AI Chat Microsoft Copilot

AI Chat Microsoft Copilot — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

Neural radiance field

A neural radiance field (NeRF) is a neural field for reconstructing a three-dimensional representation of a scene from two-dimensional images. The NeRF model enables downstream applications of novel view synthesis, scene geometry reconstruction, and obtaining the reflectance properties of the scene. Additional scene properties such as camera poses may also be jointly learned. First introduced in 2020, it has since gained significant attention for its potential applications in computer graphics and content creation. == Algorithm == The NeRF algorithm represents a scene as a radiance field parametrized by a deep neural network (DNN). The network predicts a volume density and view-dependent emitted radiance given the spatial location ( x , y , z ) {\displaystyle (x,y,z)} and viewing direction in Euler angles ( θ , Φ ) {\displaystyle (\theta ,\Phi )} of the camera. By sampling many points along camera rays, traditional volume rendering techniques can produce an image. === Data collection === A NeRF needs to be retrained for each unique scene. The first step is to collect images of the scene from different angles and their respective camera pose. These images are standard 2D images and do not require a specialized camera or software. Any camera is able to generate datasets, provided the settings and capture method meet the requirements for SfM (Structure from Motion). This requires tracking of the camera position and orientation, often through some combination of SLAM, GPS, or inertial estimation. Researchers often use synthetic data to evaluate NeRF and related techniques. For such data, images (rendered through traditional non-learned methods) and respective camera poses are reproducible and error-free. === Training === For each sparse viewpoint (image and camera pose) provided, camera rays are marched through the scene, generating a set of 3D points with a given radiance direction (into the camera). For these points, volume density and emitted radiance are predicted using the multi-layer perceptron (MLP). An image is then generated through classical volume rendering. Because this process is fully differentiable, the error between the predicted image and the original image can be minimized with gradient descent over multiple viewpoints, encouraging the MLP to develop a coherent model of the scene. == Variations and improvements == Early versions of NeRF were slow to optimize and required that all input views were taken with the same camera in the same lighting conditions. These performed best when limited to orbiting around individual objects, such as a drum set, plants or small toys. Since the original paper in 2020, many improvements have been made to the NeRF algorithm, with variations for special use cases. === Fourier feature mapping === In 2020, shortly after the release of NeRF, the addition of Fourier Feature Mapping improved training speed and image accuracy. Deep neural networks struggle to learn high frequency functions in low dimensional domains; a phenomenon known as spectral bias. To overcome this shortcoming, points are mapped to a higher dimensional feature space before being fed into the MLP. γ ( v ) = [ a 1 cos ⁡ ( 2 π B 1 T v ) a 1 sin ⁡ ( 2 π B 1 T v ) ⋮ a m cos ⁡ ( 2 π B m T v ) a m sin ⁡ ( 2 π B m T v ) ] {\displaystyle \gamma (\mathrm {v} )={\begin{bmatrix}a_{1}\cos(2{\pi }{\mathrm {B} }_{1}^{T}\mathrm {v} )\\a_{1}\sin(2\pi {\mathrm {B} }_{1}^{T}\mathrm {v} )\\\vdots \\a_{m}\cos(2{\pi }{\mathrm {B} }_{m}^{T}\mathrm {v} )\\a_{m}\sin(2{\pi }{\mathrm {B} }_{m}^{T}\mathrm {v} )\end{bmatrix}}} Where v {\displaystyle \mathrm {v} } is the input point, B i {\displaystyle \mathrm {B} _{i}} are the frequency vectors, and a i {\displaystyle a_{i}} are coefficients. This allows for rapid convergence to high frequency functions, such as pixels in a detailed image. === Bundle-adjusting neural radiance fields === One limitation of NeRFs is the requirement of knowing accurate camera poses to train the model. Often times, pose estimation methods are not completely accurate, nor is the camera pose even possible to know. These imperfections result in artifacts and suboptimal convergence. So, a method was developed to optimize the camera pose along with the volumetric function itself. Called Bundle-Adjusting Neural Radiance Field (BARF), the technique uses a dynamic low-pass filter (DLPF) to go from coarse to fine adjustment, minimizing error by finding the geometric transformation to the desired image. This corrects imperfect camera poses and greatly improves the quality of NeRF renders. === Multiscale representation === Conventional NeRFs struggle to represent detail at all viewing distances, producing blurry images up close and overly aliased images from distant views. In 2021, researchers introduced a technique to improve the sharpness of details at different viewing scales known as mip-NeRF (comes from mipmap). Rather than sampling a single ray per pixel, the technique fits a gaussian to the conical frustum cast by the camera. This improvement effectively anti-aliases across all viewing scales. mip-NeRF also reduces overall image error and is faster to converge at about half the size of ray-based NeRF. === Learned initializations === In 2021, researchers applied meta-learning to assign initial weights to the MLP. This rapidly speeds up convergence by effectively giving the network a head start in gradient descent. Meta-learning also allowed the MLP to learn an underlying representation of certain scene types. For example, given a dataset of famous tourist landmarks, an initialized NeRF could partially reconstruct a scene given one image. === NeRF in the wild === Conventional NeRFs are vulnerable to slight variations in input images (objects, lighting) often resulting in ghosting and artifacts. As a result, NeRFs struggle to represent dynamic scenes, such as bustling city streets with changes in lighting and dynamic objects. In 2021, researchers at Google developed a new method for accounting for these variations, named NeRF in the Wild (NeRF-W). This method splits the neural network (MLP) into three separate models. The main MLP is retained to encode the static volumetric radiance. However, it operates in sequence with a separate MLP for appearance embedding (changes in lighting, camera properties) and an MLP for transient embedding (changes in scene objects). This allows the NeRF to be trained on diverse photo collections, such as those taken by mobile phones at different times of day. === Relighting === In 2021, researchers added more outputs to the MLP at the heart of NeRFs. The output now included: volume density, surface normal, material parameters, distance to the first surface intersection (in any direction), and visibility of the external environment in any direction. The inclusion of these new parameters lets the MLP learn material properties, rather than pure radiance values. This facilitates a more complex rendering pipeline, calculating direct and global illumination, specular highlights, and shadows. As a result, the NeRF can render the scene under any lighting conditions with no re-training. === Plenoctrees === Although NeRFs had reached high levels of fidelity, their costly compute time made them useless for many applications requiring real-time rendering, such as VR/AR and interactive content. Introduced in 2021, Plenoctrees (plenoptic octrees) enabled real-time rendering of pre-trained NeRFs through division of the volumetric radiance function into an octree. Rather than assigning a radiance direction into the camera, viewing direction is taken out of the network input and spherical radiance is predicted for each region. This makes rendering over 3000x faster than conventional NeRFs. === Sparse Neural Radiance Grid === Similar to Plenoctrees, this method enabled real-time rendering of pretrained NeRFs. To avoid querying the large MLP for each point, this method bakes NeRFs into Sparse Neural Radiance Grids (SNeRG). A SNeRG is a sparse voxel grid containing opacity and color, with learned feature vectors to encode view-dependent information. A lightweight, more efficient MLP is then used to produce view-dependent residuals to modify the color and opacity. To enable this compressive baking, small changes to the NeRF architecture were made, such as running the MLP once per pixel rather than for each point along the ray. These improvements make SNeRG extremely efficient, outperforming Plenoctrees. === Instant NeRFs === In 2022, researchers at Nvidia enabled real-time training of NeRFs through a technique known as Instant Neural Graphics Primitives. An innovative input encoding reduces computation, enabling real-time training of a NeRF, an improvement orders of magnitude above previous methods. The speedup stems from the use of spatial hash functions, which have O ( 1 ) {\displaystyle O(1)} access times, and parallelized architectures which run fast on modern GPUs. == Related techniques == === Plenoxels === Plen
Read more →
Spatial Analysis of Principal Components

Spatial Principal Component Analysis (sPCA) is a multivariate statistical technique that complements the traditional Principal Component Analysis (PCA) by incorporating spatial information into the analysis of genetic variation. While traditional PCA can be used to find spatial patterns, it focuses on reducing data dimensionality by identifying uncorrelated principal components that capture maximum variance, thus often lacking power to identify non-trivial spatial genetic patterns. By accounting for spatial autocorrelation, sPCA is able to uncover spatial patterns in the data and find the spatial structure of datasets where observations are either geographically or topologically linked. This statistical power improvement allows the investigation of cryptic spatial patterns of genetic variability otherwise overlooked. sPCA has been applied in various fields, including geography, ecology and genetics. == History == sPCA was introduced in 2008 by Thibaut Jombart, Sébastien Devillard, Anne-Béatrice Dufour, and D. Pontier as a spatially explicit method to investigate the spatial pattern of genetic variation among individuals or populations. In 2017, Valeria Montano and Thibaut Jombart published an alternative non-parametric test to evaluate the significance of global and local spatial genetic patterns with improved statistical power. == Details == sPCA modifies the PCA framework by integrating spatial weights, typically in the form of connectivity matrices or spatial adjacency graphs. It identifies principal components (PCs) that maximize both genentic variance and spatial autocorreation, as measured by Moran's I. These weights represent relationships between observations based on geographic distance or other spatial criteria. The method decomposes variance into two components: Global structures, correspond to positive autocorrelation, that is, reflect broad-scale spatial patterns where similar values cluster over large regions. Local structures, correspond to negative autocorrelation, that is, capture fine-scale spatial variations or localized patterns. The core of sPCA relies on the eigenanalysis of a spatially weighted covariance or correlation matrix. The spatial weight matrix can be constructed using techniques such as Delaunay triangulation, nearest-neighbor graphs, or distance-based criteria. Applications of sPCA should be used only as an explorative tool. == Applications == sPCA has been widely used in many fields, including: Ecology: To find spatial patterns in species distributions and environmental gradients. Genetics: Population structure and gene flow analysis while allowing for spatial autocorrelation considerations. Biogeography: To identify historical dispersal routes, and barriers to gene flow, providing insights into species distribution patterns and evolutionary history. == Software/Source Code == sPCA implementations are available in R in adegenet and ntbox . These tools facilitate the application of sPCA by providing functions for constructing spatial weight matrices, performing eigenanalysis, and obtaining spatial principal components in an easy-to-read form.
Read more →
Locality-sensitive hashing

In computer science, locality-sensitive hashing (LSH) is a fuzzy hashing technique that hashes similar input items into the same "buckets" with high probability. The number of buckets is much smaller than the universe of possible input items. Since similar items end up in the same buckets, this technique can be used for data clustering and nearest neighbor search. It differs from conventional hashing techniques in that hash collisions are maximized, not minimized. Alternatively, the technique can be seen as a way to reduce the dimensionality of high-dimensional data; high-dimensional input items can be reduced to low-dimensional versions while preserving relative distances between items. Hashing-based approximate nearest-neighbor search algorithms generally use one of two main categories of hashing methods: either data-independent methods, such as locality-sensitive hashing (LSH); or data-dependent methods, such as locality-preserving hashing (LPH). Locality-preserving hashing was initially devised as a way to facilitate data pipelining in implementations of massively parallel algorithms that use randomized routing and universal hashing to reduce memory contention and network congestion. == Definitions == A finite family F {\displaystyle {\mathcal {F}}} of functions h : M → S {\displaystyle h\colon M\to S} is defined to be an LSH family for a metric space M = ( M , d ) {\displaystyle {\mathcal {M}}=(M,d)} , a threshold r > 0 {\displaystyle r>0} , an approximation factor c > 1 {\displaystyle c>1} , and probabilities p 1 > p 2 {\displaystyle p_{1}>p_{2}} if it satisfies the following condition. For any two points a , b ∈ M {\displaystyle a,b\in M} and a hash function h {\displaystyle h} chosen uniformly at random from F {\displaystyle {\mathcal {F}}} : If d ( a , b ) ≤ r {\displaystyle d(a,b)\leq r} , then h ( a ) = h ( b ) {\displaystyle h(a)=h(b)} (i.e., a and b collide) with probability at least p 1 {\displaystyle p_{1}} , If d ( a , b ) ≥ c r {\displaystyle d(a,b)\geq cr} , then h ( a ) = h ( b ) {\displaystyle h(a)=h(b)} with probability at most p 2 {\displaystyle p_{2}} . Such a family F {\displaystyle {\mathcal {F}}} is called ( r , c r , p 1 , p 2 ) {\displaystyle (r,cr,p_{1},p_{2})} -sensitive. === LSH with respect to a similarity measure === Alternatively it is possible to define an LSH family on a universe of items U endowed with a similarity function ϕ : U × U → [ 0 , 1 ] {\displaystyle \phi \colon U\times U\to [0,1]} . In this setting, a LSH scheme is a family of hash functions H coupled with a probability distribution D over H such that a function h ∈ H {\displaystyle h\in H} chosen according to D satisfies P r [ h ( a ) = h ( b ) ] = ϕ ( a , b ) {\displaystyle Pr[h(a)=h(b)]=\phi (a,b)} for each a , b ∈ U {\displaystyle a,b\in U} . === Amplification === Given a ( d 1 , d 2 , p 1 , p 2 ) {\displaystyle (d_{1},d_{2},p_{1},p_{2})} -sensitive family F {\displaystyle {\mathcal {F}}} , we can construct new families G {\displaystyle {\mathcal {G}}} by either the AND-construction or OR-construction of F {\displaystyle {\mathcal {F}}} . To create an AND-construction, we define a new family G {\displaystyle {\mathcal {G}}} of hash functions g, where each function g is constructed from k random functions h 1 , … , h k {\displaystyle h_{1},\ldots ,h_{k}} from F {\displaystyle {\mathcal {F}}} . We then say that for a hash function g ∈ G {\displaystyle g\in {\mathcal {G}}} , g ( x ) = g ( y ) {\displaystyle g(x)=g(y)} if and only if all h i ( x ) = h i ( y ) {\displaystyle h_{i}(x)=h_{i}(y)} for i = 1 , 2 , … , k {\displaystyle i=1,2,\ldots ,k} . Since the members of F {\displaystyle {\mathcal {F}}} are independently chosen for any g ∈ G {\displaystyle g\in {\mathcal {G}}} , G {\displaystyle {\mathcal {G}}} is a ( d 1 , d 2 , p 1 k , p 2 k ) {\displaystyle (d_{1},d_{2},p_{1}^{k},p_{2}^{k})} -sensitive family. To create an OR-construction, we define a new family G {\displaystyle {\mathcal {G}}} of hash functions g, where each function g is constructed from k random functions h 1 , … , h k {\displaystyle h_{1},\ldots ,h_{k}} from F {\displaystyle {\mathcal {F}}} . We then say that for a hash function g ∈ G {\displaystyle g\in {\mathcal {G}}} , g ( x ) = g ( y ) {\displaystyle g(x)=g(y)} if and only if h i ( x ) = h i ( y ) {\displaystyle h_{i}(x)=h_{i}(y)} for one or more values of i. Since the members of F {\displaystyle {\mathcal {F}}} are independently chosen for any g ∈ G {\displaystyle g\in {\mathcal {G}}} , G {\displaystyle {\mathcal {G}}} is a ( d 1 , d 2 , 1 − ( 1 − p 1 ) k , 1 − ( 1 − p 2 ) k ) {\displaystyle (d_{1},d_{2},1-(1-p_{1})^{k},1-(1-p_{2})^{k})} -sensitive family. == Applications == LSH has been applied to several problem domains, including: Near-duplicate detection Hierarchical clustering Genome-wide association study Image similarity identification VisualRank Gene expression similarity identification Audio similarity identification Nearest neighbor search Audio fingerprint Digital video fingerprinting Shared memory organization in parallel computing Physical data organization in database management systems Training fully connected neural networks Computer security Machine learning == Methods == === Bit sampling for Hamming distance === One of the easiest ways to construct an LSH family is by bit sampling. This approach works for the Hamming distance over d-dimensional vectors { 0 , 1 } d {\displaystyle \{0,1\}^{d}} . Here, the family F {\displaystyle {\mathcal {F}}} of hash functions is simply the family of all the projections of points on one of the d {\displaystyle d} coordinates, i.e., F = { h : { 0 , 1 } d → { 0 , 1 } ∣ h ( x ) = x i for some i ∈ { 1 , … , d } } {\displaystyle {\mathcal {F}}=\{h\colon \{0,1\}^{d}\to \{0,1\}\mid h(x)=x_{i}{\text{ for some }}i\in \{1,\ldots ,d\}\}} , where x i {\displaystyle x_{i}} is the i {\displaystyle i} th coordinate of x {\displaystyle x} . A random function h {\displaystyle h} from F {\displaystyle {\mathcal {F}}} simply selects a random bit from the input point. This family has the following parameters: P 1 = 1 − R / d {\displaystyle P_{1}=1-R/d} , P 2 = 1 − c R / d {\displaystyle P_{2}=1-cR/d} . That is, any two vectors x , y {\displaystyle x,y} with Hamming distance at most R {\displaystyle R} collide under a random h {\displaystyle h} with probability at least P 1 {\displaystyle P_{1}} . Any x , y {\displaystyle x,y} with Hamming distance at least c R {\displaystyle cR} collide with probability at most P 2 {\displaystyle P_{2}} . === Min-wise independent permutations === Suppose U is composed of subsets of some ground set of enumerable items S and the similarity function of interest is the Jaccard index J. If π is a permutation on the indices of S, for A ⊆ S {\displaystyle A\subseteq S} let h ( A ) = min a ∈ A { π ( a ) } {\displaystyle h(A)=\min _{a\in A}\{\pi (a)\}} . Each possible choice of π defines a single hash function h mapping input sets to elements of S. Define the function family H to be the set of all such functions and let D be the uniform distribution. Given two sets A , B ⊆ S {\displaystyle A,B\subseteq S} the event that h ( A ) = h ( B ) {\displaystyle h(A)=h(B)} corresponds exactly to the event that the minimizer of π over A ∪ B {\displaystyle A\cup B} lies inside A ∩ B {\displaystyle A\cap B} . As h was chosen uniformly at random, P r [ h ( A ) = h ( B ) ] = J ( A , B ) {\displaystyle Pr[h(A)=h(B)]=J(A,B)\,} and ( H , D ) {\displaystyle (H,D)\,} define an LSH scheme for the Jaccard index. Because the symmetric group on n elements has size n!, choosing a truly random permutation from the full symmetric group is infeasible for even moderately sized n. Because of this fact, there has been significant work on finding a family of permutations that is "min-wise independent" — a permutation family for which each element of the domain has equal probability of being the minimum under a randomly chosen π. It has been established that a min-wise independent family of permutations is at least of size lcm ⁡ { 1 , 2 , … , n } ≥ e n − o ( n ) {\displaystyle \operatorname {lcm} \{\,1,2,\ldots ,n\,\}\geq e^{n-o(n)}} , and that this bound is tight. Because min-wise independent families are too big for practical applications, two variant notions of min-wise independence are introduced: restricted min-wise independent permutations families, and approximate min-wise independent families. Restricted min-wise independence is the min-wise independence property restricted to certain sets of cardinality at most k. Approximate min-wise independence differs from the property by at most a fixed ε. === Open source methods === ==== Nilsimsa Hash ==== Nilsimsa is a locality-sensitive hashing algorithm used in anti-spam efforts. The goal of Nilsimsa is to generate a hash digest of an email message such that the digests of two similar messages are similar to each other. The paper suggests that the Nilsimsa satisfies three requirements: The digest identifying each message should not
Read more →
Evolutionary programming

Evolutionary programming is an evolutionary algorithm, where a share of new population is created by mutation of previous population without crossover. Evolutionary programming differs from evolution strategy ES( μ + λ {\displaystyle \mu +\lambda } ) in one detail. All individuals are selected for the new population, while in ES( μ + λ {\displaystyle \mu +\lambda } ), every individual has the same probability to be selected. It is one of the four major evolutionary algorithm paradigms. == History == It was first used by Lawrence J. Fogel in the US in 1960 in order to use simulated evolution as a learning process aiming to generate artificial intelligence. It was used to evolve finite-state machines as predictors.
Read more →
Meta AI

Meta AI is a research division of Meta (formerly Facebook) that develops artificial intelligence and augmented reality technologies. == History == Meta AI was founded in 2013 as Facebook Artificial Intelligence Research (FAIR). It has workspaces in Menlo Park, London, New York City, Paris, Seattle, Pittsburgh, Tel Aviv, and Montreal as of 2025. In 2016, FAIR partnered with Google, Amazon, IBM, and Microsoft in creating the Partnership on Artificial Intelligence to Benefit People and Society. Meta AI was directed by Yann LeCun until 2018, when Jérôme Pesenti succeeded the role. Pesenti is formerly the CTO of IBM's big data group. FAIR's research includes self-supervised learning, generative adversarial networks, document classification and translation, and computer vision. FAIR released Torch deep-learning modules as well as PyTorch in 2017, an open-source machine learning framework, which was subsequently used in several deep learning technologies, such as Tesla's autopilot and Uber's Pyro. That same year, a pair of chatbots were falsely rumored to be discontinued for developing a language that was unintelligible to humans. FAIR clarified that the research had been shut down because they had accomplished their initial goal to understand how languages are generated by their models, rather than out of fear. FAIR was renamed Meta AI following the rebranding that changed Facebook, Inc. to Meta Platforms Inc. On October 1, 2025, Facebook announced "We will soon use your interactions with AI at Meta to personalize the content and ads you see". == Virtual assistant == Meta AI is also the name of the virtual assistant developed by the team, now integrated as a chatbot into Meta's social networking products. It is also available as a subscription-based stand-alone app. The virtual assistant was pre-installed on the second generation of Ray-Ban Meta smartglasses, and can incorporate inputs from the glasses' cameras after an update. It is also available on Quest 2 and newer HMDs. Since May 2024, the chatbot has summarized news from various outlets without linking directly to original articles, including in Canada, where news links are banned on its platforms. This use of news content without compensation and attribution has raised ethical and legal concerns, especially as Meta continues to reduce news visibility on its platforms. == Current research == === Natural language processing and chatbot === Natural language processing is the ability for machines to understand and generate natural language. The team is also researching unsupervised machine translation and multilingual chatbots. ==== Galactica ==== Galactica is a large language model (LLM) designed for generating scientific text. It was available for three days from 15 November 2022, before being withdrawn for generating racist and inaccurate content. ==== Llama ==== Llama is an LLM released in February 2023. As of January 2026, the most recent release is the Llama 4. === Hardware === Meta used CPUs and in-house custom chips before 2022; they switched to Nvidia GPUs since then. MTIA v1, one of their early chips, is designed for the company's content recommendation algorithms. It was fabricated on TSMC's 7 nm process technology and consumed 25W, capable of 51.2 TFlops FP16. == Controversy == The French media outlet Mediapart reports that in 2022, Facebook's parent company illegally used works accumulated by the pirate site LibGen to train its artificial intelligence.
Read more →
ARKA descriptors in QSAR

In computational chemistry and cheminformatics, ARKA descriptors in QSAR are a class of molecular descriptors used in quantitative structure–activity relationship (QSAR) modeling (or related approaches such as QSPR and QSTR), a computational method for predicting the biological activity or toxicity of chemical compounds based on their molecular structure. Molecular descriptors are numerical values that summarize information about a molecule's structure, topology, geometry, or physicochemical properties in a form suitable for machine learning or statistical modeling. ARKA (Arithmetic Residuals in K-Groups Analysis) descriptors differ from traditional descriptors by encoding atomic-level information through recursive autoregression techniques, which aim to capture subtle structural patterns and improve predictive accuracy. They are designed to be both interpretable and well-suited to modeling nonlinear relationships in QSAR studies. == Comparisons == While QSAR is essentially a similarity-based approach, the occurrence of activity/property cliffs may greatly reduce the predictive accuracy of the developed models. The novel Arithmetic Residuals in K-groups Analysis (ARKA) approach is a supervised dimensionality reduction technique developed by the DTC Laboratory, Jadavpur University that can easily identify activity cliffs in a data set. Activity cliffs are similar in their structures but differ considerably in their activity. The basic idea of the ARKA descriptors is to group the conventional QSAR descriptors based on a predefined criterion and then assign weightage to each descriptor in each group. ARKA descriptors have also been used to develop classification-based and regression-based QSAR models with acceptable quality statistics. The ARKA descriptors have been used for the identification of activity cliffs in QSAR studies and/or model development by multiple researchers. A tutorial presentation on the ARKA descriptors is available. Recently a multi-class ARKA framework has been proposed for improved q-RASAR model generation.
Read more →
Optical character recognition

Optical character recognition (OCR) or optical character reader is the electronic or mechanical conversion of images of typed, handwritten or printed text into machine-encoded text, whether from a scanned document, a photo of a document, a scene photo (for example the text on signs and billboards in a landscape photo) or from subtitle text superimposed on an image (for example: from a television broadcast). Widely used as a form of data entry from printed paper data records – whether passport documents, invoices, bank statements, computerized receipts, business cards, mail, printed data, or any suitable documentation – it is a common method of digitizing printed texts so that they can be electronically edited, searched, stored more compactly, displayed online, and used in machine processes such as cognitive computing, machine translation, (extracted) text-to-speech, key data and text mining. OCR is a field of research in pattern recognition, artificial intelligence and computer vision. Early versions needed to be trained with images of each character, and worked on one font at a time. Advanced systems capable of producing a high degree of accuracy for most fonts are now common, and with support for a variety of image file format inputs. Some systems are capable of reproducing formatted output that closely approximates the original page including images, columns, and other non-textual components. == History == Early optical character recognition may be traced to technologies involving telegraphy and creating reading devices for the blind. In 1914, Emanuel Goldberg developed a machine that read characters and converted them into standard telegraph code. Concurrently, Edmund Fournier d'Albe developed the Optophone, a handheld scanner that when moved across a printed page, produced tones that corresponded to specific letters or characters. In the late 1920s and into the 1930s, Emanuel Goldberg developed what he called a "Statistical Machine" for searching microfilm archives using an optical code recognition system. In 1931, he was granted US Patent number 1,838,389 for the invention. The patent was acquired by IBM. === Visually impaired users === In 1974, Ray Kurzweil started the company Kurzweil Computer Products, Inc. and continued development of omni-font OCR, which could recognize text printed in virtually any font. (Kurzweil is often credited with inventing omni-font OCR, but it was in use by companies, including CompuScan, in the late 1960s and 1970s.) Kurzweil used the technology to create a reading machine for blind people to have a computer read text to them out loud. The device included a CCD-type flatbed scanner and a text-to-speech synthesizer. On January 13, 1976, the finished product was unveiled during a widely reported news conference headed by Kurzweil and the leaders of the National Federation of the Blind. In 1978, Kurzweil Computer Products began selling a commercial version of the optical character recognition computer program. LexisNexis was one of the first customers, and bought the program to upload legal paper and news documents onto its nascent online databases. Two years later, Kurzweil sold his company to Xerox, which eventually spun it off as Scansoft, which merged with Nuance Communications. In the 2000s, OCR was made available online as a service (WebOCR), in a cloud computing environment, and in mobile applications like real-time translation of foreign-language signs on a smartphone. With the advent of smartphones and smartglasses, OCR can be used in internet connected mobile device applications that extract text captured using the device's camera. These devices that do not have built-in OCR functionality will typically use an OCR API to extract the text from the image file captured by the device. The OCR API returns the extracted text, along with information about the location of the detected text in the original image back to the device app for further processing (such as text-to-speech) or display. Various commercial and open source OCR systems are available for most common writing systems, including Latin, Cyrillic, Arabic, Hebrew, Indic, Bengali (Bangla), Devanagari, Tamil, Chinese, Japanese, and Korean characters. == Applications == OCR engines have been developed into software applications specializing in various subjects such as receipts, invoices, checks, and legal billing documents. The software can be used for: Entering data for business documents, e.g. checks, passports, invoices, bank statements and receipts Automatic number-plate recognition Passport recognition and information extraction in airports Automatically extracting key information from insurance documents Traffic-sign recognition Extracting business card information into a contact list Creating textual versions of printed documents, e.g. book scanning for Project Gutenberg Making electronic images of printed documents searchable, e.g. Google Books Converting handwriting in real-time to control a computer (pen computing) Defeating or testing the robustness of CAPTCHA anti-bot systems, though these are specifically designed to prevent OCR. Assistive technology for blind and visually impaired users Writing instructions for vehicles by identifying CAD images in a database that are appropriate to the vehicle design as it changes in real time Making scanned documents searchable by converting them to PDFs == Types == Optical character recognition (OCR) – targets typewritten text, one glyph or character at a time. Optical word recognition – targets typewritten text, one word at a time (for languages that use a space as a word divider). Usually just called "OCR". Intelligent character recognition (ICR) – also targets handwritten printscript or cursive text one glyph or character at a time, usually involving machine learning. Intelligent word recognition (IWR) – also targets handwritten printscript or cursive text, one word at a time. This is especially useful for languages where glyphs are not separated in cursive script. OCR is generally an offline process, which analyses a static document. There are cloud based services which provide an online OCR API service. Handwriting movement analysis can be used as input to handwriting recognition. Instead of merely using the shapes of glyphs and words, this technique is able to capture motion, such as the order in which segments are drawn, the direction, and the pattern of putting the pen down and lifting it. This additional information can make the process more accurate. This technology is also known as "online character recognition", "dynamic character recognition", "real-time character recognition", and "intelligent character recognition". == Techniques == === Pre-processing === OCR software often pre-processes images to improve the chances of successful recognition. Techniques include: De-skewing – if the document was not aligned properly when scanned, it may need to be tilted a few degrees clockwise or counterclockwise in order to make lines of text perfectly horizontal or vertical. Despeckling – removal of positive and negative spots, smoothing edges Binarization – conversion of an image from color or greyscale to black-and-white (called a binary image because there are two colors). The task is performed as a simple way of separating the text (or any other desired image component) from the background. The task of binarization is necessary since most commercial recognition algorithms work only on binary images, as it is simpler to do so. In addition, the effectiveness of binarization influences to a significant extent the quality of character recognition, and careful decisions are made in the choice of the binarization employed for a given input image type; since the quality of the method used to obtain the binary result depends on the type of image (scanned document, scene text image, degraded historical document, etc.). Line removal – Cleaning up non-glyph boxes and lines Layout analysis or zoning – Identification of columns, paragraphs, captions, etc. as distinct blocks. Especially important in multi-column layouts and tables. Line and word detection – Establishment of a baseline for word and character shapes, separating words as necessary. Script recognition – In multilingual documents, the script may change at the level of the words and hence, identification of the script is necessary, before the right OCR can be invoked to handle the specific script. Character isolation or segmentation – For per-character OCR, multiple characters that are connected due to image artifacts must be separated; single characters that are broken into multiple pieces due to artifacts must be connected. Normalization of aspect ratio and scale Segmentation of fixed-pitch fonts is accomplished relatively simply by aligning the image to a uniform grid based on where vertical grid lines will least often intersect black areas. For proportional fonts, more sophisticated techniques are needed because whitespace bet
Read more →
Density-based clustering validation

Density-Based Clustering Validation (DBCV) is a metric designed to assess the quality of clustering solutions, particularly for density-based clustering algorithms like DBSCAN, Mean shift, and OPTICS. This metric is particularly suited for identifying concave and nested clusters, where traditional metrics such as the Silhouette coefficient, Davies–Bouldin index, or Calinski–Harabasz index often struggle to provide meaningful evaluations. Unlike traditional validation measures, which often rely on compact and well-separated clusters, DBCV index evaluates how well clusters are defined in terms of local density variations and structural coherence. This metric was introduced in 2014 by David Moulavi and colleagues in their work. It utilizes density connectivity principles to quantify clustering structures, making it especially effective at detecting arbitrarily shaped clusters in concave datasets, where traditional metrics may be less reliable. The DBCV index has been employed for clustering analysis in bioinformatics, ecology, techno-economy, and health informatics , as well as in numerous other fields. == Definition == DBCV index evaluates clustering structures by analyzing the relationships between data points within and across clusters. Given a dataset X = x 1 , x 2 , . . . , x n {\displaystyle X={x_{1},x_{2},...,x_{n}}} , a density-based algorithm partitions it into K clusters C 1 , C 2 , . . . , C K {\displaystyle {C_{1},C_{2},...,C_{K}}} . Each point x i {\displaystyle x_{i}} belongs to a specific cluster, denoted as C c l u s t e r ( x i ) {\displaystyle C_{cluster(x_{i})}} A key concept in DBCV index is the notion of density-connected paths. Two points within the same cluster are considered density-connected if there exists a sequence of intermediate points linking them, where each consecutive pair meets a predefined density criterion. The density-based distance between two points is determined by identifying the optimal path that minimizes the maximum local reachability distance along its trajectory. DBCV index extends the Silhouette coefficient by redefining cluster cohesion and separation using density-based distances: Within-cluster density distance measures how closely a point is related to other members of its cluster: a i = 1 | C c l u s t e r ( x i ) | − 1 ∑ x j ∈ C c l u s t e r ( x i ) , y ≠ x d d e n s i t y ( x j , x i ) {\displaystyle a_{i}={\frac {1}{|C_{cluster(x_{i})}|-1}}\sum _{x_{j}\in C_{cluster(x_{i})},y\neq x}d_{density}(x_{j},x_{i})} Nearest-cluster density distance quantifies how far a point is from the closest external cluster: b i = min C ≠ C cluster ( x i ) C ∈ { C 1 , … , C K } ( 1 | C | ∑ x j ∈ C d density ( x i , x j ) ) . {\displaystyle b_{i}=\min _{C\neq C_{{\text{cluster}}(x_{i})} \atop C\in \{C_{1},\dots ,C_{K}\}}\left({\frac {1}{|C|}}\sum _{x_{j}\in C}d_{\text{density}}(x_{i},x_{j})\right).} Using these measures, the DBCV index is computed as: D B C V = 1 n ∑ i = 1 n b i − a i max ( a i , b i ) {\displaystyle DBCV={\frac {1}{n}}\sum _{i=1}^{n}{\frac {b_{i}-a_{i}}{\max(a_{i},b_{i})}}} == Explanation == DBCV index values range between −1 and +1: +1: Strongly cohesive and well-separated clusters. 0: Ambiguous clustering structure. −1: Poorly formed clusters or incorrect assignments. By leveraging density-based distances instead of traditional Euclidean measures, DBCV index provides a more robust evaluation of clustering performance in datasets with irregular or non-spherical distributions.
Read more →
Multimodal representation learning

Multimodal representation learning is a subfield of representation learning focused on integrating and interpreting information from different modalities, such as text, images, audio, or video, by projecting them into a shared latent space. This allows for semantically similar content across modalities to be mapped to nearby points within that space, facilitating a unified understanding of diverse data types. By automatically learning meaningful features from each modality and capturing their inter-modal relationships, multimodal representation learning enables a unified representation that enhances performance in cross-media analysis tasks such as video classification, event detection, and sentiment analysis. It also supports cross-modal retrieval and translation, including image captioning, video description, and text-to-image synthesis. == Motivation == The primary motivations for multimodal representation learning arise from the inherent nature of real-world data and the limitations of unimodal approaches. Since multimodal data offers complementary and supplementary information about an object or event from different perspectives, it is more informative than relying on a single modality. A key motivation is to narrow the heterogeneity gap that exists between different modalities by projecting their features into a shared semantic subspace. This allows semantically similar content across modalities to be represented by similar vectors, facilitating the understanding of relationships and correlations between them. Multimodal representation learning aims to leverage the unique information provided by each modality to achieve a more comprehensive and accurate understanding of concepts. These unified representations are crucial for improving performance in various cross-media analysis tasks such as video classification, event detection, and sentiment analysis. They also enable cross-modal retrieval, allowing users to search and retrieve content across different modalities. Additionally, it facilitates cross-modal translation, where information can be converted from one modality to another, as seen in applications like image captioning and text-to-image synthesis. The abundance of ubiquitous multimodal data in real-world applications, including understudied areas like healthcare, finance, and human-computer interaction (HCI), further motivates the development of effective multimodal representation learning techniques. == Approaches and methods == === Canonical-correlation analysis based methods === Canonical-correlation analysis (CCA) was first introduced in 1936 by Harold Hotelling and is a fundamental approach for multimodal learning. CCA aims to find linear relationships between two sets of variables. Given two data matrices X ∈ R n × p {\displaystyle X\in \mathbb {R} ^{n\times p}} and Y ∈ R n × q {\displaystyle Y\in \mathbb {R} ^{n\times q}} representing different modalities, CCA finds projection vectors w x ∈ R p {\displaystyle w_{x}\in \mathbb {R} ^{p}} and w y ∈ R q {\displaystyle w_{y}\in \mathbb {R} ^{q}} that maximizes the correlation between the projected variables: ρ = max w x , w y w x ⊤ Σ x y w y w x ⊤ Σ x x w x w y ⊤ Σ y y w y {\displaystyle \rho =\max _{w_{x},w_{y}}{\frac {w_{x}^{\top }\Sigma _{xy}w_{y}}{{\sqrt {w_{x}^{\top }\Sigma _{xx}w_{x}}}{\sqrt {w_{y}^{\top }\Sigma _{yy}w_{y}}}}}} such that Σ x x {\displaystyle \Sigma _{xx}} and Σ y y {\displaystyle \Sigma _{yy}} are the within-modality covariance matrices, and Σ x y {\displaystyle \Sigma _{xy}} is the between-modality covariance matrix. However, standard CCA is limited by its linearity, which led to the development of nonlinear extensions, such as kernel CCA and deep CCA. ==== Kernel CCA ==== Kernel canonical correlation analysis (KCCA) extends traditional CCA to capture nonlinear relationships between modalities by implicitly mapping the data into high dimensional feature spaces using kernel functions. Given kernel functions K x {\displaystyle K_{x}} and K y {\displaystyle K_{y}} with corresponding Gram matrices K x ∈ R n × n {\displaystyle K_{x}\in \mathbb {R} ^{n\times n}} and K y ∈ R n × n {\displaystyle K_{y}\in \mathbb {R} ^{n\times n}} , KCCA seeks coefficients α {\displaystyle \alpha } and β {\displaystyle \beta } that maximize: ρ = max α , β α ⊤ K x K y β α ⊤ K x 2 α β ⊤ K y 2 β {\displaystyle \rho =\max _{\alpha ,\beta }{\frac {\alpha ^{\top }K_{x}Ky\beta }{{\sqrt {\alpha ^{\top }K_{x}^{2}\alpha }}{\sqrt {\beta ^{\top }K_{y}^{2}\beta }}}}} To prevent overfitting, regularization terms are typically added, resulting in: ρ = max α , β α T K x K y β α T ( K x 2 + λ x K x ) α β T ( K y 2 + λ y K y ) β {\displaystyle \rho =\max _{\alpha ,\beta }{\frac {\alpha ^{T}K_{x}K_{y}\beta }{{\sqrt {\alpha ^{T}\left(K_{x}^{2}+\lambda _{x}K_{x}\right)\alpha }}{\sqrt {\;\beta ^{T}\left(K_{y}^{2}+\lambda _{y}K_{y}\right)\beta }}}}} where λ x {\displaystyle \lambda _{x}} and λ y {\displaystyle \lambda _{y}} are regularization parameters. KCCA has proven effective for tasks such as cross-modal retrieval and semantic analysis, though it faces computational challenges with large datasets due to its O ( n 2 ) {\displaystyle O(n^{2})} memory requirement for sorting kernel matrices. KCCA was proposed independently by several researchers. ==== Deep CCA ==== Deep canonical correlation analysis (DCCA), introduced in 2013, employs neural networks to learn nonlinear transformations for maximizing the correlation between modalities. DCCA uses separate neural networks f x {\displaystyle f_{x}} and f y {\displaystyle f_{y}} for each modality to transform the original data before applying CCA: max W x , W y , θ x , θ y corr ⁡ ( f x ( X ; θ x ) , f y ( Y ; θ y ) ) {\displaystyle \max _{W_{x},W_{y},\theta _{x},\theta _{y}}\operatorname {corr} \left(f_{x}(X;\theta _{x}),f_{y}(Y;\theta _{y})\right)} where θ x {\displaystyle \theta _{x}} and θ y {\displaystyle \theta _{y}} represent the parameters of the neural networks, and W x {\displaystyle W_{x}} and W y {\displaystyle W_{y}} are the CCA projection matrices. The correlation objective is computed as: corr ⁡ ( H x , H y ) = tr ⁡ ( T − 1 / 2 H x T H y S − 1 / 2 ) {\displaystyle \operatorname {corr} (H_{x},H_{y})=\operatorname {tr} \left(T^{-1/2}H_{x}^{T}H_{y}S^{-1/2}\right)} where H x = f x ( X ) {\displaystyle H_{x}=f_{x}(X)} and H y = f y ( Y ) {\displaystyle H_{y}=f_{y}(Y)} are the network outputs, T = H x T H x + r x I {\displaystyle T=H_{x}^{T}H_{x}+r_{x}I} , S = H y T H y + r y I {\displaystyle S=H_{y}^{T}H_{y}+r_{y}I} and r x , r y {\displaystyle r_{x},r_{y}} are the regularization parameters. DCCA overcomes the limitations of linear CCA and kernel CCA by learning complex nonlinear relationships while maintaining computational efficiency for large datasets through mini-batch optimization. === Graph-based methods === Graph-based approaches for multimodal representation learning leverage graph structure to model relationships between entities across different modalities. These methods typically represent each modality as a graph and then learn embedding that preserve cross-modal similarities, enabling more effective joint representation of heterogeneous data. One such method is cross-modal graph neural networks (CMGNNs) that extend traditional graph neural networks (GNNs) to handle data from multiple modalities by constructing graphs that capture both intra-modal and inter-modal relationships. These networks model interactions across modalities by representing them as nodes and their relationships as edges. Other graph-based methods include Probabilistic Graphical Models (PGMs) such as deep belief networks (DBN) and deep Boltzmann machines (DBM). These models can learn a joint representation across modalities, for instance, a multimodal DBN achieves this by adding a shared restricted Boltzmann Machine (RBM) hidden layer on top of modality-specific DBNs. Additionally, the structure of data in some domains like Human-Computer Interaction (HCI), such as the view hierarchy of app screens, can potentially be modeled using graph-like structures. The field of graph representation learning is also relevant, with ongoing progress in developing evaluation benchmarks. === Diffusion maps === Another set of methods relevant to multimodal representation learning are based on diffusion maps and their extensions to handle multiple modalities. ==== Multi-view diffusion maps ==== Multi-view diffusion maps address the challenge of achieving multi-view dimensionality reduction by effectively utilizing the availability of multiple views to extract a coherent low-dimensional representation of the data. The core idea is to exploit both the intrinsic relations within each view and the mutual relations between the different views, defining a cross-view model where a random walk process implicitly hops between objects in different views. A multi-view kernel matrix is constructed by combining these relations, defining a cross-view diffusion process and associ
Read more →
Multifactor dimensionality reduction

Multifactor dimensionality reduction (MDR) is a statistical approach, also used in machine learning automatic approaches, for detecting and characterizing combinations of attributes or independent variables that interact to influence a dependent or class variable. MDR was designed specifically to identify nonadditive interactions among discrete variables that influence a binary outcome and is considered a nonparametric and model-free alternative to traditional statistical methods such as logistic regression. The basis of the MDR method is a constructive induction or feature engineering algorithm that converts two or more variables or attributes to a single attribute. This process of constructing a new attribute changes the representation space of the data. The end goal is to create or discover a representation that facilitates the detection of nonlinear or nonadditive interactions among the attributes such that prediction of the class variable is improved over that of the original representation of the data. == Illustrative example == Consider the following simple example using the exclusive OR (XOR) function. XOR is a logical operator that is commonly used in data mining and machine learning as an example of a function that is not linearly separable. The table below represents a simple dataset where the relationship between the attributes (X1 and X2) and the class variable (Y) is defined by the XOR function such that Y = X1 XOR X2. Table 1 A machine learning algorithm would need to discover or approximate the XOR function in order to accurately predict Y using information about X1 and X2. An alternative strategy would be to first change the representation of the data using constructive induction to facilitate predictive modeling. The MDR algorithm would change the representation of the data (X1 and X2) in the following manner. MDR starts by selecting two attributes. In this simple example, X1 and X2 are selected. Each combination of values for X1 and X2 are examined and the number of times Y=1 and/or Y=0 is counted. In this simple example, Y=1 occurs zero times and Y=0 occurs once for the combination of X1=0 and X2=0. With MDR, the ratio of these counts is computed and compared to a fixed threshold. Here, the ratio of counts is 0/1 which is less than our fixed threshold of 1. Since 0/1 < 1 we encode a new attribute (Z) as a 0. When the ratio is greater than one we encode Z as a 1. This process is repeated for all unique combinations of values for X1 and X2. Table 2 illustrates our new transformation of the data. Table 2 The machine learning algorithm now has much less work to do to find a good predictive function. In fact, in this very simple example, the function Y = Z has a classification accuracy of 1. A nice feature of constructive induction methods such as MDR is the ability to use any data mining or machine learning method to analyze the new representation of the data. Decision trees, neural networks, or a naive Bayes classifier could be used in combination with measures of model quality such as balanced accuracy and mutual information. == Machine learning with MDR == As illustrated above, the basic constructive induction algorithm in MDR is very simple. However, its implementation for mining patterns from real data can be computationally complex. As with any machine learning algorithm there is always concern about overfitting. That is, machine learning algorithms are good at finding patterns in completely random data. It is often difficult to determine whether a reported pattern is an important signal or just chance. One approach is to estimate the generalizability of a model to independent datasets using methods such as cross-validation. Models that describe random data typically don't generalize. Another approach is to generate many random permutations of the data to see what the data mining algorithm finds when given the chance to overfit. Permutation testing makes it possible to generate an empirical p-value for the result. Replication in independent data may also provide evidence for an MDR model but can be sensitive to difference in the data sets. These approaches have all been shown to be useful for choosing and evaluating MDR models. An important step in a machine learning exercise is interpretation. Several approaches have been used with MDR including entropy analysis and pathway analysis. Tips and approaches for using MDR to model gene-gene interactions have been reviewed. == Extensions to MDR == Numerous extensions to MDR have been introduced. These include family-based methods, fuzzy methods, covariate adjustment, odds ratios, risk scores, survival methods, robust methods, methods for quantitative traits, and many others. == Applications of MDR == MDR has mostly been applied to detecting gene-gene interactions or epistasis in genetic studies of common human diseases such as atrial fibrillation, autism, bladder cancer, breast cancer, cardiovascular disease, hypertension, obesity, pancreatic cancer, prostate cancer and tuberculosis. It has also been applied to other biomedical problems such as the genetic analysis of pharmacology outcomes. A central challenge is the scaling of MDR to big data such as that from genome-wide association studies (GWAS). Several approaches have been used. One approach is to filter the features prior to MDR analysis. This can be done using biological knowledge through tools such as BioFilter. It can also be done using computational tools such as ReliefF. Another approach is to use stochastic search algorithms such as genetic programming to explore the search space of feature combinations. Yet another approach is a brute-force search using high-performance computing. == Implementations == www.epistasis.org provides an open-source and freely-available MDR software package. An R package for MDR. An sklearn-compatible Python implementation. An R package for Model-Based MDR. MDR in Weka. Generalized MDR.
Read more →
NSynth

NSynth (a portmanteau of "Neural Synthesis") is a WaveNet-based autoencoder for synthesizing audio, outlined in a paper in April 2017. == Overview == The model generates sounds through a neural network based synthesis, employing a WaveNet-style autoencoder to learn its own temporal embeddings from four different sounds. Google then released an open source hardware interface for the algorithm called NSynth Super, used by notable musicians such as Grimes and YACHT to generate experimental music using artificial intelligence. The research and development of the algorithm was part of a collaboration between Google Brain, Magenta and DeepMind. == Technology == === Dataset === The NSynth dataset is composed of 305,979 one-shot instrumental notes featuring a unique pitch, timbre, and envelope, sampled from 1,006 instruments from commercial sample libraries. For each instrument the dataset contains four-second 16 kHz audio snippets by ranging over every pitch of a standard MIDI piano, as well as five different velocities. The dataset is made available under a Creative Commons Attribution 4.0 International (CC BY 4.0) license. === Machine learning model === A spectral autoencoder model and a WaveNet autoencoder model are publicly available on GitHub. The baseline model uses a spectrogram with fft_size 1024 and hop_size 256, MSE loss on the magnitudes, and the Griffin-Lim algorithm for reconstruction. The WaveNet model trains on mu-law encoded waveform chunks of size 6144. It learns embeddings with 16 dimensions that are downsampled by 512 in time. == NSynth Super == In 2018 Google released a hardware interface for the NSynth algorithm, called NSynth Super, designed to provide an accessible physical interface to the algorithm for musicians to use in their artistic production. Design files, source code and internal components are released under an open source Apache License 2.0, enabling hobbyists and musicians to freely build and use the instrument. At the core of the NSynth Super there is a Raspberry Pi, extended with a custom printed circuit board to accommodate the interface elements. == Influence == Despite not being publicly available as a commercial product, NSynth Super has been used by notable artists, including Grimes and YACHT. Grimes reported using the instrument in her 2020 studio album Miss Anthropocene. YACHT announced an extensive use of NSynth Super in their album Chain Tripping. Claire L. Evans compared the potential influence of the instrument to the Roland TR-808. The NSynth Super design was honored with a D&AD Yellow Pencil award in 2018.
Read more →
Triplet loss

Triplet loss is a machine learning loss function widely used in one-shot learning, a setting where models are trained to generalize effectively from limited examples. It was conceived by Google researchers for their prominent FaceNet algorithm for face detection. Triplet loss is designed to support metric learning. Namely, to assist training models to learn an embedding (mapping to a feature space) where similar data points are closer together and dissimilar ones are farther apart, enabling robust discrimination across varied conditions. In the context of face detection, data points correspond to images. == Definition == The loss function is defined using triplets of training points of the form ( A , P , N ) {\displaystyle (A,P,N)} . In each triplet, A {\displaystyle A} (called an "anchor point") denotes a reference point of a particular identity, P {\displaystyle P} (called a "positive point") denotes another point of the same identity in point A {\displaystyle A} , and N {\displaystyle N} (called a "negative point") denotes a point of an identity different from the identity in point A {\displaystyle A} and P {\displaystyle P} . Let x {\displaystyle x} be some point and let f ( x ) {\displaystyle f(x)} be the embedding of x {\displaystyle x} in the finite-dimensional Euclidean space. It shall be assumed that the L2-norm of f ( x ) {\displaystyle f(x)} is unity (the L2 norm of a vector X {\displaystyle X} in a finite dimensional Euclidean space is denoted by ‖ X ‖ {\displaystyle \Vert X\Vert } .) We assemble m {\displaystyle m} triplets of points from the training dataset. The goal of training here is to ensure that, after learning, the following condition (called the "triplet constraint") is satisfied by all triplets ( A ( i ) , P ( i ) , N ( i ) ) {\displaystyle (A^{(i)},P^{(i)},N^{(i)})} in the training data set: ‖ f ( A ( i ) ) − f ( P ( i ) ) ‖ 2 2 + α < ‖ f ( A ( i ) ) − f ( N ( i ) ) ‖ 2 2 {\displaystyle \Vert f(A^{(i)})-f(P^{(i)})\Vert _{2}^{2}+\alpha <\Vert f(A^{(i)})-f(N^{(i)})\Vert _{2}^{2}} The variable α {\displaystyle \alpha } is a hyperparameter called the margin, and its value must be set manually. In the FaceNet system, its value was set as 0.2. Thus, the full form of the function to be minimized is the following: L = ∑ i = 1 m max ( ‖ f ( A ( i ) ) − f ( P ( i ) ) ‖ 2 2 − ‖ f ( A ( i ) ) − f ( N ( i ) ) ‖ 2 2 + α , 0 ) {\displaystyle L=\sum _{i=1}^{m}\max {\Big (}\Vert f(A^{(i)})-f(P^{(i)})\Vert _{2}^{2}-\Vert f(A^{(i)})-f(N^{(i)})\Vert _{2}^{2}+\alpha ,0{\Big )}} == Intuition == A baseline for understanding the effectiveness of triplet loss is the contrastive loss, which operates on pairs of samples (rather than triplets). Training with the contrastive loss pulls embeddings of similar pairs closer together, and pushes dissimilar pairs apart. Its pairwise approach is greedy, as it considers each pair in isolation. Triplet loss innovates by considering relative distances. Its goal is that the embedding of an anchor (query) point be closer to positive points than to negative points (also accounting for the margin). It does not try to further optimize the distances once this requirement is met. This is approximated by simultaneously considering two pairs (anchor-positive and anchor-negative), rather than each pair in isolation. == Triplet "mining" == One crucial implementation detail when training with triplet loss is triplet "mining", which focuses on the smart selection of triplets for optimization. This process adds an additional layer of complexity compared to contrastive loss. A naive approach to preparing training data for the triplet loss involves randomly selecting triplets from the dataset. In general, the set of valid triplets of the form ( A ( i ) , P ( i ) , N ( i ) ) {\displaystyle (A^{(i)},P^{(i)},N^{(i)})} is very large. To speed-up training convergence, it is essential to focus on challenging triplets. In the FaceNet paper, several options were explored, eventually arriving at the following. For each anchor-positive pair, the algorithm considers only semi-hard negatives. These are negatives that violate the triplet requirement (i.e, are "hard"), but lie farther from the anchor than the positive (not too hard). Restated, for each A ( i ) {\displaystyle A^{(i)}} and P ( i ) {\displaystyle P^{(i)}} , they seek N ( i ) {\displaystyle N^{(i)}} such that: The rationale for this design choice is heuristic. It may appear puzzling that the mining process neglects "very hard" negatives (i.e., closer to the anchor than the positive). Experiments conducted by the FaceNet designers found that this often leads to a convergence to degenerate local minima. Triplet mining is performed at each training step, from within the sample points contained in the training batch (this is known as online mining), after embeddings were computed for all points in the batch. While ideally the entire dataset could be used, this is impractical in general. To support a large search space for triplets, the FaceNet authors used very large batches (1800 samples). Batches are constructed by selecting a large number of same-category sample points (40), and randomly selected negatives for them. == Extensions == Triplet loss has been extended to simultaneously maintain a series of distance orders by optimizing a continuous relevance degree with a chain (i.e., ladder) of distance inequalities. This leads to the Ladder Loss, which has been demonstrated to offer performance enhancements of visual-semantic embedding in learning to rank tasks. In Natural Language Processing, triplet loss is one of the loss functions considered for BERT fine-tuning in the SBERT architecture. Other extensions involve specifying multiple negatives (multiple negatives ranking loss).
Read more →
FMLLR

In signal processing, Feature space Maximum Likelihood Linear Regression (fMLLR) is a global feature transform that are typically applied in a speaker adaptive way, where fMLLR transforms acoustic features to speaker adapted features by a multiplication operation with a transformation matrix. In some literature, fMLLR is also known as the Constrained Maximum Likelihood Linear Regression (cMLLR). == Overview == fMLLR transformations are trained in a maximum likelihood sense on adaptation data. These transformations may be estimated in many ways, but only maximum likelihood (ML) estimation is considered in fMLLR. The fMLLR transformation is trained on a particular set of adaptation data, such that it maximizes the likelihood of that adaptation data given a current model-set. This technique is a widely used approach for speaker adaptation in HMM-based speech recognition. Later research also shows that fMLLR is an excellent acoustic feature for DNN/HMM hybrid speech recognition models. The advantage of fMLLR includes the following: the adaptation process can be performed within a pre-processing phase, and is independent of the ASR training and decoding process. this type of adapted feature can be applied to deep neural networks (DNN) to replace traditionally used mel-spectrogram in end-to-end speech recognition models. fMLLR's speaker adaptation process leads to a significant performance boost for ASR models, hence outperforming other transform or features like MFCCs (Mel-Frequency Cepstral Coefficients) and FBANKs (Filter bank) coefficients. fMLLR features can be efficiently realized with speech toolkits like Kaldi. Major problem and disadvantage of fMLLR: when the amount of adaptation data is limited, the transformation matrices tends to easily overfit the given data. == Computing fMLLR transform == Feature transform of fMLLR can be easily computed with the open source speech tool Kaldi, the Kaldi script uses the standard estimation scheme described in Appendix B of the original paper, in particular the section Appendix B.1 "Direct method over rows". In the Kaldi formulation, fMLLR is an affine feature transform of the form x {\displaystyle x} → A {\displaystyle A} x {\displaystyle x} + b {\displaystyle +b} , which can be written in the form x {\displaystyle x} →W x ^ {\displaystyle {\hat {x}}} , where x ^ {\displaystyle {\hat {x}}} = [ x 1 ] {\displaystyle {\begin{bmatrix}x\\1\end{bmatrix}}} is the acoustic feature x {\displaystyle x} with a 1 appended. Note that this differs from some of the literature where the 1 comes first as x ^ {\displaystyle {\hat {x}}} = [ 1 x ] {\displaystyle {\begin{bmatrix}1\\x\end{bmatrix}}} . The sufficient statistics stored are: K = ∑ t , j , m γ j , m ( t ) Σ j m − 1 μ j m x ( t ) + {\displaystyle K=\sum _{t,j,m}\gamma _{j,m}(t)\textstyle \Sigma _{jm}^{-1}\mu _{jm}x(t)^{+}\displaystyle } where Σ j m − 1 {\displaystyle \textstyle \Sigma _{jm}^{-1}\displaystyle } is the inverse co-variance matrix. And for 0 ≤ i ≤ D {\displaystyle 0\leq i\leq D} where D {\displaystyle D} is the feature dimension: G ( i ) = ∑ t , j , m γ j , m ( t ) ( 1 σ j , m 2 ( i ) ) x ( t ) + x ( t ) + T {\displaystyle G^{(i)}=\sum _{t,j,m}\gamma _{j,m}(t)\left({\frac {1}{\sigma _{j,m}^{2}(i)}}\right)x(t)^{+}x(t)^{+T}\displaystyle } For a thorough review that explains fMLLR and the commonly used estimation techniques, see the original paper "Maximum likelihood linear transformations for HMM-based speech recognition ". Note that the Kaldi script that performs the feature transforms of fMLLR differs with by using a column of the inverse in place of the cofactor row. In other words, the factor of the determinant is ignored, as it does not affect the transform result and can causes potential danger of numerical underflow or overflow. == Comparing with other features or transforms == Experiment result shows that by using the fMLLR feature in speech recognition, constant improvement is gained over other acoustic features on various commonly used benchmark datasets (TIMIT, LibriSpeech, etc). In particular, fMLLR features outperform MFCCs and FBANKs coefficients, which is mainly due to the speaker adaptation process that fMLLR performs. In, phoneme error rate (PER, %) is reported for the test set of TIMIT with various neural architectures: As expected, fMLLR features outperform MFCCs and FBANKs coefficients despite the use of different model architecture. Where MLP (multi-layer perceptron) serves as a simple baseline, on the other hand RNN, LSTM, and GRU are all well known recurrent models. The Li-GRU architecture is based on a single gate and thus saves 33% of the computations over a standard GRU model, Li-GRU thus effectively address the gradient vanishing problem of recurrent models. As a result, the best performance is obtained with the Li-GRU model on fMLLR features. == Extract fMLLR features with Kaldi == fMLLR can be extracted as reported in the s5 recipe of Kaldi. Kaldi scripts can certainly extract fMLLR features on different dataset, below are the basic example steps to extract fMLLR features from the open source speech corpora Librispeech. Note that the instructions below are for the subsets train-clean-100,train-clean-360,dev-clean, and test-clean, but they can be easily extended to support the other sets dev-other, test-other, and train-other-500. These instruction are based on the codes provided in this GitHub repository, which contains Kaldi recipes on the LibriSpeech corpora to execute the fMLLR feature extraction process, replace the files under $KALDI_ROOT/egs/librispeech/s5/ with the files in the repository. Install Kaldi. Install Kaldiio. If running on a single machine, change the following lines in $KALDI_ROOT/egs/librispeech/s5/cmd.sh to replace queue.pl to run.pl: Change the data path in run.sh to your LibriSpeech data path, the directory LibriSpeech/ should be under that path. For example: Install flac with: sudo apt-get install flac Run the Kaldi recipe run.sh for LibriSpeech at least until Stage 13 (included), for simplicity you can use the modified run.sh. Copy exp/tri4b/trans. files into exp/tri4b/decode_tgsmall_train_clean_/ with the following command: Compute the fMLLR features by running the following script, the script can also be downloaded here: Compute alignments using: Apply CMVN and dump the fMLLR features to new .ark files, the script can also be downloaded here: Use the Python script to convert Kaldi generated .ark features to .npy for your own dataloader, an example Python script is provided:
Read more →
Confirmatory blockmodeling

Confirmatory blockmodeling is a deductive approach in blockmodeling, where a blockmodel (or part of it) is prespecify before the analysis, and then the analysis is fit to this model. When only a part of analysis is prespecify (like individual cluster(s) or location of the block types), it is called partially confirmatory blockmodeling. This is so-called indirect approach, where the blockmodeling is done on the blockmodel fitting (e.g., a priori hypothesized blockmodel). Opposite approach to the confirmatory blockmodeling is an inductive exploratory blockmodeling.
Read more →
Exploratory blockmodeling

Exploratory blockmodeling is an (inductive) approach (or a group of approaches) in blockmodeling regarding the specification of an ideal blockmodel. This approach, also known as hypotheses-generating, is the simplest approach, as it "merely involves the definition of the block types permitted as well as of the number of clusters." With this approach, researcher usually defines the best possible blockmodel, which then represent the base for the analysis of the whole network. This approach is usually based on: previous analyses and theoretical considerations, using stricker blockmodel and block types, where the structural equivalence is stricker than the regular equivalence and using smaller number of classes. The opposite approach is called a confirmatory blockmodeling.
Read more →