DECORANA; however, DCA is the underlying algorithm, while DECORANA is a tool implementing it. == Issues addressed == According to Hill and Gauch, DCA suppresses two artifacts inherent in most other multivariate analyses when applied to gradient data. An example is a time-series of plant species colonising a new habitat; early successional species are replaced by mid-successional species, then by late successional ones (see example below). When such data are analysed by a standard ordination such as a correspondence analysis: the ordination scores of the samples will exhibit the 'edge effect', i.e. the variance of the scores at the beginning and the end of a regular succession of species will be considerably smaller than that in the middle, when presented as a graph the points will be seen to follow a horseshoe shaped curve rather than a straight line ('arch effect'), even though the process under analysis is a steady and continuous change that human intuition would prefer to see as a linear trend. Outside ecology, the same artifacts occur when gradient data are analysed (e.g. soil properties along a transect running between 2 different geologies, or behavioural data over the lifespan of an individual) because the curved projection is an accurate representation of the shape of the data in multivariate space. Ter Braak and Prentice (1987, p. 121) cite a simulation study analysing two-dimensional species packing models resulting in a better performance of DCA compared to CA. == Method == DCA is an iterative algorithm that has shown itself to be a highly reliable and useful tool for data exploration and summary in community ecology (Shaw 2003). It starts by running a standard ordination (CA or reciprocal averaging) on the data, to produce the initial horse-shoe curve in which the 1st ordination axis distorts into the 2nd axis. It then divides the first axis into segments (default = 26), and rescales each segment to have mean value of zero on the 2nd axis - this effectively squashes the curve flat. It also rescales the axis so that the ends are no longer compressed relative to the middle, so that 1 DCA unit approximates to the same rate of turnover all the way through the data: the rule of thumb is that 4 DCA units mean that there has been a total turnover in the community. Ter Braak and Prentice (1987, p. 122) warn against the non-linear rescaling of the axes due to robustness issues and recommend using detrending-by-polynomials only. == Drawbacks == No significance tests are available with DCA, although there is a constrained (canonical) version called DCCA in which the axes are forced by Multiple linear regression to correlate optimally with a linear combination of other (usually environmental) variables; this allows testing of a null model by Monte-Carlo permutation analysis. == Example == The example shows an ideal data set: The species data is in rows, samples in columns. For each sample along the gradient, a new species is introduced but another species is no longer present. The result is a sparse matrix. Ones indicate the presence of a species in a sample. Except at the edges each sample contains five species. The plot of the first two axes of the correspondence analysis result on the right hand side clearly shows the disadvantages of this procedure: the edge effect, i.e. the points are clustered at the edges of the first axis, and the arch effect. == Software == An open source implementation of DCA, based on the original FORTRAN code, is available in the vegan R-package.

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  Multi-surface method

  The multi-surface method (MSM) is a form of decision making using the concept of piecewise-linear separability of datasets to categorize data. == Introduction == Two datasets are linearly separable if their convex hulls do not intersect. The method may be formulated as a feedforward neural network with weights that are trained via linear programming. Comparisons between neural networks trained with the MSM versus backpropagation show MSM is better able to classify data. The decision problem associated linear program for the MSM is NP-complete. == Mathematical formulation == Given two finite disjoint point sets A , B ∈ R n {\displaystyle {\mathcal {A,B}}\in \mathbb {R} ^{n}} , find a discriminant, f : R n → R {\displaystyle f:\mathbb {R} ^{n}\to \mathbb {R} } such that f ( A ) > 0 , f ( B ) ≤ 0 {\displaystyle f({\mathcal {A}})>0,f({\mathcal {B}})\leq 0} . If the intersection of convex hulls of the two sets is the empty set, then it is possible to use a single linear program to obtain a linear discriminant of the form, f ( x ) = c x + γ {\displaystyle f(x)=cx+\gamma } . Usually, in real applications, the sets' convex hulls do intersect, and a (often non-convex) piecewise-linear discriminant can be used, through the use of several linear programs.

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  Automated negotiation

  Automated negotiation is a form of interaction in systems that are composed of multiple autonomous agents, in which the aim is to reach agreements through an iterative process of making offers. Automated negotiation can be employed for many tasks human negotiators regularly engage in, such as bargaining and joint decision making. The main topics in automated negotiation revolve around the design of protocols and negotiating strategies. == History == Through digitization, the beginning of the 21st century has seen a growing interest in the automation of negotiation and e-negotiation systems, for example in the setting of e-commerce. This interest is fueled by the promise of automated agents being able to negotiate on behalf of human negotiators, and to find better outcomes than human negotiators. == Examples == Examples of automated negotiation include: Online dispute resolution, in which disagreements between parties are settled. Sponsored search auction, where bids are placed on advertisement keywords. Content negotiation, in which user agents negotiate over HTTP about how to best represent a web resource. Negotiation support systems, in which negotiation decision-making activities are supported by an information system.

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  FERET (facial recognition technology)

  The Facial Recognition Technology (FERET) program was a government-sponsored project that aimed to create a large, automatic face-recognition system for intelligence, security, and law enforcement purposes. The program began in 1993 under the combined leadership of Dr. Harry Wechsler at George Mason University (GMU) and Dr. Jonathon Phillips at the Army Research Laboratory (ARL) in Adelphi, Maryland and resulted in the development of the Facial Recognition Technology (FERET) database. The goal of the FERET program was to advance the field of face recognition technology by establishing a common database of facial imagery for researchers to use and setting a performance baseline for face-recognition algorithms. Potential areas where this face-recognition technology could be used include: Automated searching of mug books using surveillance photos Controlling access to restricted facilities or equipment Checking the credentials of personnel for background and security clearances Monitoring airports, border crossings, and secure manufacturing facilities for particular individuals Finding and logging multiple appearances of individuals over time in surveillance videos Verifying identities at ATM machines Searching photo ID records for fraud detection The FERET database has been used by more than 460 research groups and is currently managed by the National Institute of Standards and Technology (NIST). By 2017, the FERET database has been used to train artificial intelligence programs and computer vision algorithms to identify and sort faces. == History == The origin of facial recognition technology is largely attributed to Woodrow Wilson Bledsoe and his work in the 1960s, when he developed a system to identify faces from a database of thousands of photographs. The FERET program first began as a way to unify a large body of face-recognition technology research under a standard database. Before the program's inception, most researchers created their own facial imagery database that was attuned to their own specific area of study. These personal databases were small and usually consisted of images from less than 50 individuals. The only notable exceptions were the following: Alex Pentland’s database of around 7500 facial images at the Massachusetts Institute of Technology (MIT) Joseph Wilder's database of around 250 individuals at Rutgers University Christoph von der Malsburg’s database of around 100 facial images at the University of Southern California (USC) The lack of a common database made it difficult to compare the results of face recognition studies in the scientific literature because each report involved different assumptions, scoring methods, and images. Most of the papers that were published did not use images from a common database nor follow a standard testing protocol. As a result, researchers were unable to make informed comparisons between the performances of different face-recognition algorithms. In September 1993, the FERET program was spearheaded by Dr. Harry Wechsler and Dr. Jonathon Phillips under the sponsorship of the U.S. Department of Defense Counterdrug Technology Development Program through DARPA with ARL serving as technical agent. === Phase I === The first facial images for the FERET database were collected from August 1993 to December 1994, a time period known as Phase I. The pictures were initially taken with a 35-mm camera at both GMU and ARL facilities, and the same physical setup was used in each photography session to keep the images consistent. For each individual, the pictures were taken in sets, including two frontal views, a right and left profile, a right and left quarter profile, a right and left half profile, and sometimes at five extra locations. Therefore, a set of images consisted of 5 to 11 images per person. At the end of Phase I, the FERET database had collected 673 sets of images, resulting in over 5000 total images. At the end of Phase I, five organizations were given the opportunity to test their face-recognition algorithm on the newly created FERET database in order to compare how they performed against each other. There five principal investigators were: MIT, led by Alex Pentland Rutgers University, led by Joseph Wilder The Analytic Science Company (TASC), led by Gale Gordon The University of Illinois at Chicago (UIC) and the University of Illinois at Urbana-Champaign, led by Lewis Sadler and Thomas Huang USC, led by Christoph von der Malsburg During this evaluation, three different automatic tests were given to the principal investigators without human intervention: The large gallery test, which served to baseline how algorithms performed against a database when it has not been properly tuned. The false-alarm test, which tested how well the algorithm monitored an airport for suspected terrorists. The rotation test, which measured how well the algorithm performed when the images of an individual in the gallery had different poses compared to those in the probe set. For most of the test trials, the algorithms developed by USC and MIT managed to outperform the other three algorithms for the Phase I evaluation. === Phase II === Phase II began after Phase I, and during this time, the FERET database acquired more sets of facial images. By the start of the Phase II evaluation in March 1995, the database contained 1109 sets of images for a total of 8525 images of 884 individuals. During the second evaluation, the same algorithms from the Phase I evaluation were given a single test. However, the database now contained significantly more duplicate images (463, compared to the previous 60), making the test more challenging. === Phase III === Afterwards, the FERET program entered Phase III where another 456 sets of facial images were added to the database. The Phase III evaluation, which took place in September 1996, aimed to not only gauge the progress of the algorithms since the Phase I assessment but also identify the strengths and weaknesses of each algorithm and determine future objectives for research. By the end of 1996, the FERET database had accumulated a total of 14,126 facial images pertaining to 1199 different individuals as well as 365 duplicate sets of images. As a result of the FERET program, researchers were able to establish a common baseline for comparing different face-recognition algorithms and create a large standard database of facial images that is open for research. In 2003, DARPA released a high-resolution, 24-bit color version of the images in the FERET database (existing reference).

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  One-class classification

  In machine learning, one-class classification (OCC), also known as unary classification or class-modelling, is an approach to the training of binary classifiers in which only examples of one of the two classes are used. Examples include the monitoring of helicopter gearboxes, motor failure prediction, or assessing the operational status of a nuclear plant as 'normal': In such scenarios, there are few, if any, examples of the catastrophic system states – rare outliers – that comprise the second class. Alternatively, the class that is being focused on may cover a small, coherent subset of the data and the training may rely on an information bottleneck approach. In practice, counter-examples from the second class may be used in later rounds of training to further refine the algorithm. == Overview == The term one-class classification (OCC) was coined by Moya & Hush (1996) and many applications can be found in scientific literature, for example outlier detection, anomaly detection, novelty detection. A feature of OCC is that it uses only sample points from the assigned class, so that a representative sampling is not strictly required for non-target classes. == Introduction == SVM based one-class classification (OCC) relies on identifying the smallest hypersphere (with radius r, and center c) consisting of all the data points. This method is called Support Vector Data Description (SVDD). Formally, the problem can be defined in the following constrained optimization form, min r , c r 2 subject to, | | Φ ( x i ) − c | | 2 ≤ r 2 ∀ i = 1 , 2 , . . . , n {\displaystyle \min _{r,c}r^{2}{\text{ subject to, }}||\Phi (x_{i})-c||^{2}\leq r^{2}\;\;\forall i=1,2,...,n} However, the above formulation is highly restrictive, and is sensitive to the presence of outliers. Therefore, a flexible formulation, that allow for the presence of outliers is formulated as shown below, min r , c , ζ r 2 + 1 ν n ∑ i = 1 n ζ i {\displaystyle \min _{r,c,\zeta }r^{2}+{\frac {1}{\nu n}}\sum _{i=1}^{n}\zeta _{i}} subject to, | | Φ ( x i ) − c | | 2 ≤ r 2 + ζ i ∀ i = 1 , 2 , . . . , n {\displaystyle {\text{subject to, }}||\Phi (x_{i})-c||^{2}\leq r^{2}+\zeta _{i}\;\;\forall i=1,2,...,n} From the Karush–Kuhn–Tucker conditions for optimality, we get c = ∑ i = 1 n α i Φ ( x i ) , {\displaystyle c=\sum _{i=1}^{n}\alpha _{i}\Phi (x_{i}),} where the α i {\displaystyle \alpha _{i}} 's are the solution to the following optimization problem: max α ∑ i = 1 n α i κ ( x i , x i ) − ∑ i , j = 1 n α i α j κ ( x i , x j ) {\displaystyle \max _{\alpha }\sum _{i=1}^{n}\alpha _{i}\kappa (x_{i},x_{i})-\sum _{i,j=1}^{n}\alpha _{i}\alpha _{j}\kappa (x_{i},x_{j})} subject to, ∑ i = 1 n α i = 1 and 0 ≤ α i ≤ 1 ν n for all i = 1 , 2 , . . . , n . {\displaystyle \sum _{i=1}^{n}\alpha _{i}=1{\text{ and }}0\leq \alpha _{i}\leq {\frac {1}{\nu n}}{\text{for all }}i=1,2,...,n.} The introduction of kernel function provide additional flexibility to the One-class SVM (OSVM) algorithm. === PU (Positive Unlabeled) learning === A similar problem is PU learning, in which a binary classifier is constructed by semi-supervised learning from only positive and unlabeled sample points. In PU learning, two sets of examples are assumed to be available for training: the positive set P {\displaystyle P} and a mixed set U {\displaystyle U} , which is assumed to contain both positive and negative samples, but without these being labeled as such. This contrasts with other forms of semisupervised learning, where it is assumed that a labeled set containing examples of both classes is available in addition to unlabeled samples. A variety of techniques exist to adapt supervised classifiers to the PU learning setting, including variants of the EM algorithm. PU learning has been successfully applied to text, time series, bioinformatics tasks, and remote sensing data. == Approaches == Several approaches have been proposed to solve one-class classification (OCC). The approaches can be distinguished into three main categories, density estimation, boundary methods, and reconstruction methods. === Density estimation methods === Density estimation methods rely on estimating the density of the data points, and set the threshold. These methods rely on assuming distributions, such as Gaussian, or a Poisson distribution. Following which discordancy tests can be used to test the new objects. These methods are robust to scale variance. Gaussian model is one of the simplest methods to create one-class classifiers. Due to Central Limit Theorem (CLT), these methods work best when large number of samples are present, and they are perturbed by small independent error values. The probability distribution for a d-dimensional object is given by: p N ( z ; μ ; Σ ) = 1 ( 2 π ) d 2 | Σ | 1 2 exp ⁡ { − 1 2 ( z − μ ) T Σ − 1 ( z − μ ) } {\displaystyle p_{\mathcal {N}}(z;\mu ;\Sigma )={\frac {1}{(2\pi )^{\frac {d}{2}}|\Sigma |^{\frac {1}{2}}}}\exp \left\{-{\frac {1}{2}}(z-\mu )^{T}\Sigma ^{-1}(z-\mu )\right\}} Where, μ {\displaystyle \mu } is the mean and Σ {\displaystyle \Sigma } is the covariance matrix. Computing the inverse of covariance matrix ( Σ − 1 {\displaystyle \Sigma ^{-1}} ) is the costliest operation, and in the cases where the data is not scaled properly, or data has singular directions pseudo-inverse Σ + {\displaystyle \Sigma ^{+}} is used to approximate the inverse, and is calculated as Σ T ( Σ Σ T ) − 1 {\displaystyle \Sigma ^{T}(\Sigma \Sigma ^{T})^{-1}} . === Boundary methods === Boundary methods focus on setting boundaries around a few set of points, called target points. These methods attempt to optimize the volume. Boundary methods rely on distances, and hence are not robust to scale variance. K-centers method, NN-d, and SVDD are some of the key examples. K-centers In K-center algorithm, k {\displaystyle k} small balls with equal radius are placed to minimize the maximum distance of all minimum distances between training objects and the centers. Formally, the following error is minimized, ε k − c e n t e r = max i ( min k | | x i − μ k | | 2 ) {\displaystyle \varepsilon _{k-center}=\max _{i}(\min _{k}||x_{i}-\mu _{k}||^{2})} The algorithm uses forward search method with random initialization, where the radius is determined by the maximum distance of the object, any given ball should capture. After the centers are determined, for any given test object z {\displaystyle z} the distance can be calculated as, d k − c e n t r ( z ) = min k | | z − μ k | | 2 {\displaystyle d_{k-centr}(z)=\min _{k}||z-\mu _{k}||^{2}} === Reconstruction methods === Reconstruction methods use prior knowledge and generating process to build a generating model that best fits the data. New objects can be described in terms of a state of the generating model. Some examples of reconstruction methods for OCC are, k-means clustering, learning vector quantization, self-organizing maps, etc. == Applications == === Document classification === The basic Support Vector Machine (SVM) paradigm is trained using both positive and negative examples, however studies have shown there are many valid reasons for using only positive examples. When the SVM algorithm is modified to only use positive examples, the process is considered one-class classification. One situation where this type of classification might prove useful to the SVM paradigm is in trying to identify a web browser's sites of interest based only off of the user's browsing history. === Biomedical studies === One-class classification can be particularly useful in biomedical studies where often data from other classes can be difficult or impossible to obtain. In studying biomedical data it can be difficult and/or expensive to obtain the set of labeled data from the second class that would be necessary to perform a two-class classification. A study from The Scientific World Journal found that the typicality approach is the most useful in analysing biomedical data because it can be applied to any type of dataset (continuous, discrete, or nominal). The typicality approach is based on the clustering of data by examining data and placing it into new or existing clusters. To apply typicality to one-class classification for biomedical studies, each new observation, y 0 {\displaystyle y_{0}} , is compared to the target class, C {\displaystyle C} , and identified as an outlier or a member of the target class. === Unsupervised Concept Drift Detection === One-class classification has similarities with unsupervised concept drift detection, where both aim to identify whether the unseen data share similar characteristics to the initial data. A concept is referred to as the fixed probability distribution which data is drawn from. In unsupervised concept drift detection, the goal is to detect if the data distribution changes without utilizing class labels. In one-class classification, the flow of data is not important. Unseen data is classified as typical or outlier depending on its characteristics, whether it is from the initi

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  K-nearest neighbors algorithm

  In statistics, the k-nearest neighbors algorithm (k-NN) is a non-parametric supervised learning method. It was first developed by Evelyn Fix and Joseph Hodges in 1951, and later expanded by Thomas Cover. In classification, a new example is assigned a label based on the labels of its k nearest training examples; in regression, the prediction is computed from the values of those neighbors. Most often, it is used for classification, as a k-NN classifier, the output of which is a class membership. An object is classified by a plurality vote of its neighbors, with the object being assigned to the class most common among its k nearest neighbors (k is a positive integer, typically small). If k = 1, then the object is simply assigned to the class of that single nearest neighbor. The k-NN algorithm can also be generalized for regression. In k-NN regression, also known as nearest neighbor smoothing, the output is the property value for the object. This value is the average of the values of k nearest neighbors. If k = 1, then the output is simply assigned to the value of that single nearest neighbor, also known as nearest neighbor interpolation. For both classification and regression, a useful technique can be to assign weights to the contributions of the neighbors, so that nearer neighbors contribute more to the average than distant ones. For example, a common weighting scheme consists of giving each neighbor a weight of 1/d, where d is the distance to the neighbor. The input consists of the k closest training examples in a data set. The neighbors are taken from a set of objects for which the class (for k-NN classification) or the object property value (for k-NN regression) is known. This can be thought of as the training set for the algorithm, though no explicit training step is required. A peculiarity (sometimes even a disadvantage) of the k-NN algorithm is its sensitivity to the local structure of the data. In k-NN classification the function is only approximated locally and all computation is deferred until function evaluation. Since this algorithm relies on distance, if the features represent different physical units or come in vastly different scales, then feature-wise normalizing of the training data can greatly improve its accuracy. == Statistical setting == Suppose we have pairs ( X 1 , Y 1 ) , ( X 2 , Y 2 ) , … , ( X n , Y n ) {\displaystyle (X_{1},Y_{1}),(X_{2},Y_{2}),\dots ,(X_{n},Y_{n})} taking values in R d × { 1 , 2 } {\displaystyle \mathbb {R} ^{d}\times \{1,2\}} , where Y is the class label of X, so that X | Y = r ∼ P r {\displaystyle X|Y=r\sim P_{r}} for r = 1 , 2 {\displaystyle r=1,2} (and probability distributions P r {\displaystyle P_{r}} ). Given some norm ‖ ⋅ ‖ {\displaystyle \|\cdot \|} on R d {\displaystyle \mathbb {R} ^{d}} and a point x ∈ R d {\displaystyle x\in \mathbb {R} ^{d}} , let ( X ( 1 ) , Y ( 1 ) ) , … , ( X ( n ) , Y ( n ) ) {\displaystyle (X_{(1)},Y_{(1)}),\dots ,(X_{(n)},Y_{(n)})} be a reordering of the training data such that ‖ X ( 1 ) − x ‖ ≤ ⋯ ≤ ‖ X ( n ) − x ‖ {\displaystyle \|X_{(1)}-x\|\leq \dots \leq \|X_{(n)}-x\|} . == Algorithm == The training examples are vectors in a multidimensional feature space, each with a class label. The training phase of the algorithm consists only of storing the feature vectors and class labels of the training samples. In the classification phase, k is a user-defined constant, and an unlabeled vector (a query or test point) is classified by assigning the label which is most frequent among the k training samples nearest to that query point. A commonly used distance metric for continuous variables is Euclidean distance. For discrete variables, such as for text classification, another metric can be used, such as the overlap metric (or Hamming distance). In the context of gene expression microarray data, for example, k-NN has been employed with correlation coefficients, such as Pearson and Spearman, as a metric. Often, the classification accuracy of k-NN can be improved significantly if the distance metric is learned with specialized algorithms such as large margin nearest neighbor or neighborhood components analysis. A drawback of the basic "majority voting" classification occurs when the class distribution is skewed. That is, examples of a more frequent class tend to dominate the prediction of the new example, because they tend to be common among the k nearest neighbors due to their large number. One way to overcome this problem is to weight the classification, taking into account the distance from the test point to each of its k nearest neighbors. The class (or value, in regression problems) of each of the k nearest points is multiplied by a weight proportional to the inverse of the distance from that point to the test point. Another way to overcome skew is by abstraction in data representation. For example, in a self-organizing map (SOM), each node is a representative (a center) of a cluster of similar points, regardless of their density in the original training data. k-NN can then be applied to the SOM. == Parameter selection == The best choice of k depends upon the data; generally, larger values of k reduces effect of the noise on the classification, but make boundaries between classes less distinct. A good k can be selected by various heuristic techniques (see hyperparameter optimization). The special case where the class is predicted to be the class of the closest training sample (i.e. when k = 1) is called the nearest neighbor algorithm. The accuracy of the k-NN algorithm can be severely degraded by the presence of noisy or irrelevant features, or if the feature scales are not consistent with their importance. Much research effort has been put into selecting or scaling features to improve classification. A particularly popular approach is the use of evolutionary algorithms to optimize feature scaling. Another popular approach is to scale features by the mutual information of the training data with the training classes. In binary (two class) classification problems, it is helpful to choose k to be an odd number as this avoids tied votes. One popular way of choosing the empirically optimal k in this setting is via bootstrap method. == The 1-nearest neighbor classifier == The most intuitive nearest neighbour type classifier is the one nearest neighbour classifier that assigns a point x to the class of its closest neighbour in the feature space, that is C n 1 n n ( x ) = Y ( 1 ) {\displaystyle C_{n}^{1nn}(x)=Y_{(1)}} . As the size of training data set approaches infinity, the one nearest neighbour classifier guarantees an error rate of no worse than twice the Bayes error rate (the minimum achievable error rate given the distribution of the data). == The weighted nearest neighbour classifier == The k-nearest neighbour classifier can be viewed as assigning the k nearest neighbours a weight 1 / k {\displaystyle 1/k} and all others 0 weight. This can be generalised to weighted nearest neighbour classifiers. That is, where the ith nearest neighbour is assigned a weight w n i {\displaystyle w_{ni}} , with ∑ i = 1 n w n i = 1 {\textstyle \sum _{i=1}^{n}w_{ni}=1} . An analogous result on the strong consistency of weighted nearest neighbour classifiers also holds. Let C n w n n {\displaystyle C_{n}^{wnn}} denote the weighted nearest classifier with weights { w n i } i = 1 n {\displaystyle \{w_{ni}\}_{i=1}^{n}} . Subject to regularity conditions, which in asymptotic theory are conditional variables which require assumptions to differentiate among parameters with some criteria. On the class distributions the excess risk has the following asymptotic expansion R R ( C n w n n ) − R R ( C Bayes ) = ( B 1 s n 2 + B 2 t n 2 ) { 1 + o ( 1 ) } , {\displaystyle {\mathcal {R}}_{\mathcal {R}}(C_{n}^{wnn})-{\mathcal {R}}_{\mathcal {R}}(C^{\text{Bayes}})=\left(B_{1}s_{n}^{2}+B_{2}t_{n}^{2}\right)\{1+o(1)\},} for constants B 1 {\displaystyle B_{1}} and B 2 {\displaystyle B_{2}} where s n 2 = ∑ i = 1 n w n i 2 {\displaystyle s_{n}^{2}=\sum _{i=1}^{n}w_{ni}^{2}} and t n = n − 2 / d ∑ i = 1 n w n i { i 1 + 2 / d − ( i − 1 ) 1 + 2 / d } {\displaystyle t_{n}=n^{-2/d}\sum _{i=1}^{n}w_{ni}\left\{i^{1+2/d}-(i-1)^{1+2/d}\right\}} . The optimal weighting scheme { w n i ∗ } i = 1 n {\displaystyle \{w_{ni}^{}\}_{i=1}^{n}} , that balances the two terms in the display above, is given as follows: set k ∗ = ⌊ B n 4 d + 4 ⌋ {\displaystyle k^{}=\lfloor Bn^{\frac {4}{d+4}}\rfloor } , w n i ∗ = 1 k ∗ [ 1 + d 2 − d 2 k ∗ 2 / d { i 1 + 2 / d − ( i − 1 ) 1 + 2 / d } ] {\displaystyle w_{ni}^{}={\frac {1}{k^{}}}\left[1+{\frac {d}{2}}-{\frac {d}{2{k^{}}^{2/d}}}\{i^{1+2/d}-(i-1)^{1+2/d}\}\right]} for i = 1 , 2 , … , k ∗ {\displaystyle i=1,2,\dots ,k^{}} and w n i ∗ = 0 {\displaystyle w_{ni}^{}=0} for i = k ∗ + 1 , … , n {\displaystyle i=k^{}+1,\dots ,n} . With optimal weights the dominant term in the asymptotic expansion of the excess risk is O ( n − 4 d + 4 ) {\displaystyle {\mathcal {O}}(n^{-{\frac {4}{d+4}}})}

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  Computer-aided lean management

  Computer-aided lean management, in business management, is a methodology of developing and using software-controlled, lean systems integration. Its goal is to drive innovation towards cost and cycle-time savings. It attempts to create an efficient use of capital and resources through the development and use of one integrated system model to run a business's planning, engineering, design, maintenance, and operations. == Overview == Computer-Aided Lean Management (CALM) is a management philosophy that uses software to reduce risk and inefficiencies. CALM acts on uncertainties and business inefficiencies to increase profitability through the use of computational decision-making tools that enable opportunities for additional value creation. It is based on the application of software to enable continuous improvement through an Integrated System Model (ISM) of the business’s physical assets, business processes, and machine learning. This integration of software applications using lean principles was developed in the aerospace industry and has migrated to the energy industry. The creation of an ISM removes the barriers posed by the silos or stovepipes inherent in the departmentalization of most companies. Integration enables lean uses of information for the creation of actionable knowledge. CALM strives to create such a lean management approach to running the company through the rigors of software enforcement. From this software enforcement comes clear policy and procedures that are adhered to, activity-based costing, measurement of effectiveness, and the capability of using advanced algorithms for dramatic improvements in optimization of resources. CALM creates business capabilities through software to enable technology application, streamlining of processes, and a lean organizational structure. The methodology is based on a common sense approach for running a business, by measuring actions taken and using those measurements to design more efficient processes. == History == CALM was inspired by lean processes and techniques that were already dominant management technologies with a wide diversity of applications and successes. Motorola and General Electric had been known for the concepts of Six Sigma; Boeing had been managing mass (using modular and flexible assembly options), and Toyota combined elements of these methodologies to create the Toyota Production System. Boeing then took the Toyota model and added computer-aided enforcement of lean methodologies throughout the manufacturing process. One of the major sources for CALM's outgrowth was integrated definition (IDEF) modeling in aerospace manufacturing that was pioneered by the U.S. Air Force in the 1970s. IDEF is a methodology designed to model the end-to-end decisions, actions, and activities of an organization or system so that costs, performance, and cycle times can be optimized. IDEF methods have been adapted for wider use in automotive, aerospace, pharmaceuticals, and software development industries. IDEF methods serve as a starting point to understand lean management through semantic data modeling. The IDEF process begins by mapping the existing functions of an enterprise, creating a graphical model, or road map, that shows what controls each important function, who performs it, what resources are required for carrying it out, what it produces, how much it costs, and what relationships it has to other functions of the organization. IDEF simulations have been found to be efficient at streamlining and modernizing both companies and governmental agencies. Perhaps the best-developed evolution of the IDEF model beyond Toyota was at Boeing. Their project life-cycle process has grown into a rigorous software system that links people, tasks, tools, materials, and the environmental impact of any newly planned project, before any building is allowed to begin. Routinely, more than half of the time for any given project is spent building the precedence diagrams, or three-dimensional process maps, integrating with outside suppliers, and designing the implementation plan–all on the computer. Once real activity is initiated, an action tracker is used to monitor inputs and outputs versus the schedule and delivery metrics in real time throughout the organization. When the execution of a new airplane design begins, it is so well organized that it consistently cuts both costs and build time in half for each successive generation of airframe. Boeing created a complex lean management process called 'define and control airplane configuration/manufacturing resource management' (DCAC/MRM). The process was built with the help of the operations research and computer sciences departments of the University of Pittsburgh. The manufacture of the Boeing 777 was ultimately a success, and it became the precursor to succeeding generations of CALM at Boeing. The methodology of CALM has recently been applied to field orientated infrastructure based businesses with highly interdependent systems, such as electric utilities where a smart grid concept is being researched and developed. The management of infrastructure-based industries like oil, gas, electricity, water, transportation, and renewables requires massive investments in interdependent, physical infrastructure, as well as simultaneous attention to disparate market forces. In infrastructure businesses that manage field assets, uncertainty is the biggest impediment to profitability, rather than the maintenance of efficient supply chains or the management of factory assembly lines. These businesses are dominated by risk from uncertainties such as weather, market variations, transportation disruptions, government actions, logistic difficulties, geology, and asset reliability. CALM has been applied to deal with these types of infrastructure based challenges.

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  Ilastik

  ilastik is free open source software for image classification and segmentation. No previous experience in image processing is required to run the software. Since 2018 ilastik is further developed and maintained by Anna Kreshuk's group at European Molecular Biology Laboratory. == Features == ilastik allows user to annotate an arbitrary number of classes in images with a mouse interface. Using these user annotations and the generic (nonlinear) image features, the user can train a random forest classifier. Trained ilastik classifiers can be applied new data not included in the training set in ilastik via its batch processing functionality, or without using the graphical user interface, in headless mode. ilastik can be integrated into various related tools: Pre-trained workflows can be executed directly from ImageJ/Fiji using the ilastik-ImageJ plugin. Pre-trained ilastik Pixel Classification workflows can be run directly in Python with the ilastik Python package, which is available via conda. ilastik has a CellProfiler module to use ilastik classifiers to process images within a CellProfiler framework. == History == ilastik was first released in 2011 by scientists at the Heidelberg Collaboratory for Image Processing (HCI), University of Heidelberg. == Application == The Interactive Learning and Segmentation Toolkit Carving Cell classification and neuron classification Synapse detection Cell tracking Neural Network Classification == Resources == ilastik project is hosted on GitHub. It is a collaborative project, any contributions such as comments, bug reports, bug fixes or code contributions are welcome. The ilastik team can be contacted for user support on the image.sc forum.

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  Boosting (machine learning)

  In machine learning (ML), boosting is an ensemble learning method that combines a set of less accurate models (called "weak learners") to create a single, highly accurate model (a "strong learner"). Unlike other ensemble methods that build models in parallel (such as bagging), boosting algorithms build models sequentially. Each new model in the sequence is trained to correct the errors made by its predecessors. This iterative process allows the overall model to improve its accuracy, particularly by reducing bias. Boosting is a popular and effective technique used in supervised learning for both classification and regression tasks. The theoretical foundation for boosting came from a question posed by Kearns and Valiant (1988, 1989): "Can a set of weak learners create a single strong learner?" A weak learner is defined as a classifier that performs only slightly better than random guessing, whereas a strong learner is a classifier that is highly correlated with the true classification. Robert Schapire's affirmative answer to this question in a 1990 paper led to the development of practical boosting algorithms. The first such algorithm was developed by Schapire, with Freund and Schapire later developing AdaBoost, which remains a foundational example of boosting. == Algorithms == While boosting is not algorithmically constrained, most boosting algorithms consist of iteratively learning weak classifiers with respect to a distribution and adding them to a final strong classifier. When they are added, they are weighted in a way that is related to the weak learners' accuracy. After a weak learner is added, the data weights are readjusted, known as "re-weighting". Misclassified input data gain a higher weight and examples that are classified correctly lose weight. Thus, future weak learners focus more on the examples that previous weak learners misclassified. There are many boosting algorithms. The original ones, proposed by Robert Schapire (a recursive majority gate formulation), and Yoav Freund (boost by majority), were not adaptive and could not take full advantage of the weak learners. Schapire and Freund then developed AdaBoost, an adaptive boosting algorithm that won the prestigious Gödel Prize. Only algorithms that are provable boosting algorithms in the probably approximately correct learning formulation can accurately be called boosting algorithms. Other algorithms that are similar in spirit to boosting algorithms are sometimes called "leveraging algorithms", although they are also sometimes incorrectly called boosting algorithms. The main variation between many boosting algorithms is their method of weighting training data points and hypotheses. AdaBoost is very popular and the most significant historically as it was the first algorithm that could adapt to the weak learners. It is often the basis of introductory coverage of boosting in university machine learning courses. There are many more recent algorithms such as LPBoost, TotalBoost, BrownBoost, xgboost, MadaBoost, LogitBoost, CatBoost and others. Many boosting algorithms fit into the AnyBoost framework, which shows that boosting performs gradient descent in a function space using a convex cost function. == Object categorization in computer vision == Given images containing various known objects in the world, a classifier can be learned from them to automatically classify the objects in future images. Simple classifiers built based on some image feature of the object tend to be weak in categorization performance. Using boosting methods for object categorization is a way to unify the weak classifiers in a special way to boost the overall ability of categorization. === Problem of object categorization === Object categorization is a typical task of computer vision that involves determining whether or not an image contains some specific category of object. The idea is closely related with recognition, identification, and detection. Appearance based object categorization typically contains feature extraction, learning a classifier, and applying the classifier to new examples. There are many ways to represent a category of objects, e.g. from shape analysis, bag of words models, or local descriptors such as SIFT, etc. Examples of supervised classifiers are Naive Bayes classifiers, support vector machines, mixtures of Gaussians, and neural networks. However, research has shown that object categories and their locations in images can be discovered in an unsupervised manner as well. === Status quo for object categorization === The recognition of object categories in images is a challenging problem in computer vision, especially when the number of categories is large. This is due to high intra class variability and the need for generalization across variations of objects within the same category. Objects within one category may look quite different. Even the same object may appear unalike under different viewpoint, scale, and illumination. Background clutter and partial occlusion add difficulties to recognition as well. Humans are able to recognize thousands of object types, whereas most of the existing object recognition systems are trained to recognize only a few, e.g. human faces, cars, simple objects, etc. Research has been very active on dealing with more categories and enabling incremental additions of new categories, and although the general problem remains unsolved, several multi-category objects detectors (for up to hundreds or thousands of categories) have been developed. One means is by feature sharing and boosting. === Boosting for binary categorization === AdaBoost can be used for face detection as an example of binary categorization. The two categories are faces versus background. The general algorithm is as follows: Form a large set of simple features Initialize weights for training images For T rounds Normalize the weights For available features from the set, train a classifier using a single feature and evaluate the training error Choose the classifier with the lowest error Update the weights of the training images: increase if classified wrongly by this classifier, decrease if correctly Form the final strong classifier as the linear combination of the T classifiers (coefficient larger if training error is small) After boosting, a classifier constructed from 200 features could yield a 95% detection rate under a 10 − 5 {\displaystyle 10^{-5}} false positive rate. Another application of boosting for binary categorization is a system that detects pedestrians using patterns of motion and appearance. This work is the first to combine both motion information and appearance information as features to detect a walking person. It takes a similar approach to the Viola-Jones object detection framework. === Boosting for multi-class categorization === Compared with binary categorization, multi-class categorization looks for common features that can be shared across the categories at the same time. They turn to be more generic edge like features. During learning, the detectors for each category can be trained jointly. Compared with training separately, it generalizes better, needs less training data, and requires fewer features to achieve the same performance. The main flow of the algorithm is similar to the binary case. What is different is that a measure of the joint training error shall be defined in advance. During each iteration the algorithm chooses a classifier of a single feature (features that can be shared by more categories shall be encouraged). This can be done via converting multi-class classification into a binary one (a set of categories versus the rest), or by introducing a penalty error from the categories that do not have the feature of the classifier. In the paper "Sharing visual features for multiclass and multiview object detection", A. Torralba et al. used GentleBoost for boosting and showed that when training data is limited, learning via sharing features does a much better job than no sharing, given same boosting rounds. Also, for a given performance level, the total number of features required (and therefore the run time cost of the classifier) for the feature sharing detectors, is observed to scale approximately logarithmically with the number of class, i.e., slower than linear growth in the non-sharing case. Similar results are shown in the paper "Incremental learning of object detectors using a visual shape alphabet", yet the authors used AdaBoost for boosting. == Convex vs. non-convex boosting algorithms == Boosting algorithms can be based on convex or non-convex optimization algorithms. Convex algorithms, such as AdaBoost and LogitBoost, can be "defeated" by random noise such that they can't learn basic and learnable combinations of weak hypotheses. This limitation was pointed out by Long & Servedio in 2008. However, by 2009, multiple authors demonstrated that boosting algorithms based on non-convex optimization, such as BrownBoost, can learn from nois

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  Polynomial kernel

  In machine learning, the polynomial kernel is a kernel function commonly used with support vector machines (SVMs) and other kernelized models, that represents the similarity of vectors (training samples) in a feature space over polynomials of the original variables, allowing learning of non-linear models. Intuitively, the polynomial kernel looks not only at the given features of input samples to determine their similarity, but also combinations of these. In the context of regression analysis, such combinations are known as interaction features. The (implicit) feature space of a polynomial kernel is equivalent to that of polynomial regression, but without the combinatorial blowup in the number of parameters to be learned. When the input features are binary-valued (booleans), then the features correspond to logical conjunctions of input features. == Definition == For degree-d polynomials, the polynomial kernel is defined as K ( x , y ) = ( x T y + c ) d {\displaystyle K(\mathbf {x} ,\mathbf {y} )=(\mathbf {x} ^{\mathsf {T}}\mathbf {y} +c)^{d}} where x and y are vectors of size n in the input space, i.e. vectors of features computed from training or test samples and c ≥ 0 is a free parameter trading off the influence of higher-order versus lower-order terms in the polynomial. When c = 0, the kernel is called homogeneous. (A further generalized polykernel divides xTy by a user-specified scalar parameter a.) As a kernel, K corresponds to an inner product in a feature space based on some mapping φ: K ( x , y ) = ⟨ φ ( x ) , φ ( y ) ⟩ {\displaystyle K(\mathbf {x} ,\mathbf {y} )=\langle \varphi (\mathbf {x} ),\varphi (\mathbf {y} )\rangle } The nature of φ can be seen from an example. Let d = 2, so we get the special case of the quadratic kernel. After using the multinomial theorem (twice—the outermost application is the binomial theorem) and regrouping, K ( x , y ) = ( ∑ i = 1 n x i y i + c ) 2 = ∑ i = 1 n ( x i 2 ) ( y i 2 ) + ∑ i = 2 n ∑ j = 1 i − 1 ( 2 x i x j ) ( 2 y i y j ) + ∑ i = 1 n ( 2 c x i ) ( 2 c y i ) + c 2 {\displaystyle K(\mathbf {x} ,\mathbf {y} )=\left(\sum _{i=1}^{n}x_{i}y_{i}+c\right)^{2}=\sum _{i=1}^{n}\left(x_{i}^{2}\right)\left(y_{i}^{2}\right)+\sum _{i=2}^{n}\sum _{j=1}^{i-1}\left({\sqrt {2}}x_{i}x_{j}\right)\left({\sqrt {2}}y_{i}y_{j}\right)+\sum _{i=1}^{n}\left({\sqrt {2c}}x_{i}\right)\left({\sqrt {2c}}y_{i}\right)+c^{2}} From this it follows that the feature map is given by: φ ( x ) = ( x n 2 , … , x 1 2 , 2 x n x n − 1 , … , 2 x n x 1 , 2 x n − 1 x n − 2 , … , 2 x n − 1 x 1 , … , 2 x 2 x 1 , 2 c x n , … , 2 c x 1 , c ) {\displaystyle \varphi (x)=\left(x_{n}^{2},\ldots ,x_{1}^{2},{\sqrt {2}}x_{n}x_{n-1},\ldots ,{\sqrt {2}}x_{n}x_{1},{\sqrt {2}}x_{n-1}x_{n-2},\ldots ,{\sqrt {2}}x_{n-1}x_{1},\ldots ,{\sqrt {2}}x_{2}x_{1},{\sqrt {2c}}x_{n},\ldots ,{\sqrt {2c}}x_{1},c\right)} generalizing for ( x T y + c ) d {\displaystyle \left(\mathbf {x} ^{T}\mathbf {y} +c\right)^{d}} , where x ∈ R n {\displaystyle \mathbf {x} \in \mathbb {R} ^{n}} , y ∈ R n {\displaystyle \mathbf {y} \in \mathbb {R} ^{n}} and applying the multinomial theorem: ( x T y + c ) d = ∑ j 1 + j 2 + ⋯ + j n + 1 = d d ! j 1 ! ⋯ j n ! j n + 1 ! x 1 j 1 ⋯ x n j n c j n + 1 d ! j 1 ! ⋯ j n ! j n + 1 ! y 1 j 1 ⋯ y n j n c j n + 1 = φ ( x ) T φ ( y ) {\displaystyle {\begin{alignedat}{2}\left(\mathbf {x} ^{T}\mathbf {y} +c\right)^{d}&=\sum _{j_{1}+j_{2}+\dots +j_{n+1}=d}{\frac {\sqrt {d!}}{\sqrt {j_{1}!\cdots j_{n}!j_{n+1}!}}}x_{1}^{j_{1}}\cdots x_{n}^{j_{n}}{\sqrt {c}}^{j_{n+1}}{\frac {\sqrt {d!}}{\sqrt {j_{1}!\cdots j_{n}!j_{n+1}!}}}y_{1}^{j_{1}}\cdots y_{n}^{j_{n}}{\sqrt {c}}^{j_{n+1}}\\&=\varphi (\mathbf {x} )^{T}\varphi (\mathbf {y} )\end{alignedat}}} The last summation has l d = ( n + d d ) {\displaystyle l_{d}={\tbinom {n+d}{d}}} elements, so that: φ ( x ) = ( a 1 , … , a l , … , a l d ) {\displaystyle \varphi (\mathbf {x} )=\left(a_{1},\dots ,a_{l},\dots ,a_{l_{d}}\right)} where l = ( j 1 , j 2 , . . . , j n , j n + 1 ) {\displaystyle l=(j_{1},j_{2},...,j_{n},j_{n+1})} and a l = d ! j 1 ! ⋯ j n ! j n + 1 ! x 1 j 1 ⋯ x n j n c j n + 1 | j 1 + j 2 + ⋯ + j n + j n + 1 = d {\displaystyle a_{l}={\frac {\sqrt {d!}}{\sqrt {j_{1}!\cdots j_{n}!j_{n+1}!}}}x_{1}^{j_{1}}\cdots x_{n}^{j_{n}}{\sqrt {c}}^{j_{n+1}}\quad |\quad j_{1}+j_{2}+\dots +j_{n}+j_{n+1}=d} == Practical use == Although the RBF kernel is more popular in SVM classification than the polynomial kernel, the latter is quite popular in natural language processing (NLP). The most common degree is d = 2 (quadratic), since larger degrees tend to overfit on NLP problems. Various ways of computing the polynomial kernel (both exact and approximate) have been devised as alternatives to the usual non-linear SVM training algorithms, including: full expansion of the kernel prior to training/testing with a linear SVM, i.e. full computation of the mapping φ as in polynomial regression; basket mining (using a variant of the apriori algorithm) for the most commonly occurring feature conjunctions in a training set to produce an approximate expansion; inverted indexing of support vectors. One problem with the polynomial kernel is that it may suffer from numerical instability: when xTy + c < 1, K(x, y) = (xTy + c)d tends to zero with increasing d, whereas when xTy + c > 1, K(x, y) tends to infinity.

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  Multiple buffering

  In computer science, multiple buffering is the use of more than one buffer to hold a block of data, so that a "reader" will see a complete (though perhaps old) version of the data instead of a partially updated version of the data being created by a "writer". It is very commonly used for computer display images. It is also used to avoid the need to use dual-ported RAM (DPRAM) when the readers and writers are different devices. == Description == === Double buffering Petri net === The Petri net in the illustration shows double buffering. Transitions W1 and W2 represent writing to buffer 1 and 2 respectively while R1 and R2 represent reading from buffer 1 and 2 respectively. At the beginning, only the transition W1 is enabled. After W1 fires, R1 and W2 are both enabled and can proceed in parallel. When they finish, R2 and W1 proceed in parallel and so on. After the initial transient where W1 fires alone, this system is periodic and the transitions are enabled – always in pairs (R1 with W2 and R2 with W1 respectively). == Double buffering in computer graphics == In computer graphics, double buffering is a technique for drawing graphics that shows less stutter, tearing, and other artifacts. It is difficult for a program to draw a display so that pixels do not change more than once. For instance, when updating a page of text, it is much easier to clear the entire page and then draw the letters than to somehow erase only the pixels that are used in old letters but not in new ones. However, this intermediate image is seen by the user as flickering. In addition, computer monitors constantly redraw the visible video page (traditionally at around 60 times a second), so even a perfect update may be visible momentarily as a horizontal divider between the "new" image and the un-redrawn "old" image, known as tearing. === Software double buffering === A software implementation of double buffering has all drawing operations store their results in some region of system RAM; any such region is often called a "back buffer". When all drawing operations are considered complete, the whole region (or only the changed portion) is copied into the video RAM (the "front buffer"); this copying is usually synchronized with the monitor's raster beam in order to avoid tearing. Software implementations of double buffering necessarily require more memory and CPU time than single buffering because of the system memory allocated for the back buffer, the time for the copy operation, and the time waiting for synchronization. Compositing window managers often combine the "copying" operation with "compositing" used to position windows, transform them with scale or warping effects, and make portions transparent. Thus, the "front buffer" may contain only the composite image seen on the screen, while there is a different "back buffer" for every window containing the non-composited image of the entire window contents. === Page flipping === In the page-flip method, instead of copying the data, both buffers are capable of being displayed. At any one time, one buffer is actively being displayed by the monitor, while the other, background buffer is being drawn. When the background buffer is complete, the roles of the two are switched. The page-flip is typically accomplished by modifying a hardware register in the video display controller—the value of a pointer to the beginning of the display data in the video memory. The page-flip is much faster than copying the data and can guarantee that tearing will not be seen as long as the pages are switched over during the monitor's vertical blanking interval—the blank period when no video data is being drawn. The currently active and visible buffer is called the front buffer, while the background page is called the back buffer. == Triple buffering == In computer graphics, triple buffering is similar to double buffering but can provide improved performance. In double buffering, the program must wait until the finished drawing is copied or swapped before starting the next drawing. This waiting period could be several milliseconds during which neither buffer can be touched. In triple buffering, the program has two back buffers and can immediately start drawing in the one that is not involved in such copying. The third buffer, the front buffer, is read by the graphics card to display the image on the monitor. Once the image has been sent to the monitor, the front buffer is flipped with (or copied from) the back buffer holding the most recent complete image. Since one of the back buffers is always complete, the graphics card never has to wait for the software to complete. Consequently, the software and the graphics card are completely independent and can run at their own pace. Finally, the displayed image was started without waiting for synchronization and thus with minimum lag. Due to the software algorithm not polling the graphics hardware for monitor refresh events, the algorithm may continuously draw additional frames as fast as the hardware can render them. For frames that are completed much faster than interval between refreshes, it is possible to replace a back buffers' frames with newer iterations multiple times before copying. This means frames may be written to the back buffer that are never used at all before being overwritten by successive frames. Nvidia has implemented this method under the name "Fast Sync". An alternative method sometimes referred to as triple buffering is a swap chain three buffers long. After the program has drawn both back buffers, it waits until the first one is placed on the screen, before drawing another back buffer (i.e. it is a 3-long first in, first out queue). Most Windows games seem to refer to this method when enabling triple buffering. == Quad buffering == The term quad buffering is the use of double buffering for each of the left and right eye images in stereoscopic implementations, thus four buffers total (if triple buffering was used then there would be six buffers). The command to swap or copy the buffer typically applies to both pairs at once, so at no time does one eye see an older image than the other eye. Quad buffering requires special support in the graphics card drivers which is disabled for most consumer cards. AMD's Radeon HD 6000 Series and newer support it. 3D standards like OpenGL and Direct3D support quad buffering. == Double buffering for DMA == The term double buffering is used for copying data between two buffers for direct memory access (DMA) transfers, not for enhancing performance, but to meet specific addressing requirements of a device (particularly 32-bit devices on systems with wider addressing provided via Physical Address Extension). Windows device drivers are a place where the term "double buffering" is likely to be used. Linux and BSD source code calls these "bounce buffers". Some programmers try to avoid this kind of double buffering with zero-copy techniques. == Other uses == Double buffering is also used as a technique to facilitate interlacing or deinterlacing of video signals.

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  Effective fitness

  In natural evolution and artificial evolution (e.g. artificial life and evolutionary computation) the fitness (or performance or objective measure) of a schema is rescaled to give its effective fitness which takes into account crossover and mutation. Effective fitness is used in Evolutionary Computation to understand population dynamics. While a biological fitness function only looks at reproductive success, an effective fitness function tries to encompass things that are needed to be fulfilled for survival on population level. In homogeneous populations, reproductive fitness and effective fitness are equal. When a population moves away from homogeneity a higher effective fitness is reached for the recessive genotype. This advantage will decrease while the population moves toward an equilibrium. The deviation from this equilibrium displays how close the population is to achieving a steady state. When this equilibrium is reached, the maximum effective fitness of the population is achieved. Problem solving with evolutionary computation is realized with a cost function. If cost functions are applied to swarm optimization they are called a fitness function. Strategies like reinforcement learning and NEAT neuroevolution are creating a fitness landscape which describes the reproductive success of cellular automata. The effective fitness function models the number of fit offspring and is used in calculations that include evolutionary processes, such as mutation and crossover, important on the population level. The effective fitness model is superior to its predecessor, the standard reproductive fitness model. It advances in the qualitatively and quantitatively understanding of evolutionary concepts like bloat, self-adaptation, and evolutionary robustness. While reproductive fitness only looks at pure selection, effective fitness describes the flow of a population and natural selection by taking genetic operators into account. A normal fitness function fits to a problem, while an effective fitness function is an assumption if the objective was reached. The difference is important for designing fitness functions with algorithms like novelty search in which the objective of the agents is unknown. In the case of bacteria effective fitness could include production of toxins and rate of mutation of different plasmids, which are mostly stochastically determined == Applications == When evolutionary equations of the studied population dynamics are available, one can algorithmically compute the effective fitness of a given population. Though the perfect effective fitness model is yet to be found, it is already known to be a good framework to the better understanding of the moving of the genotype-phenotype map, population dynamics, and the flow on fitness landscapes. Models using a combination of Darwinian fitness functions and effective functions are better at predicting population trends. Effective models could be used to determine therapeutic outcomes of disease treatment. Other models could determine effective protein engineering and works towards finding novel or heightened biochemistry.

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  Cellular evolutionary algorithm

  A cellular evolutionary algorithm (cEA) is a kind of evolutionary algorithm (EA) in which individuals cannot mate arbitrarily, but every one interacts with its closer neighbors on which a basic EA is applied (selection, variation, replacement). The cellular model simulates natural evolution from the point of view of the individual, which encodes a tentative optimization, learning, or search problem solution. The essential idea of this model is to provide the EA population with a special structure defined as a connected graph, in which each vertex is an individual who communicates with his nearest neighbors. Particularly, individuals are conceptually set in a toroidal mesh, and are only allowed to recombine with close individuals. This leads to a kind of locality known as "isolation by distance". The set of potential mates of an individual is called its "neighborhood". It is known that, in this kind of algorithm, similar individuals tend to cluster creating niches, and these groups operate as if they were separate sub-populations (islands). There is no clear borderline between adjacent groups, and close niches could be easily colonized by competitive niches and potentially merge solution contents during the process. Simultaneously, farther niches can be affected more slowly. == Introduction == A cellular evolutionary algorithm (cEA) usually evolves a structured bidimensional grid of individuals, although other topologies are also possible. In this grid, clusters of similar individuals are naturally created during evolution, promoting exploration in their boundaries, while exploitation is mainly performed by direct competition and merging inside them. The grid is usually 2D toroidal structure, although the number of dimensions can be easily extended (to 3D) or reduced (to 1D, e.g. a ring). The neighborhood of a particular point of the grid (where an individual is placed) is defined in terms of the Manhattan distance from it to others in the population. Each point of the grid has a neighborhood that overlaps the neighborhoods of nearby individuals. In the basic algorithm, all the neighborhoods have the same size and identical shapes. The two most commonly used neighborhoods are L5, also called the Von Neumann or NEWS (North, East, West and South) neighborhood, and C9, also known as the Moore neighborhood. Here, L stands for "linear" while C stands for "compact". In cEAs, the individuals can only interact with their neighbors in the reproductive cycle where the variation operators are applied. This reproductive cycle is executed inside the neighborhood of each individual and, generally, consists in selecting two parents among its neighbors according to a certain criterion, applying the variation operators to them (recombination and mutation for example), and replacing the considered individual by the recently created offspring following a given criterion, for instance, replace if the offspring represents a better solution than the considered individual. == Synchronous versus asynchronous == In a regular synchronous cEA, the algorithm proceeds from the very first top left individual to the right and then to the several rows by using the information in the population to create a new temporary population. After finishing with the bottom-right last individual the temporary population is full with the newly computed individuals, and the replacement step starts. In it, the old population is completely and synchronously replaced with the newly computed one according to some criterion. Usually, the replacement keeps the best individual in the same position of both populations, that is, elitism is used. According to the update policy of the population used, an asynchronous cEA may also be defined and is a well-known issue in cellular automata. In asynchronous cEAs the order in which the individuals in the grid are update changes depending on the choice of criterion: line sweep, fixed random sweep, new random sweep, and uniform choice. All four proceed using the newly computed individual (or the original if better) for the computations of its neighbors. The overlap of the neighborhoods provides an implicit mechanism of solution migration to the cEA. Since the best solutions spread smoothly through the whole population, genetic diversity in the population is preserved longer than in non structured EAs. This soft dispersion of the best solutions through the population is one of the main issues of the good tradeoff between exploration and exploitation that cEAs perform during the search. This tradeoff can be tuned (and by extension the genetic diversity level along the evolution) by modifying (for instance) the size of the neighborhood used, as the overlap degree between the neighborhoods grows according to the size of the neighborhood. A cEA can be seen as a cellular automaton (CA) with probabilistic rewritable rules, where the alphabet of the CA is equivalent to the potential number of solutions of the problem. Hence, knowledge from research in CAs can be applied to cEAs. == Parallelism == Cellular EAs are very amenable to parallelism, thus usually found in the literature of parallel metaheuristics. In particular, fine grain parallelism can be used to assign independent threads of execution to every individual, thus allowing the whole cEA to run on a concurrent or actually parallel hardware platform. In this way, large time reductions can be obtained when running cEAs on FPGAs or GPUs. However, it is important to stress that cEAs are a model of search, in many senses different from traditional EAs. Also, they can be run in sequential and parallel platforms, reinforcing the fact that the model and the implementation are two different concepts. See here for a complete description on the fundamentals for the understanding, design, and application of cEAs.

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