Himmat is a women's safety mobile application of Delhi Police. It was launched by Home Minister Rajnath Singh on 1 January 2015. The app is freely available for Android mobile phones and can be downloaded from Delhi Police website. Delhi Police plans to launch app for other platforms in future. Low registrations and other problems resulted in a parliamentary panel calling the app a failure in 2018. Himmat has gone on to be called as one of India's best safety apps for women.
StyleGAN
The Style Generative Adversarial Network, or StyleGAN for short, is an extension to the GAN architecture introduced by Nvidia researchers in December 2018, and made source available in February 2019. StyleGAN depends on Nvidia's CUDA software, GPUs, and Google's TensorFlow, or Meta AI's PyTorch, which supersedes TensorFlow as the official implementation library in later StyleGAN versions. The second version of StyleGAN, called StyleGAN2, was published on February 5, 2020. It removes some of the characteristic artifacts and improves the image quality. Nvidia introduced StyleGAN3, described as an "alias-free" version, on June 23, 2021, and made source available on October 12, 2021. == History == A direct predecessor of the StyleGAN series is the Progressive GAN, published in 2017. In December 2018, Nvidia researchers distributed a preprint with accompanying software introducing StyleGAN, a GAN for producing an unlimited number of (often convincing) portraits of fake human faces. StyleGAN was able to run on Nvidia's commodity GPU processors. In February 2019, Uber engineer Phillip Wang used the software to create the website This Person Does Not Exist, which displayed a new face on each web page reload. Wang himself has expressed amazement, given that humans are evolved to specifically understand human faces, that nevertheless StyleGAN can competitively "pick apart all the relevant features (of human faces) and recompose them in a way that's coherent." In September 2019, a website called Generated Photos published 100,000 images as a collection of stock photos. The collection was made using a private dataset shot in a controlled environment with similar light and angles. Similarly, two faculty at the University of Washington's Information School used StyleGAN to create Which Face is Real?, which challenged visitors to differentiate between a fake and a real face side by side. The faculty stated the intention was to "educate the public" about the existence of this technology so they could be wary of it, "just like eventually most people were made aware that you can Photoshop an image". The second version of StyleGAN, called StyleGAN2, was published on February 5, 2020. It removes some of the characteristic artifacts and improves the image quality. In 2021, a third version was released, improving consistency between fine and coarse details in the generator. Dubbed "alias-free", this version was implemented with PyTorch. === Illicit use === In December 2019, Facebook took down a network of accounts with false identities, and mentioned that some of them had used profile pictures created with machine learning techniques. == Architecture == === Progressive GAN === Progressive GAN is a method for training GAN for large-scale image generation stably, by growing a GAN generator from small to large scale in a pyramidal fashion. Like SinGAN, it decomposes the generator as G = G 1 ∘ G 2 ∘ ⋯ ∘ G N {\displaystyle G=G_{1}\circ G_{2}\circ \cdots \circ G_{N}} , and the discriminator as D = D N ∘ D N − 1 ∘ ⋯ ∘ D 1 {\displaystyle D=D_{N}\circ D_{N-1}\circ \cdots \circ D_{1}} . During training, at first only G N , D N {\displaystyle G_{N},D_{N}} are used in a GAN game to generate 4x4 images. Then G N − 1 , D N − 1 {\displaystyle G_{N-1},D_{N-1}} are added to reach the second stage of GAN game, to generate 8x8 images, and so on, until we reach a GAN game to generate 1024x1024 images. To avoid discontinuity between stages of the GAN game, each new layer is "blended in" (Figure 2 of the paper). For example, this is how the second stage GAN game starts: Just before, the GAN game consists of the pair G N , D N {\displaystyle G_{N},D_{N}} generating and discriminating 4x4 images. Just after, the GAN game consists of the pair ( ( 1 − α ) + α ⋅ G N − 1 ) ∘ u ∘ G N , D N ∘ d ∘ ( ( 1 − α ) + α ⋅ D N − 1 ) {\displaystyle ((1-\alpha )+\alpha \cdot G_{N-1})\circ u\circ G_{N},D_{N}\circ d\circ ((1-\alpha )+\alpha \cdot D_{N-1})} generating and discriminating 8x8 images. Here, the functions u , d {\displaystyle u,d} are image up- and down-sampling functions, and α {\displaystyle \alpha } is a blend-in factor (much like an alpha in image composing) that smoothly glides from 0 to 1. === StyleGAN === StyleGAN is designed as a combination of Progressive GAN with neural style transfer. The key architectural choice of StyleGAN-1 is a progressive growth mechanism, similar to Progressive GAN. Each generated image starts as a constant 4 × 4 × 512 {\displaystyle 4\times 4\times 512} array, and repeatedly passed through style blocks. Each style block applies a "style latent vector" via affine transform ("adaptive instance normalization"), similar to how neural style transfer uses Gramian matrix. It then adds noise, and normalize (subtract the mean, then divide by the variance). At training time, usually only one style latent vector is used per image generated, but sometimes two ("mixing regularization") in order to encourage each style block to independently perform its stylization without expecting help from other style blocks (since they might receive an entirely different style latent vector). After training, multiple style latent vectors can be fed into each style block. Those fed to the lower layers control the large-scale styles, and those fed to the higher layers control the fine-detail styles. Style-mixing between two images x , x ′ {\displaystyle x,x'} can be performed as well. First, run a gradient descent to find z , z ′ {\displaystyle z,z'} such that G ( z ) ≈ x , G ( z ′ ) ≈ x ′ {\displaystyle G(z)\approx x,G(z')\approx x'} . This is called "projecting an image back to style latent space". Then, z {\displaystyle z} can be fed to the lower style blocks, and z ′ {\displaystyle z'} to the higher style blocks, to generate a composite image that has the large-scale style of x {\displaystyle x} , and the fine-detail style of x ′ {\displaystyle x'} . Multiple images can also be composed this way. === StyleGAN2 === StyleGAN2 improves upon StyleGAN in two ways. One, it applies the style latent vector to transform the convolution layer's weights instead, thus solving the "blob" problem. The "blob" problem roughly speaking is because using the style latent vector to normalize the generated image destroys useful information. Consequently, the generator learned to create a "distraction" by a large blob, which absorbs most of the effect of normalization (somewhat similar to using flares to distract a heat-seeking missile). Two, it uses residual connections, which helps it avoid the phenomenon where certain features are stuck at intervals of pixels. For example, the seam between two teeth may be stuck at pixels divisible by 32, because the generator learned to generate teeth during stage N-5, and consequently could only generate primitive teeth at that stage, before scaling up 5 times (thus intervals of 32). This was updated by the StyleGAN2-ADA ("ADA" stands for "adaptive"), which uses invertible data augmentation. It also tunes the amount of data augmentation applied by starting at zero, and gradually increasing it until an "overfitting heuristic" reaches a target level, thus the name "adaptive". === StyleGAN3 === StyleGAN3 improves upon StyleGAN2 by solving the "texture sticking" problem, which can be seen in the official videos. They analyzed the problem by the Nyquist–Shannon sampling theorem, and argued that the layers in the generator learned to exploit the high-frequency signal in the pixels they operate upon. To solve this, they proposed imposing strict lowpass filters between each generator's layers, so that the generator is forced to operate on the pixels in a way faithful to the continuous signals they represent, rather than operate on them as merely discrete signals. They further imposed rotational and translational invariance by using more signal filters. The resulting StyleGAN-3 is able to generate images that rotate and translate smoothly, and without texture sticking.
Distinguishable interfaces
Distinguishable interfaces use computer graphic principles to automatically generate easily distinguishable appearance for computer data. Although the desktop metaphor revolutionized user interfaces, there is evidence that a spatial layout alone does little to help in locating files and other data; distinguishable appearance is also required. Studies have shown that average users have considerable difficulty finding files on their personal computers, even ones that they created the same day. Search engines do not always help, since it has been found that users often know of the existence of a file without being able to specify relevant search terms. On the contrary, people appear to incrementally search for files using some form of context. Recently researchers and web developers have argued that the problem is the lack of distinguishable appearance: in the traditional computer interface most objects and locations appear identical. This problem rarely occurs in the real world, where both objects and locations generally have easily distinguishable appearance. Discriminability was one of the recommendations in the ISO 9241-12 recommendation on presentation of information on visual displays (part of the overall report on Ergonomics of Human System Interaction), however it was assumed in that report that this would be achieved by manual design of graphical symbols. == VisualIDs, semanticons, and identicons == The mass availability of computer graphics supported the introduction of approaches that make better use of the brain's "visual hardware", by providing individual files and other abstract data with distinguishable appearance. This idea initially appeared in strictly academic VisualIDs and Semanticons works, but the web community has explored and rapidly adopted similar ideas, such as the Identicon. The VisualIDs project automatically generated icons for files or other data based on a hash of the data identifier, so the icons had no relation to the content or meaning of the data. It was argued not only that generating meaningful icons is unnecessary (their user study showed rapid learning of the arbitrary icons), but also that basing icons on content is actually incorrect ("contrasting visualization with visual identifiers"). The Semanticons project developed by Setlur et al. demonstrated an algorithm to create icons that reflect the content of files. In this work the name, location and content of a file are parsed and used to retrieve related image(s) from an image database. These are then processed using a Non-photorealistic rendering technique in order to generate graphical icons. Developer Don Park introduced the identicon library for making a visual icon from a hash of a data identifier. This initial public implementation has spawned a large number of implementations for various environments. In particular, identicons are now being used as default visual user identifiers (avatars) for several widely used systems. They are also used as a complement to Gravatars, which are pre-existing avatar images created or chosen by users, instead of automatically generated images. (see #External links). == Current research == While current web practice has followed the semantics-free approach of VisualIDs, recent research has followed the semantics-based approach of Semanticons. Examples include using data mining principles to automatically create "intelligent icons" that reflect the contents of files and creating icons for music files that reflect audio characteristics or affective content.
Line integral convolution
In scientific visualization, line integral convolution (LIC) is a method to visualize a vector field (such as fluid motion) at high spatial resolutions. The LIC technique was first proposed by Brian Cabral and Leith Casey Leedom in 1993. In LIC, discrete numerical line integration is performed along the field lines (curves) of the vector field on a uniform grid. The integral operation is a convolution of a filter kernel and an input texture, often white noise. In signal processing, this process is known as a discrete convolution. == Overview == Traditional visualizations of vector fields use small arrows or lines to represent vector direction and magnitude. This method has a low spatial resolution, which limits the density of presentable data and risks obscuring characteristic features in the data. More sophisticated methods, such as streamlines and particle tracing techniques, can be more revealing but are highly dependent on proper seed points. Texture-based methods, like LIC, avoid these problems since they depict the entire vector field at point-like (pixel) resolution. Compared to other integration-based techniques that compute field lines of the input vector field, LIC has the advantage that all structural features of the vector field are displayed, without the need to adapt the start and end points of field lines to the specific vector field. In other words, it shows the topology of the vector field. In user testing, LIC was found to be particularly good for identifying critical points. == Algorithm == === Informal description === LIC causes output values to be strongly correlated along the field lines, but uncorrelated in orthogonal directions. As a result, the field lines contrast each other and stand out visually from the background. Intuitively, the process can be understood with the following example: the flow of a vector field can be visualized by overlaying a fixed, random pattern of dark and light paint. As the flow passes by the paint, the fluid picks up some of the paint's color, averaging it with the color it has already acquired. The result is a randomly striped, smeared texture where points along the same streamline tend to have a similar color. Other physical examples include: whorl patterns of paint, oil, or foam on a river visualisation of magnetic field lines using randomly distributed iron filings fine sand being blown by strong wind === Formal mathematical description === Although the input vector field and the result image are discretized, it pays to look at it from a continuous viewpoint. Let v {\displaystyle \mathbf {v} } be the vector field given in some domain Ω {\displaystyle \Omega } . Although the input vector field is typically discretized, we regard the field v {\displaystyle \mathbf {v} } as defined in every point of Ω {\displaystyle \Omega } , i.e. we assume an interpolation. Streamlines, or more generally field lines, are tangent to the vector field in each point. They end either at the boundary of Ω {\displaystyle \Omega } or at critical points where v = 0 {\displaystyle \mathbf {v} =\mathbf {0} } . For the sake of simplicity, critical points and boundaries are ignored in the following. A field line σ {\displaystyle {\boldsymbol {\sigma }}} , parametrized by arc length s {\displaystyle s} , is defined as d σ ( s ) d s = v ( σ ( s ) ) | v ( σ ( s ) ) | . {\displaystyle {\frac {d{\boldsymbol {\sigma }}(s)}{ds}}={\frac {\mathbf {v} ({\boldsymbol {\sigma }}(s))}{|\mathbf {v} ({\boldsymbol {\sigma }}(s))|}}.} Let σ r ( s ) {\displaystyle {\boldsymbol {\sigma }}_{\mathbf {r} }(s)} be the field line that passes through the point r {\displaystyle \mathbf {r} } for s = 0 {\displaystyle s=0} . Then the image gray value at r {\displaystyle \mathbf {r} } is set to D ( r ) = ∫ − L / 2 L / 2 k ( s ) N ( σ r ( s ) ) d s {\displaystyle D(\mathbf {r} )=\int _{-L/2}^{L/2}k(s)N({\boldsymbol {\sigma }}_{\mathbf {r} }(s))ds} where k ( s ) {\displaystyle k(s)} is the convolution kernel, N ( r ) {\displaystyle N(\mathbf {r} )} is the noise image, and L {\displaystyle L} is the length of field line segment that is followed. D ( r ) {\displaystyle D(\mathbf {r} )} has to be computed for each pixel in the LIC image. If carried out naively, this is quite expensive. First, the field lines have to be computed using a numerical method for solving ordinary differential equations, like a Runge–Kutta method, and then for each pixel the convolution along a field line segment has to be calculated. The final image will normally be colored in some way. Typically, some scalar field in Ω {\displaystyle \Omega } (like the vector length) is used to determine the hue, while the grayscale LIC output determines the brightness. Different choices of convolution kernels and random noise produce different textures; for example, pink noise produces a cloudy pattern where areas of higher flow stand out as smearing, suitable for weather visualization. Further refinements in the convolution can improve the quality of the image. === Programming description === Algorithmically, LIC takes a vector field and noise texture as input, and outputs a texture. The process starts by generating in the domain of the vector field a random gray level image at the desired output resolution. Then, for every pixel in this image, the forward and backward streamline of a fixed arc length is calculated. The value assigned to the current pixel is computed by a convolution of a suitable convolution kernel with the gray levels of all the noise pixels lying on a segment of this streamline. This creates a gray level LIC image. == Versions == === Basic === Basic LIC images are grayscale images, without color and animation. While such LIC images convey the direction of the field vectors, they do not indicate orientation; for stationary fields, this can be remedied by animation. Basic LIC images do not show the length of the vectors (or the strength of the field). === Color === The length of the vectors (or the strength of the field) is usually coded in color; alternatively, animation can be used. === Animation === LIC images can be animated by using a kernel that changes over time. Samples at a constant time from the streamline would still be used, but instead of averaging all pixels in a streamline with a static kernel, a ripple-like kernel constructed from a periodic function multiplied by a Hann function acting as a window (in order to prevent artifacts) is used. The periodic function is then shifted along the period to create an animation. === Fast LIC (FLIC) === The computation can be significantly accelerated by re-using parts of already computed field lines, specializing to a box function as convolution kernel k ( s ) {\displaystyle k(s)} and avoiding redundant computations during convolution. The resulting fast LIC method can be generalized to convolution kernels that are arbitrary polynomials. === Oriented Line Integral Convolution (OLIC) === Because LIC does not encode flow orientation, it cannot distinguish between streamlines of equal direction but opposite orientation. Oriented Line Integral Convolution (OLIC) solves this issue by using a ramp-like asymmetric kernel and a low-density noise texture. The kernel asymmetrically modulates the intensity along the streamline, producing a trace that encodes orientation; the low-density of the noise texture prevents smeared traces from overlapping, aiding readability. Fast Rendering of Oriented Line Integral Convolution (FROLIC) is a variation that approximates OLIC by rendering each trace in discrete steps instead of as a continuous smear. === Unsteady Flow LIC (UFLIC) === For time-dependent vector fields (unsteady flow), a variant called Unsteady Flow LIC has been designed that maintains the coherence of the flow animation. An interactive GPU-based implementation of UFLIC has been presented. === Parallel === Since the computation of an LIC image is expensive but inherently parallel, the process has been parallelized and, with availability of GPU-based implementations, interactive on PCs. === Multidimensional === Note that the domain Ω {\displaystyle \Omega } does not have to be a 2D domain: the method is applicable to higher dimensional domains using multidimensional noise fields. However, the visualization of the higher-dimensional LIC texture is problematic; one way is to use interactive exploration with 2D slices that are manually positioned and rotated. The domain Ω {\displaystyle \Omega } does not have to be flat either; the LIC texture can be computed also for arbitrarily shaped 2D surfaces in 3D space. == Applications == This technique has been applied to a wide range of problems since it first was published in 1993, both scientific and creative, including: Representing vector fields: visualization of steady (time-independent) flows (streamlines) visual exploration of 2D autonomous dynamical systems wind mapping water flow mapping Artistic effects for image generation and stylization: pencil drawing (auto
Hexagonal sampling
A multidimensional signal is a function of M independent variables where M ≥ 2 {\displaystyle M\geq 2} . Real world signals, which are generally continuous time signals, have to be discretized (sampled) in order to ensure that digital systems can be used to process the signals. It is during this process of discretization where sampling comes into picture. Although there are many ways of obtaining a discrete representation of a continuous time signal, periodic sampling is by far the simplest scheme. Theoretically, sampling can be performed with respect to any set of points. But practically, sampling is carried out with respect to a set of points that have a certain algebraic structure. Such structures are called lattices. Mathematically, the process of sampling an N {\displaystyle N} -dimensional signal can be written as: w ( t ^ ) = w ( V . n ^ ) {\displaystyle w({\hat {t}})=w(V.{\hat {n}})} where t ^ {\displaystyle {\hat {t}}} is continuous domain M-dimensional vector (M-D) that is being sampled, n ^ {\displaystyle {\hat {n}}} is an M-dimensional integer vector corresponding to indices of a sample, and V is an N × N {\displaystyle N\times N} sampling matrix. == Motivation == Multidimensional sampling provides the opportunity to look at digital methods to process signals. Some of the advantages of processing signals in the digital domain include flexibility via programmable DSP operations, signal storage without the loss of fidelity, opportunity for encryption in communication, lower sensitivity to hardware tolerances. Thus, digital methods are simultaneously both powerful and flexible. In many applications, they act as less expensive alternatives to their analog counterparts. Sometimes, the algorithms implemented using digital hardware are so complex that they have no analog counterparts. Multidimensional digital signal processing deals with processing signals represented as multidimensional arrays such as 2-D sequences or sampled images.[1] Processing these signals in the digital domain permits the use of digital hardware where in signal processing operations are specified by algorithms. As real world signals are continuous time signals, multidimensional sampling plays a crucial role in discretizing the real world signals. The discrete time signals are in turn processed using digital hardware to extract information from the signal. == Preliminaries == === Region of Support === The region outside of which the samples of the signal take zero values is known as the Region of support (ROS). From the definition, it is clear that the region of support of a signal is not unique. === Fourier transform === The Fourier transform is a tool that allows us to simplify mathematical operations performed on the signal. The transform basically represents any signal as a weighted combination of sinusoids. The Fourier and the inverse Fourier transform of an M-dimensional signal can be defined as follows: X a ( Ω ^ ) = ∫ − ∞ + ∞ x a ( t ^ ) e − j Ω ^ T t ^ d t ^ {\displaystyle X_{a}({\hat {\Omega }})=\int _{-\infty }^{+\infty }\!x_{a}({\hat {t}})e^{-j{\hat {\Omega }}^{T}{\hat {t}}}d{\hat {t}}} x a ( t ^ ) = 1 2 π M ∫ − ∞ + ∞ X ( Ω ^ ) e ( j Ω ^ T t ^ ) d Ω ^ {\displaystyle x_{a}({\hat {t}})={\frac {1}{2\pi ^{M}}}\int _{-\infty }^{+\infty }\!X({\hat {\Omega }})e^{(j{\hat {\Omega }}^{T}{\hat {t}})}\,\mathrm {d} {\hat {\Omega }}} The cap symbol ^ indicates that the operation is performed on vectors. The Fourier transform of the sampled signal is observed to be a periodic extension of the continuous time Fourier transform of the signal. This is mathematically represented as: X ( ω ) = 1 | d e t ( V ) | ∑ k X a ( Ω ^ − U k ) {\displaystyle X(\omega )={\frac {1}{|det(V)|}}\sum _{k}\!X_{a}({\hat {\Omega }}-Uk)} where ω = V ~ Ω {\displaystyle \omega ={\tilde {V}}\Omega } and U = 2 π V ~ {\displaystyle U=2\pi {\tilde {V}}} is the periodicity matrix where ~ denotes matrix transposition. Thus sampling in the spatial domain results in periodicity in the Fourier domain. === Aliasing === A band limited signal may be periodically replicated in many ways. If the replication results in an overlap between replicated regions, the signal suffers from aliasing. Under such conditions, a continuous time signal cannot be perfectly recovered from its samples. Thus in order to ensure perfect recovery of the continuous signal, there must be zero overlap multidimensional sampling of the replicated regions in the transformed domain. As in the case of 1-dimensional signals, aliasing can be prevented if the continuous time signal is sampled at an adequate sufficiently high rate. === Sampling density === It is a measure of the number of samples per unit area. It is defined as: S . D = 1 | d e t ( V ) | = | d e t ( U ) | 4 π 2 {\displaystyle S.D={\frac {1}{|det(V)|}}={\frac {|det(U)|}{4\pi ^{2}}}} . The minimum number of samples per unit area required to completely recover the continuous time signal is termed as optimal sampling density. In applications where memory or processing time are limited, emphasis must be given to minimizing the number of samples required to represent the signal completely. == Existing approaches == For a bandlimited waveform, there are infinitely many ways the signal can be sampled without producing aliases in the Fourier domain. But only two strategies are commonly used: rectangular sampling and hexagonal sampling. === Rectangular and Hexagonal sampling === In rectangular sampling, a 2-dimensional signal, for example, is sampled according to the following V matrix: V r e c t = [ T 1 0 0 T 2 ] {\displaystyle V_{rect}={\begin{bmatrix}T1&0\\0&T2\end{bmatrix}}} where T1 and T2 are the sampling periods along the horizontal and vertical direction respectively. In hexagonal sampling, the V matrix assumes the following general form: V h e x = [ T 1 T 1 − T 2 T 2 ] {\displaystyle V_{hex}={\begin{bmatrix}T1&T1\\-T2&T2\end{bmatrix}}} The difference in the efficiency of the two schemes is highlighted using a bandlimited signal with a circular region of support of radius R. The circle can be inscribed in a square of length 2R or a regular hexagon of length 2 R 3 {\displaystyle {\frac {2R}{\sqrt {3}}}} . Consequently, the region of support is now transformed into a square and a hexagon respectively. If these regions are periodically replicated in the frequency domain such that there is zero overlap between any two regions, then by periodically replicating the square region of support, we effectively sample the continuous signal on a rectangular lattice. Similarly periodic replication of the hexagonal region of support maps to sampling the continuous signal on a hexagonal lattice. From U, the periodicity matrix, we can calculate the optimal sampling density for both the rectangular and hexagonal schemes. It is found that in order to completely recover the circularly band-limited signal, the hexagonal sampling scheme requires 13.4% fewer samples than the rectangular sampling scheme. The reduction may appear to be of little significance for a 2-dimensional signal. But as the dimensionality of the signal increases, the efficiency of the hexagonal sampling scheme will become far more evident. For instance, the reduction achieved for an 8-dimensional signal is 93.8%. To highlight the importance of the obtained result [2], try and visualize an image as a collection of infinite number of samples. The primary entity responsible for vision, i.e. the photoreceptors (rods and cones) are present on the retina of all mammals. These cells are not arranged in rows and columns. By adapting a hexagonal sampling scheme, our eyes are able to process images much more efficiently. The importance of hexagonal sampling lies in the fact that the photoreceptors of the human vision system lie on a hexagonal sampling lattice and, thus, perform hexagonal sampling.[3] In fact, it can be shown that the hexagonal sampling scheme is the optimal sampling scheme for a circularly band-limited signal. == Applications == === Aliasing effects minimized by the use of optimal sampling grids === Recent advances in the CCD technology has made hexagonal sampling feasible for real life applications. Historically, because of technology constraints, detector arrays were implemented only on 2-dimensional rectangular sampling lattices with rectangular shape detectors. But the super [CCD] detector introduced by Fuji has an octagonal shaped pixel in a hexagonal grid. Theoretically, the performance of the detector was greatly increased by introducing an octagonal pixel. The number of pixels required to represent the sample was reduced and there was significant improvement in the Signal-to-Noise Ratio (SNR) when compared with that of a rectangular pixel. But the drawback of using hexagonal pixels is that the associated fill factor will be less than 82%. An alternative method would be to interpolate hexagonal pixels in such a manner that we ultimately end up with a rectangular grid. The Spot 5 satellite incorporates a
Feature engineering
Feature engineering is a preprocessing step in supervised machine learning and statistical modeling which transforms raw data into a more effective set of inputs. Each input comprises several attributes, known as features. By providing models with relevant information, feature engineering significantly enhances their predictive accuracy and decision-making capability. Beyond machine learning, the principles of feature engineering are applied in various scientific fields, including physics. For example, physicists construct dimensionless numbers such as the Reynolds number in fluid dynamics, the Nusselt number in heat transfer, and the Archimedes number in sedimentation. They also develop first approximations of solutions, such as analytical solutions for the strength of materials in mechanics. == Clustering == One of the applications of feature engineering has been clustering of feature-objects or sample-objects in a dataset. Especially, feature engineering based on matrix decomposition has been extensively used for data clustering under non-negativity constraints on the feature coefficients. These include Non-Negative Matrix Factorization (NMF), Non-Negative Matrix-Tri Factorization (NMTF), Non-Negative Tensor Decomposition/Factorization (NTF/NTD), etc. The non-negativity constraints on coefficients of the feature vectors mined by the above-stated algorithms yields a part-based representation, and different factor matrices exhibit natural clustering properties. Several extensions of the above-stated feature engineering methods have been reported in literature, including orthogonality-constrained factorization for hard clustering, and manifold learning to overcome inherent issues with these algorithms. Other classes of feature engineering algorithms include leveraging a common hidden structure across multiple inter-related datasets to obtain a consensus (common) clustering scheme. An example is Multi-view Classification based on Consensus Matrix Decomposition (MCMD), which mines a common clustering scheme across multiple datasets. MCMD is designed to output two types of class labels (scale-variant and scale-invariant clustering), and: is computationally robust to missing information, can obtain shape- and scale-based outliers, and can handle high-dimensional data effectively. Coupled matrix and tensor decompositions are popular in multi-view feature engineering. == Predictive modelling == Feature engineering in machine learning and statistical modeling involves selecting, creating, transforming, and extracting data features. Key components include feature creation from existing data, transforming and imputing missing or invalid features, reducing data dimensionality through methods like Principal Components Analysis (PCA), Independent Component Analysis (ICA), and Linear Discriminant Analysis (LDA), and selecting the most relevant features for model training based on importance scores and correlation matrices. Features vary in significance. Even relatively insignificant features may contribute to a model. Feature selection can reduce the number of features to prevent a model from becoming too specific to the training data set (overfitting). Feature explosion occurs when the number of identified features is too large for effective model estimation or optimization. Common causes include: Feature templates - implementing feature templates instead of coding new features Feature combinations - combinations that cannot be represented by a linear system Feature explosion can be limited via techniques such as regularization, kernel methods, and feature selection. == Automation == Automation of feature engineering is a research topic that dates back to the 1990s. Machine learning software that incorporates automated feature engineering has been commercially available since 2016. Related academic literature can be roughly separated into two types: Multi-relational Decision Tree Learning (MRDTL) uses a supervised algorithm that is similar to a decision tree. Deep Feature Synthesis uses simpler methods. === Multi-relational Decision Tree Learning (MRDTL) === Multi-relational Decision Tree Learning (MRDTL) extends traditional decision tree methods to relational databases, handling complex data relationships across tables. It innovatively uses selection graphs as decision nodes, refined systematically until a specific termination criterion is reached. Most MRDTL studies base implementations on relational databases, which results in many redundant operations. These redundancies can be reduced by using techniques such as tuple id propagation. === Open-source implementations === There are a number of open-source libraries and tools that automate feature engineering on relational data and time series: featuretools is a Python library for transforming time series and relational data into feature matrices for machine learning. MCMD: An open-source feature engineering algorithm for joint clustering of multiple datasets. OneBM or One-Button Machine combines feature transformations and feature selection on relational data with feature selection techniques. OneBM helps data scientists reduce data exploration time allowing them to try and error many ideas in short time. On the other hand, it enables non-experts, who are not familiar with data science, to quickly extract value from their data with a little effort, time, and cost. getML community is an open source tool for automated feature engineering on time series and relational data. It is implemented in C/C++ with a Python interface. It has been shown to be at least 60 times faster than tsflex, tsfresh, tsfel, featuretools or kats. tsfresh is a Python library for feature extraction on time series data. It evaluates the quality of the features using hypothesis testing. tsflex is an open source Python library for extracting features from time series data. Despite being 100% written in Python, it has been shown to be faster and more memory efficient than tsfresh, seglearn or tsfel. seglearn is an extension for multivariate, sequential time series data to the scikit-learn Python library. tsfel is a Python package for feature extraction on time series data. kats is a Python toolkit for analyzing time series data. === Deep feature synthesis === The deep feature synthesis (DFS) algorithm beat 615 of 906 human teams in a competition. == Feature stores == The feature store is where the features are stored and organized for the explicit purpose of being used to either train models (by data scientists) or make predictions (by applications that have a trained model). It is a central location where you can either create or update groups of features created from multiple different data sources, or create and update new datasets from those feature groups for training models or for use in applications that do not want to compute the features but just retrieve them when it needs them to make predictions. A feature store includes the ability to store code used to generate features, apply the code to raw data, and serve those features to models upon request. Useful capabilities include feature versioning and policies governing the circumstances under which features can be used. Feature stores can be standalone software tools or built into machine learning platforms. == Alternatives == Feature engineering can be a time-consuming and error-prone process, as it requires domain expertise and often involves trial and error. Deep learning algorithms may be used to process a large raw dataset without having to resort to feature engineering. However, deep learning algorithms still require careful preprocessing and cleaning of the input data. In addition, choosing the right architecture, hyperparameters, and optimization algorithm for a deep neural network can be a challenging and iterative process.
QANDA
QANDA (stands for 'Q and A') is an AI-based learning platform developed by Mathpresso Inc., a South Korea-based education technology company. Its best known feature is a solution search, which uses optical character recognition technology to scan problems and provide step-by-step solutions and learning content. As of March 2024, QANDA solved over 6.3 billion questions. QANDA has 90 million total registered users and has reached 8 million monthly active users (MAU) in 50 countries. 90% of the cumulative users are from overseas such as Vietnam and Indonesia. In January 2024, its MathGPT, a math-specific small large language model set a new world record, surpassed Microsoft's 'ToRA 13B', the previous record holder in benchmarks assessing mathematical performance such as 'MATH' (high school math) and 'GSM8K' (grade school math). 'MathGPT' was co-developed with Upstage and KT. In March 2024, Mathpresso launched 'Cramify' (formerly known as Prep.Pie), an AI-powered study material generator designed to create personalized exam prep materials for U.S. college students. It uses generative AI to create customized study materials uploaded by students. Its features include a range of tools including study summarizer and question solver. == History == Co-founder Jongheun ‘Ray’ Lee first came up with the idea of QANDA during his freshman year in college. While he was tutoring to earn money, Lee realized that the quality of education a student receives is greatly based on their location. Lee saw his K-12 students were regularly asking similar questions and realized that these questions were from a pre-selected number of textbooks currently being used in schools. He decided to team up with his high school friend, Yongjae ‘Jake’ Lee to build a platform whereby, one uses a mobile app to scan and submit questions, and students can ask and receive detailed responses. Lee's school friends, Wonguk Jung and Hojae Jeong, joined the team. In June 2015, Mathpresso, Inc. was founded in Seoul, South Korea. In January 2016, Mathpresso's first product QANDA was launched. It supported a Q&A feature between students and tutors. In October 2017, QANDA introduced an AI-based search capability that permitted users to search for answers in seconds. In April 2020, Jake Yongjae Lee(CEO & co-founder) and Ray Jongheun Lee (co-founder) were selected as Forbes 30 under 30 Asia. In June 2021, QANDA raised $50 million in series C funding. Jake Yongjae Lee was recognized as an Innovator Under 35 by MIT Technology Review. In November 2021, QANDA secured a strategic investment from Google. Since its inception, it has received backing in Series C funding from investors namely Google, Yellowdog, GGV Capital, Goodwater Capital, KDB, and SKS Private Equity with participation from SoftBank Ventures Asia, Legend Capital, Mirae Asset Venture Investment, and Smilegate Investment. In September 2023, Mathpresso has raised $8 million (10 billion KRW) from Korea's telecom giant, KT. The total cumulative investment is about 130 million US dollars. The partnership aims to accelerate the development of an education-specific Large Language Model. The company intends to incorporate the LLM model to fortify its AI tutor, which later will be integrated into the existing services: QANDA App, B2B & B2G Saas, and 1:1 online tutoring (QANDA Tutor). == Features == QANDA features OCR-based solution search, one-on-one Q&A tutoring, a study timer. In 2021, QANDA launched additional features, including the premium subscription model that offers unlimited “byte-sized” micro-video lectures and the community feature that enhances collaborative learning. In 2021, QANDA launched QANDA Tutor, a tablet-based 1:1 tutoring service and QANDA Study, a 1:N online school in Vietnam. In 2022, QANDA launched an exam prep feature that offers past exam materials from school via online. This feature is currently available in South Korea. In August 2023, QANDA launched a beta version of an LLM-powered AI Tutor. == Awards and recognition == Best Hidden Gems of 2017 by Google Playstore 2018 AWS AI Startup Challenge Award National representative for the Google AI for Social Good APAC, 2018 Best Self-Improvement Apps of 2018 by Google Playstore GSV Edtech 150 — the Most Transformational Growth Companies in Digital Learning Speaker at the Google App Summit, 2021 Selected as a prospect unicorn company by Korea Technology Finance Corporation in 2023 Winner of G20-DIA Global Pitching in 2023 2021, 2022, 2023 East Asia EdTech 150 by HolonIQ