AI Coding Kids

AI Coding Kids — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

Webull

Webull Corporation, often stylized as simply Webull, is a U.S.-based financial services holding company headquartered in St. Petersburg, Florida. It owns and operates the Webull electronic trading platform for self-directed retail investors. Depending on jurisdiction, the Webull platform offers trading in stocks, exchange-traded funds (ETFs), options, margin, bonds, cryptocurrency and futures, as well as market-data tools. Webull began operations in 2016 under Hunan Fumi Information Technology, a China-based financial technology company founded by Wang Anquan. It launched U.S. brokerage services through Webull Financial LLC in 2018 and expanded during the retail-trading boom of 2020 and 2021. In April 2025, Webull became a publicly traded company on the Nasdaq through a merger with special-purpose acquisition company SK Growth Opportunities Corporation. The company's U.S. brokerage revenue relies substantially on payment for order flow, with options trading accounting for the larger share of its order-flow rebates in 2025. Webull has faced regulatory actions related to options customer approvals, complaint handling, suspicious activity reporting, social-media marketing and customer disclosures. It has also faced scrutiny from U.S. lawmakers and state officials over its historical and operational ties to China and the handling of U.S. customer data. == History == === Founding === Webull was founded in 2016 under Hunan Fumi Information Technology, a China-based financial technology company, by Wang Anquan, a former employee of Alibaba Group and Xiaomi. Hunan Fumi Information Technology received backing from Xiaomi, Shunwei Capital, and other investors in China. Fumi Technology was a Hunan-based fintech start-up incubated by Xiaomi and raised about CNY200 million (approximately US$30 million) in a Series B financing round in 2018. On May 24, 2017, Webull Financial LLC was established as a Delaware limited liability company. It began offering brokerage services in the United States in May 2018. Wang hired Anthony Denier as CEO of the U.S. brokerage that year and the two mapped out their strategy on napkins at a Mexican restaurant in New York City. Webull Corporation was incorporated in the Cayman Islands in September 2019 as the group's holding company. === Retail trading boom === In May 2020, the company received SEC approval to launch a robo-advisor on its platform. By August 2020, the platform had over 11 million registered users, and in October 2020, it had 750,000 daily active users. Webull introduced options trading in 2020 and later added cryptocurrency trading through a separate digital-asset business. In November 2020, Webull began supporting cryptocurrency transactions. In December 2020, Webull launched trading services in Hong Kong. During the GameStop short squeeze in January 2021, Webull gained attention as some retail traders looked for alternatives to Robinhood. On January 27, 2021, Webull recorded its highest-ever number of active daily users, at 952,000, and the Webull app was downloaded across the Apple App and Google Play stores an estimated 100,000 times. That week, approximately 1.2 million people downloaded the Webull mobile app, which the company reported as a 1,548% week-over-week increase. On January 28, 2021, Webull was directed by its clearing house to temporarily halt buy orders for stocks affected by the GameStop short squeeze. In June 2021, Webull was reported to be considering a U.S. initial public offering that could raise up to $400 million. === Restructuring and expansion === Webull restructured its China-related corporate arrangements in 2022 and later stated that Hunan Fumi was no longer affiliated with the group. In 2022 and 2023, Webull expanded in several non-U.S. markets, including Singapore, Australia, South Africa, Japan, the United Kingdom and Indonesia. In June 2023, Webull moved cryptocurrency trading to a separate app called Webull Pay. By the end of 2023, Webull had 4.3 million funded accounts and US$8.2 billion in customer assets. In January 2024, Anthony Denier was promoted to group president of Webull Corporation. In November 2024, Webull launched overnight, or extended-hours, trading, expanding the trading window of U.S. stocks for users inside and outside the United States. === SPAC merger and Nasdaq listing === On February 28, 2024, Webull agreed to go public through a business combination with SK Growth Opportunities Corporation (NASDAQ: SKGR), a special-purpose acquisition company, in a deal that valued the company at approximately US$7.3 billion. The proposed valuation drew scrutiny because of Webull's limited financial disclosure at announcement, reliance on payment for order flow and small expected public float. SK Growth shareholders approved the business combination on March 30, 2025, and the transaction closed on April 10, 2025. Webull's Class A ordinary shares and warrants began trading on the Nasdaq on April 11, 2025 under the ticker symbols BULL and BULLW (incentive warrants traded under BULLZ until their redemption in June 2025). The merger brought Webull to the public market but generated little cash for the company: after shareholder redemptions, Webull disclosed net proceeds of US$430,066 from the transaction. After the listing, Webull's shares experienced extreme volatility, rising as much as 500% to US$79.56 on April 14, 2025, after closing at US$13.25 on the prior trading day. The initial post-listing surge increased the value of Webull holdings owned by earlier investors, including RIT Capital Partners, which had first invested in Webull in 2021. In April 2026, after Webull's shares had fallen about 70% over the previous year, the company authorized a US$100 million share repurchase program. == Business model and financials == Webull provides a self-directed electronic trading platform available through mobile, desktop and web applications. Depending on jurisdiction, the platform offers trading in stocks, exchange-traded funds, options, margin, futures, fixed income products, cryptocurrency, cash management features and market data tools. In the United States, Webull Financial LLC is a registered broker-dealer and member of FINRA and the Securities Investor Protection Corporation, while Webull operates in other markets through locally licensed brokerage subsidiaries. Webull operates a commission-free or low-cost brokerage model for self-directed retail investors. In the United States, a substantial part of its trading-related revenue comes from payment for order flow, while in some non-U.S. markets the company more commonly charges commissions directly to customers. The platform is aimed at more active retail investors, including users seeking options tools, extended-hours trading and real-time market data. For 2025, Webull reported total revenue of US$571.0 million, up from US$390.2 million in 2024. Equity and option order-flow rebates accounted for US$304.1 million, or 53.3% of revenue, making order-flow rebates the company's largest reported revenue category. Interest-related income accounted for US$154.3 million, handling charge income for US$87.3 million and other revenue for US$25.3 million. Options were the larger component of the company's order-flow rebates in 2025, generating US$210.0 million compared with US$94.2 million from equities. Webull also generates revenue from interest-related activities, including margin financing, customer bank deposits, stock lending and corporate bank deposits. The company has stated that its interest-related income is affected by interest rates, customer cash balances, margin balances and demand for stock lending. The company had approximately 20 million registered users worldwide as of February 2024. As of December 31, 2025, it reported 26.8 million registered users, 5.0 million funded accounts and US$24.6 billion in customer assets. As of March 2025, Webull operated in Hong Kong, Singapore, Australia, South Africa, Japan, the United Kingdom, the United States, Indonesia, Canada, Brazil, Thailand, Malaysia and Mexico. == Marketing and sponsorships == Webull has used paid digital advertising, referral incentives, free-stock promotions, affiliate marketing and sports sponsorships to acquire customers and promote its brand. In its 2025 annual filing, the company reported marketing and branding expenses of US$152.3 million in 2023, US$138.7 million in 2024 and US$135.9 million in 2025. Webull said most of its advertising and promotion costs were related to paid search and paid social advertising, and that it had reduced free-stock promotions while shifting toward deposit- and asset-transfer-based incentives. In September 2021, BSE Global, the parent company of the Brooklyn Nets and New York Liberty, entered into a global multi-year agreement with Webull. Under the agreement, Webull became an official sponsor and online brokerage partner of the teams, with branding that included a jersey patch on Brooklyn Nets uniforms. Spo
Read more →
Top 10 AI Video Editors Compared (2026)

Looking for the best AI video editor? An AI video editor is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI video editor slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
Read more →
Leo Breiman

Leo Breiman (January 27, 1928 – July 5, 2005) was an American statistician at the University of California, Berkeley and a member of the United States National Academy of Sciences. Breiman's work helped to bridge the gap between statistics and computer science, particularly in the field of machine learning. His most important contributions were his work on classification and regression trees and ensembles of trees fit to bootstrap samples. Bootstrap aggregation was given the name bagging by Breiman. Another of Breiman's ensemble approaches is the random forest.
Read more →
Unsupervised learning

Unsupervised learning is a framework in machine learning where, in contrast to supervised learning, algorithms learn patterns exclusively from unlabeled data. Other frameworks in the spectrum of supervisions include weak- or semi-supervision, where a small portion of the data is tagged, and self-supervision. Some researchers consider self-supervised learning a form of unsupervised learning. Conceptually, unsupervised learning divides into the aspects of data, training, algorithm, and downstream applications. Typically, the dataset is harvested cheaply "in the wild", such as massive text corpus obtained by web crawling, with only minor filtering (such as Common Crawl). This compares favorably to supervised learning, where the dataset (such as the ImageNet1000) is typically constructed manually, which is much more expensive. There are algorithms designed specifically for unsupervised learning, such as clustering algorithms like k-means, dimensionality reduction techniques like principal component analysis (PCA), Boltzmann machine learning, and autoencoders. After the rise of deep learning, most large-scale unsupervised learning has been done by training general-purpose neural network architectures by gradient descent, adapted to performing unsupervised learning by designing an appropriate training procedure. Sometimes a trained model can be used as-is, but more often they are modified for downstream applications. For example, the generative pretraining method trains a model to generate a textual dataset, before finetuning it for other applications, such as text classification. As another example, autoencoders are trained to produce good features, which can then be used as a module for other models, such as in a latent diffusion model. == Tasks == Tasks are often categorized as discriminative (recognition) or generative (imagination). Often but not always, discriminative tasks use supervised methods and generative tasks use unsupervised (see Venn diagram); however, the separation is very hazy. For example, object recognition favors supervised learning but unsupervised learning can also cluster objects into groups. Furthermore, as progress marches onward, some tasks employ both methods, and some tasks swing from one to another. For example, image recognition started off as heavily supervised, but became hybrid by employing unsupervised pre-training, and then moved towards supervision again with the advent of dropout, ReLU, and adaptive learning rates. A typical generative task is as follows. At each step, a datapoint is sampled from the dataset, and part of the data is removed, and the model must infer the removed part. This is particularly clear for the denoising autoencoders and BERT. == Neural network architectures == === Training === During the learning phase, an unsupervised network tries to mimic the data it is given and uses the error in its mimicked output to correct itself (i.e. correct its weights and biases). Sometimes the error is expressed as a low probability that the erroneous output occurs, or it might be expressed as an unstable high energy state in the network. In contrast to supervised methods' dominant use of backpropagation, unsupervised learning also employs other methods including: Hopfield learning rule, Boltzmann learning rule, Contrastive Divergence, Wake Sleep, Variational Inference, Maximum Likelihood, Maximum A Posteriori, Gibbs Sampling, and backpropagating reconstruction errors or hidden state reparameterizations. See the table below for more details. === Energy === An energy function is a macroscopic measure of a network's activation state. In Boltzmann machines, it plays the role of the Cost function. This analogy with physics is inspired by Ludwig Boltzmann's analysis of a gas' macroscopic energy from the microscopic probabilities of particle motion p ∝ e − E / k T {\displaystyle p\propto e^{-E/kT}} , where k is the Boltzmann constant and T is temperature. In the RBM network the relation is p = e − E / Z {\displaystyle p=e^{-E}/Z} , where p {\displaystyle p} and E {\displaystyle E} vary over every possible activation pattern and Z = ∑ All Patterns e − E ( pattern ) {\displaystyle \textstyle {Z=\sum _{\scriptscriptstyle {\text{All Patterns}}}e^{-E({\text{pattern}})}}} . To be more precise, p ( a ) = e − E ( a ) / Z {\displaystyle p(a)=e^{-E(a)}/Z} , where a {\displaystyle a} is an activation pattern of all neurons (visible and hidden). Hence, some early neural networks bear the name Boltzmann Machine. Paul Smolensky calls − E {\displaystyle -E\,} the Harmony. A network seeks low energy which is high Harmony. === Networks === This table shows connection diagrams of various unsupervised networks, the details of which will be given in the section Comparison of Networks. Circles are neurons and edges between them are connection weights. As network design changes, features are added on to enable new capabilities or removed to make learning faster. For instance, neurons change between deterministic (Hopfield) and stochastic (Boltzmann) to allow robust output, weights are removed within a layer (RBM) to hasten learning, or connections are allowed to become asymmetric (Helmholtz). Of the networks bearing people's names, only Hopfield worked directly with neural networks. Boltzmann and Helmholtz came before artificial neural networks, but their work in physics and physiology inspired the analytical methods that were used. === History === === Specific Networks === Here, we highlight some characteristics of select networks. The details of each are given in the comparison table below. Hopfield Network Ferromagnetism inspired Hopfield networks. A neuron corresponds to an iron domain with binary magnetic moments Up and Down, and neural connections correspond to the domain's influence on each other. Symmetric connections enable a global energy formulation. During inference the network updates each state using the standard activation step function. Symmetric weights and the right energy functions guarantees convergence to a stable activation pattern. Asymmetric weights are difficult to analyze. Hopfield nets are used as Content Addressable Memories (CAM). Boltzmann Machine These are stochastic Hopfield nets. Their state value is sampled from this pdf as follows: suppose a binary neuron fires with the Bernoulli probability p(1) = 1/3 and rests with p(0) = 2/3. One samples from it by taking a uniformly distributed random number y, and plugging it into the inverted cumulative distribution function, which in this case is the step function thresholded at 2/3. The inverse function = { 0 if x <= 2/3, 1 if x > 2/3 }. Sigmoid Belief Net Introduced by Radford Neal in 1992, this network applies ideas from probabilistic graphical models to neural networks. A key difference is that nodes in graphical models have pre-assigned meanings, whereas Belief Net neurons' features are determined after training. The network is a sparsely connected directed acyclic graph composed of binary stochastic neurons. The learning rule comes from Maximum Likelihood on p(X): Δwij ∝ {\displaystyle \propto } sj (si - pi), where pi = 1 / ( 1 + eweighted inputs into neuron i ). sj's are activations from an unbiased sample of the posterior distribution and this is problematic due to the Explaining Away problem raised by Judea Perl. Variational Bayesian methods uses a surrogate posterior and blatantly disregard this complexity. Deep Belief Network Introduced by Hinton, this network is a hybrid of RBM and Sigmoid Belief Network. The top 2 layers is an RBM and the second layer downwards form a sigmoid belief network. One trains it by the stacked RBM method and then throw away the recognition weights below the top RBM. As of 2009, 3-4 layers seems to be the optimal depth. Helmholtz machine These are early inspirations for the Variational Auto Encoders. Its 2 networks combined into one—forward weights operates recognition and backward weights implements imagination. It is perhaps the first network to do both. Helmholtz did not work in machine learning but he inspired the view of "statistical inference engine whose function is to infer probable causes of sensory input". the stochastic binary neuron outputs a probability that its state is 0 or 1. The data input is normally not considered a layer, but in the Helmholtz machine generation mode, the data layer receives input from the middle layer and has separate weights for this purpose, so it is considered a layer. Hence this network has 3 layers. Variational autoencoder These are inspired by Helmholtz machines and combines probability network with neural networks. An Autoencoder is a 3-layer CAM network, where the middle layer is supposed to be some internal representation of input patterns. The encoder neural network is a probability distribution qφ(z given x) and the decoder network is pθ(x given z). The weights are named phi & theta rather than W and V as in Helmholtz—a cosmetic difference. These 2 networks h
Read more →
Starlight Information Visualization System

Starlight is a software product originally developed at Pacific Northwest National Laboratory and now by Future Point Systems. It is an advanced visual analysis environment. In addition to using information visualization to show the importance of individual pieces of data by showing how they relate to one another, it also contains a small suite of tools useful for collaboration and data sharing, as well as data conversion, processing, augmentation and loading. The software, originally developed for the intelligence community, allows users to load data from XML files, databases, RSS feeds, web services, HTML files, Microsoft Word, PowerPoint, Excel, CSV, Adobe PDF, TXT files, etc. and analyze it with a variety of visualizations and tools. The system integrates structured, unstructured, geospatial, and multimedia data, offering comparisons of information at multiple levels of abstraction, simultaneously and in near real-time. In addition Starlight allows users to build their own named entity-extractors using a combination of algorithms, targeted normalization lists and regular expressions in the Starlight Data Engineer (SDE). As an example, Starlight might be used to look for correlations in a database containing records about chemical spills. An analyst could begin by grouping records according to the cause of the spill to reveal general trends. Sorting the data a second time, they could apply different colors based on related details such as the company responsible, age of equipment or geographic location. Maps and photographs could be integrated into the display, making it even easier to recognize connections among multiple variables. Starlight has been deployed to both the Iraq and Afghanistan wars and used on a number of large-scale projects. PNNL began developing Starlight in the mid-1990s, with funding from the Land Information Warfare Agency, a part of the Army Intelligence and Security Command and continued developed at the laboratory with funding from the NSA and the CIA. Starlight integrates visual representations of reports, radio transcripts, radar signals, maps and other information. The software system was recently honored with an R&D 100 Award for technical innovation. In 2006 Future Point Systems, a Silicon Valley startup, acquired rights to jointly develop and distribute the Starlight product in cooperation with the Pacific Northwest National Laboratory. The software is now also used outside of the military/intelligence communities in a number of commercial environments.
Read more →
Top 10 AI Clip Makers Compared (2026)

Comparing the best AI clip maker? An AI clip maker is software that uses machine learning to help you get more done — it lowers the barrier so anyone can produce professional output. Privacy matters too: check whether your data trains the model and whether a no-log or enterprise tier is available. Whether you are a beginner or a pro, the right AI clip maker slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.
Read more →
AI Paraphrasing Tools: Free vs Paid (2026)

In search of the best AI paraphrasing tool? An AI paraphrasing tool is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI paraphrasing tool slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.
Read more →
Vector quantization

Vector quantization (VQ) is a classical quantization technique from signal processing that allows the modeling of probability density functions by the distribution of prototype vectors. Developed in the early 1980s by Robert M. Gray, it was originally used for data compression. It works by dividing a large set of points (vectors) into groups having approximately the same number of points closest to them. Each group is represented by its centroid point, as in k-means and some other clustering algorithms. In simpler terms, vector quantization chooses a set of points to represent a larger set of points. The density matching property of vector quantization is powerful, especially for identifying the density of large and high-dimensional data. Since data points are represented by the index of their closest centroid, commonly occurring data have low error, and rare data high error. This is why VQ is suitable for lossy data compression. It can also be used for lossy data correction and density estimation. Vector quantization is based on the competitive learning paradigm, so it is closely related to the self-organizing map model and to sparse coding models used in deep learning algorithms such as autoencoder. == Training == One simple training algorithm for vector quantization is: Pick a sample point at random Move the nearest quantization vector centroid towards this sample point, by a small fraction of the distance Repeat A more sophisticated algorithm reduces the bias in the density matching estimation and ensures that all points are used, by including an extra sensitivity parameter: Increase each centroid's sensitivity s i {\displaystyle s_{i}} by a small amount Pick a sample point P {\displaystyle P} at random For each quantization vector centroid c i {\displaystyle c_{i}} , let d ( P , c i ) {\displaystyle d(P,c_{i})} denote the distance of P {\displaystyle P} and c i {\displaystyle c_{i}} Find the centroid c i {\displaystyle c_{i}} for which d ( P , c i ) − s i {\displaystyle d(P,c_{i})-s_{i}} is the smallest Move c i {\displaystyle c_{i}} towards P {\displaystyle P} by a small fraction of the distance Set s i {\displaystyle s_{i}} to zero Repeat It is desirable to use a cooling schedule to produce convergence: see Simulated annealing. Another simple method is LBG, which is based on k-means. The algorithm can be iteratively updated with "live" data, rather than by picking random points from a data set, but this will introduce some bias if the data are temporally correlated over many samples. == Applications == Vector quantization is used for lossy data compression, lossy data correction, pattern recognition, density estimation and clustering. Lossy data correction, or prediction, is used to recover data missing from some dimensions. It is done by finding the nearest group with the data dimensions available, then predicting the result based on the values for the missing dimensions, assuming that they will have the same value as the group's centroid. For density estimation, the area/volume that is closer to a particular centroid than to any other is inversely proportional to the density (due to the density matching property of the algorithm). === Use in data compression === Vector quantization, also called "block quantization" or "pattern matching quantization" is often used in lossy data compression. It works by encoding values from a multidimensional vector space into a finite set of values from a discrete subspace of lower dimension. A lower-space vector requires less storage space, so the data is compressed. Due to the density matching property of vector quantization, the compressed data has errors that are inversely proportional to density. The transformation is usually done by projection or by using a codebook. In some cases, a codebook can be also used to entropy code the discrete value in the same step, by generating a prefix coded variable-length encoded value as its output. The set of discrete amplitude levels is quantized jointly rather than each sample being quantized separately. Consider a k-dimensional vector [ x 1 , x 2 , . . . , x k ] {\displaystyle [x_{1},x_{2},...,x_{k}]} of amplitude levels. It is compressed by choosing the nearest matching vector from a set of n-dimensional vectors [ y 1 , y 2 , . . . , y n ] {\displaystyle [y_{1},y_{2},...,y_{n}]} , with n < k. All possible combinations of the n-dimensional vector [ y 1 , y 2 , . . . , y n ] {\displaystyle [y_{1},y_{2},...,y_{n}]} form the vector space to which all the quantized vectors belong. Only the index of the codeword in the codebook is sent instead of the quantized values. This conserves space and achieves more compression. Twin vector quantization (VQF) is part of the MPEG-4 standard dealing with time domain weighted interleaved vector quantization. === Video codecs based on vector quantization === Bink video Cinepak Daala is transform-based but uses pyramid vector quantization on transformed coefficients Digital Video Interactive: Production-Level Video and Real-Time Video Indeo Microsoft Video 1 QuickTime: Apple Video (RPZA) and Graphics Codec (SMC) Sorenson SVQ1 and SVQ3 Smacker video VQA format, used in many games The usage of video codecs based on vector quantization has declined significantly in favor of those based on motion compensated prediction combined with transform coding, e.g. those defined in MPEG standards, as the low decoding complexity of vector quantization has become less relevant. === Audio codecs based on vector quantization === AMR-WB+ CELP CELT (now part of Opus) is transform-based but uses pyramid vector quantization on transformed coefficients Codec 2 DTS G.729 iLBC Ogg Vorbis TwinVQ === Use in pattern recognition === VQ was also used in the eighties for speech and speaker recognition. Recently it has also been used for efficient nearest neighbor search and on-line signature recognition. In pattern recognition applications, one codebook is constructed for each class (each class being a user in biometric applications) using acoustic vectors of this user. In the testing phase the quantization distortion of a testing signal is worked out with the whole set of codebooks obtained in the training phase. The codebook that provides the smallest vector quantization distortion indicates the identified user. The main advantage of VQ in pattern recognition is its low computational burden when compared with other techniques such as dynamic time warping (DTW) and hidden Markov model (HMM). The main drawback when compared to DTW and HMM is that it does not take into account the temporal evolution of the signals (speech, signature, etc.) because all the vectors are mixed up. In order to overcome this problem a multi-section codebook approach has been proposed. The multi-section approach consists of modelling the signal with several sections (for instance, one codebook for the initial part, another one for the center and a last codebook for the ending part). === Use as clustering algorithm === As VQ is seeking for centroids as density points of nearby lying samples, it can be also directly used as a prototype-based clustering method: each centroid is then associated with one prototype. By aiming to minimize the expected squared quantization error and introducing a decreasing learning gain fulfilling the Robbins-Monro conditions, multiple iterations over the whole data set with a concrete but fixed number of prototypes converges to the solution of k-means clustering algorithm in an incremental manner. === Generative adversarial networks (GAN) === VQ has been used to quantize a feature representation layer in the discriminator of generative adversarial networks. The feature quantization (FQ) technique performs implicit feature matching. It improves the GAN training, and yields an improved performance on a variety of popular GAN models: BigGAN for image generation, StyleGAN for face synthesis, and U-GAT-IT for unsupervised image-to-image translation.
Read more →
Eigenface

An eigenface ( EYE-gən-) is the name given to a set of eigenvectors when used in the computer vision problem of human face recognition. The approach of using eigenfaces for recognition was developed by Sirovich and Kirby and used by Matthew Turk and Alex Pentland in face classification. The eigenvectors are derived from the covariance matrix of the probability distribution over the high-dimensional vector space of face images. The eigenfaces themselves form a basis set of all images used to construct the covariance matrix. This produces dimension reduction by allowing the smaller set of basis images to represent the original training images. Classification can be achieved by comparing how faces are represented by the basis set. == History == The eigenface approach began with a search for a low-dimensional representation of face images. Sirovich and Kirby showed that principal component analysis could be used on a collection of face images to form a set of basis features. These basis images, known as eigenpictures, could be linearly combined to reconstruct images in the original training set. If the training set consists of M images, principal component analysis could form a basis set of N images, where N < M. The reconstruction error is reduced by increasing the number of eigenpictures; however, the number needed is always chosen less than M. For example, if you need to generate a number of N eigenfaces for a training set of M face images, you can say that each face image can be made up of "proportions" of all the K "features" or eigenfaces: Face image1 = (23% of E1) + (2% of E2) + (51% of E3) + ... + (1% En). In 1991 M. Turk and A. Pentland expanded these results and presented the eigenface method of face recognition. In addition to designing a system for automated face recognition using eigenfaces, they showed a way of calculating the eigenvectors of a covariance matrix such that computers of the time could perform eigen-decomposition on a large number of face images. Face images usually occupy a high-dimensional space and conventional principal component analysis was intractable on such data sets. Turk and Pentland's paper demonstrated ways to extract the eigenvectors based on matrices sized by the number of images rather than the number of pixels. Once established, the eigenface method was expanded to include methods of preprocessing to improve accuracy. Multiple manifold approaches were also used to build sets of eigenfaces for different subjects and different features, such as the eyes. == Generation == A set of eigenfaces can be generated by performing a mathematical process called principal component analysis (PCA) on a large set of images depicting different human faces. Informally, eigenfaces can be considered a set of "standardized face ingredients", derived from statistical analysis of many pictures of faces. Any human face can be considered to be a combination of these standard faces. For example, one's face might be composed of the average face plus 10% from eigenface 1, 55% from eigenface 2, and even −3% from eigenface 3. Remarkably, it does not take many eigenfaces combined together to achieve a fair approximation of most faces. Also, because a person's face is not recorded by a digital photograph, but instead as just a list of values (one value for each eigenface in the database used), much less space is taken for each person's face. The eigenfaces that are created will appear as light and dark areas that are arranged in a specific pattern. This pattern is how different features of a face are singled out to be evaluated and scored. There will be a pattern to evaluate symmetry, whether there is any style of facial hair, where the hairline is, or an evaluation of the size of the nose or mouth. Other eigenfaces have patterns that are less simple to identify, and the image of the eigenface may look very little like a face. The technique used in creating eigenfaces and using them for recognition is also used outside of face recognition: handwriting recognition, lip reading, voice recognition, sign language/hand gestures interpretation and medical imaging analysis. Therefore, some do not use the term eigenface, but prefer to use 'eigenimage'. === Practical implementation === To create a set of eigenfaces, one must: Prepare a training set of face images. The pictures constituting the training set should have been taken under the same lighting conditions, and must be normalized to have the eyes and mouths aligned across all images. They must also be all resampled to a common pixel resolution (r × c). Each image is treated as one vector, simply by concatenating the rows of pixels in the original image, resulting in a single column with r × c elements. For this implementation, it is assumed that all images of the training set are stored in a single matrix T, where each column of the matrix is an image. Subtract the mean. The average image a has to be calculated and then subtracted from each original image in T. Calculate the eigenvectors and eigenvalues of the covariance matrix S. Each eigenvector has the same dimensionality (number of components) as the original images, and thus can itself be seen as an image. The eigenvectors of this covariance matrix are therefore called eigenfaces. They are the directions in which the images differ from the mean image. Usually this will be a computationally expensive step (if at all possible), but the practical applicability of eigenfaces stems from the possibility to compute the eigenvectors of S efficiently, without ever computing S explicitly, as detailed below. Choose the principal components. Sort the eigenvalues in descending order and arrange eigenvectors accordingly. The number of principal components k is determined arbitrarily by setting a threshold ε on the total variance. Total variance ⁠ v = ( λ 1 + λ 2 + . . . + λ n ) {\displaystyle v=(\lambda _{1}+\lambda _{2}+...+\lambda _{n})} ⁠, n = number of components, and λ {\displaystyle \lambda } represents component eigenvalue. k is the smallest number that satisfies ( λ 1 + λ 2 + . . . + λ k ) v > ϵ {\displaystyle {\frac {(\lambda _{1}+\lambda _{2}+...+\lambda _{k})}{v}}>\epsilon } These eigenfaces can now be used to represent both existing and new faces: we can project a new (mean-subtracted) image on the eigenfaces and thereby record how that new face differs from the mean face. The eigenvalues associated with each eigenface represent how much the images in the training set vary from the mean image in that direction. Information is lost by projecting the image on a subset of the eigenvectors, but losses are minimized by keeping those eigenfaces with the largest eigenvalues. For instance, working with a 100 × 100 image will produce 10,000 eigenvectors. In practical applications, most faces can typically be identified using a projection on between 100 and 150 eigenfaces, so that most of the 10,000 eigenvectors can be discarded. === Matlab example code === Here is an example of calculating eigenfaces with Extended Yale Face Database B. To evade computational and storage bottleneck, the face images are sampled down by a factor 4×4=16. Note that although the covariance matrix S generates many eigenfaces, only a fraction of those are needed to represent the majority of the faces. For example, to represent 95% of the total variation of all face images, only the first 43 eigenfaces are needed. To calculate this result, implement the following code: === Computing the eigenvectors === Performing PCA directly on the covariance matrix of the images is often computationally infeasible. If small images are used, say 100 × 100 pixels, each image is a point in a 10,000-dimensional space and the covariance matrix S is a matrix of 10,000 × 10,000 = 108 elements. However the rank of the covariance matrix is limited by the number of training examples: if there are N training examples, there will be at most N − 1 eigenvectors with non-zero eigenvalues. If the number of training examples is smaller than the dimensionality of the images, the principal components can be computed more easily as follows. Let T be the matrix of preprocessed training examples, where each column contains one mean-subtracted image. The covariance matrix can then be computed as S = TTT and the eigenvector decomposition of S is given by S v i = T T T v i = λ i v i {\displaystyle \mathbf {Sv} _{i}=\mathbf {T} \mathbf {T} ^{T}\mathbf {v} _{i}=\lambda _{i}\mathbf {v} _{i}} However TTT is a large matrix, and if instead we take the eigenvalue decomposition of T T T u i = λ i u i {\displaystyle \mathbf {T} ^{T}\mathbf {T} \mathbf {u} _{i}=\lambda _{i}\mathbf {u} _{i}} then we notice that by pre-multiplying both sides of the equation with T, we obtain T T T T u i = λ i T u i {\displaystyle \mathbf {T} \mathbf {T} ^{T}\mathbf {T} \mathbf {u} _{i}=\lambda _{i}\mathbf {T} \mathbf {u} _{i}} Meaning that, if ui is an eigenvector of TTT, then vi = Tui is an eigenvector of S. If we have
Read more →
AI Video Generators: Free vs Paid (2026)

In search of the best AI video generator? An AI video generator is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI video generator slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.
Read more →
RAMnets

RAMnets is one of the oldest practical neurally inspired classification algorithms. The RAMnets is also known as a type of "n-tuple recognition method" or "weightless neural network". == Algorithm == Consider (let us say N) sets of n distinct bit locations are selected randomly. These are the n-tuples. The restriction of a pattern to an n-tuple can be regarded as an n-bit number which, together with the identity of the n-tuple, constitutes a `feature' of the pattern. The standard n-tuple recognizer operates simply as follows: A pattern is classified as belonging to the class for which it has the most features in common with at least one training pattern of that class. This is the Θ {\displaystyle \Theta } = 0 case of a more general rule whereby the class assigned to unclassified pattern u is a c r g m a x ( ∑ i = 1 N Θ ( ∑ v ∈ D c δ ( α i ( u ) , α i ( v ) ) ) ) {\displaystyle {\begin{aligned}{\underset {c}{a}}rgmax(\sum _{i=1}^{N}\Theta (\sum _{v\in D_{c}}\delta (\alpha _{i}(u),\alpha _{i}(v))))\end{aligned}}} where Dc is the set of training patterns in class c, Θ ( x ) {\displaystyle \Theta (x)} = x for 0 ≤ x ≤ θ {\displaystyle 0\leq x\leq \theta } , Θ ( x ) = θ {\displaystyle \Theta (x)=\theta } for x ≥ θ {\displaystyle x\geq \theta } , δ i , j {\displaystyle \delta _{i,j}} is the Kronecker delta( δ i , j {\displaystyle \delta _{i,j}} =1 if i=j and 0 otherwise.)and ( α i ( u ) ) {\displaystyle (\alpha _{i}(u))} is the ith feature of the pattern u: ∑ j = 0 n − 1 u η i ( j ) 2 j {\displaystyle \sum _{j=0}^{n-1}u_{\eta }i(j)2^{j}} Here uk is the kth bit of u and u η i ( j ) {\displaystyle u_{\eta }i(j)} is the jth bit location of the ith n-tuple. With C classes to distinguish, the system can be implemented as a network of NC nodes, each of which is a random access memory (RAM); hence the term RAMnet. The memory content m c i α {\displaystyle m_{ci\alpha }} at address α {\displaystyle \alpha } of the ith node allocated to class c is set to m c i α {\displaystyle m_{ci\alpha }} = Θ ( ∑ v ∈ D c δ ( α , α i ( v ) ) ) {\displaystyle \Theta (\sum _{v\in D_{c}}\delta (\alpha ,\alpha _{i}(v)))} In the usual θ {\displaystyle \theta } = 1 case, the 1-bit content of m c i α {\displaystyle m_{ci\alpha }} is set if any pattern of Dc has feature α {\displaystyle \alpha } and unset otherwise. Recognition is accomplished by summing the contents of the nodes of each class at the addresses given by the features of the unclassified pattern. That is, pattern u is assigned to class a c r g m a x ( ∑ i = 1 N m c i α ( u ) ) {\displaystyle {\begin{aligned}{\underset {c}{a}}rgmax(\sum _{i=1}^{N}m_{ci\alpha }(u))\end{aligned}}} == RAM-discriminators and WiSARD == The RAMnets formed the basis of a commercial product known as WiSARD (Wilkie, Stonham and Aleksander Recognition Device) was the first artificial neural network machine to be patented. A RAM-discriminator consists of a set of X one-bit word RAMs with n inputs and a summing device (Σ). Any such RAM-discriminator can receive a binary pattern of X⋅n bits as input. The RAM input lines are connected to the input pattern by means of a biunivocal pseudo-random mapping. The summing device enables this network of RAMs to exhibit – just like other ANN models based on synaptic weights – generalization and noise tolerance. In order to train the discriminator one has to set all RAM memory locations to 0 and choose a training set formed by binary patterns of X⋅n bits. For each training pattern, a 1 is stored in the memory location of each RAM addressed by this input pattern. Once the training of patterns is completed, RAM memory contents will be set to a certain number of 0's and 1's. The information stored by the RAM during the training phase is used to deal with previous unseen patterns. When one of these is given as input, the RAM memory contents addressed by the input pattern are read and summed by Σ. The number r thus obtained, which is called the discriminator response, is equal to the number of RAMs that output 1. r reaches the maximum X if the input belongs to the training set. r is equal to 0 if no n-bit component of the input pattern appears in the training set (not a single RAM outputs 1). Intermediate values of r express a kind of “similarity measure” of the input pattern with respect to the patterns in the training set. A system formed by various RAM-discriminators is called WiSARD. Each RAM-discriminator is trained on a particular class of patterns, and classification by the multi-discriminator system is performed in the following way. When a pattern is given as input, each RAM-discriminator gives a response to that input. The various responses are evaluated by an algorithm which compares them and computes the relative confidence c of the highest response (e.g., the difference d between the highest response and the second highest response, divided by the highest response). A schematic representation of a RAM-discriminator and a 10 RAM-discriminator WiSARD is shown in Figure 1.
Read more →
Interactive machine translation

Interactive machine translation (IMT), is a specific sub-field of computer-aided translation. Under this translation paradigm, the computer software that assists the human translator attempts to predict the text the user is going to input by taking into account all the information it has available. Whenever such prediction is wrong and the user provides feedback to the system, a new prediction is performed considering the new information available. Such process is repeated until the translation provided matches the user's expectations. Interactive machine translation is specially interesting when translating texts in domains where it is not admissible to output a translation containing errors, hence requiring a human user to amend the translations provided by the system. In such cases, interactive machine translation has been proved to provide benefit to potential users. Nevertheless, there are few commercial software that implements interactive machine translation and work done in the field is mostly restrained to academic research. == History == Historically, interactive machine translation is born as an evolution of the computer-aided translation paradigm, where the human translator and the machine translation system were intended to work as a tandem. This first work was extended within the TransType research project, funded by the Canadian government. In this project, the human interaction was aimed towards producing the target text for the first time by embedding data-driven machine translation techniques within the interactive translation environment with the goal of achieving the best of both actors: the efficiency of the automatic system and the reliability of human translators. Later, a larger-scale research project, TransType2, funded by the European Commission extended such work by analyzing the incorporation of a complete machine translation system into the process, with the goal of producing a complete translation hypothesis, which the human user is allowed to amend or accept. If the user decides to amend the hypothesis, the system then attempts to make the best use of such feedback in order to produce a new translation hypothesis that takes into account the modifications introduced by the user. More recently, CASMACAT, also funded by the European Commission, aimed at developing novel types of assistance to human translators and integrated them into a new workbench, consisting of an editor, a server, and analysis and visualisation tools. The workbench was designed in a modular fashion and can be combined with existing computer aided translation tools. Furthermore, the CASMACAT workbench can learn from the interaction with the human translator by updating and adapting its models instantly based on the translation choices of the user. Recent work on involving an extensive evaluation with human users revealed the fact that interactive machine translation may even be used by users that do not speak the source language in order to achieve near professional translation quality. Moreover, it also elucidated the fact that an interactive scenario is more beneficial than a classic post-edition scenario. The previously described approaches rely on a tightly coupled underlying corpus-based machine translation system (usually, a Statistical machine translation system) that is used as a glass box, therefore inheriting the shortcomings of the translation systems and limiting the usage of interactive machine translation for some scenarios. For this reason, an approach that uses any kind of bilingual resource (not limited to machine translation) as a black-box to provide interactive machine translation was developed. This approach is not able to extract as much information from the bilingual resources used, due to the black-box nature of the interaction, but can use any resource available to the user. Forecat is a black-box interactive machine translation implementation that is available both as a web application (that includes a webpage and a web services interface) and as a plugin for OmegaT (Forecat-OmegaT). == Process == The interactive machine translation process starts with the system suggesting a translation hypothesis to the user. Then, the user may accept the complete sentence as correct, or may modify it if he considers there is some error. Typically, when modifying a given word, it is assumed that the prefix until that word is correct, leading to a left-to-right interaction scheme. Once the user has changed the word considered incorrect, the system then proposes a new suffix, i.e. the remainder of the sentence. Such process continues until the translation provided satisfies the user. Although explained at the word level, the previous process may also be implemented at the character level, and hence the system provides a suffix whenever the human translator types in a single character. In addition, there is ongoing effort towards changing the typical left-to-right interaction scheme in order to make human-machine interaction easier. A similar approach is used in the Caitra translation tool. == Evaluation == Evaluation is a difficult issue in interactive machine translation. Ideally, evaluation should take place in experiments involving human users. However, given the high monetary cost this would imply, this is seldom the case. Moreover, even when considering human translators in order to perform a true evaluation of interactive machine translation techniques, it is not clear what should be measured in such experiments, since there are many different variables that should be taken into account and cannot be controlled, as is for instance the time the user takes in order to get used to the process. In the CASMACAT project, some field trials have been carried out to study some of these variables. For quick evaluations in laboratory conditions, interactive machine translation is measured by using the key stroke ratio or the word stroke ratio. Such criteria attempt to measure how many key-strokes or words did the user need to introduce before producing the final translated document. == Differences with classical computer-aided translation == Although interactive machine translation is a sub-field of computer-aided translation, the main attractive of the former with respect to the latter is the interactivity. In classical computer-aided translation, the translation system may suggest one translation hypothesis in the best case, and then the user is required to post-edit such hypothesis. In contrast, in interactive machine translation the system produces a new translation hypothesis each time the user interacts with the system, i.e. after each word (or letter) has been introduced.
Read more →
List of security-focused operating systems

This is a list of operating systems specifically focused on security. Similar concepts include security-evaluated operating systems that have achieved certification from an auditing organization, and trusted operating systems that provide sufficient support for multilevel security and evidence of correctness to meet a particular set of requirements. == Linux == === Android-based === GrapheneOS is a security-focused, Android-based mobile OS that uses a hardened kernel, C library, custom memory allocator (hardened_malloc), and a hardened Chromium-based browser named Vanadium. It also offers privacy/security features, such as Duress PIN/Password or disabling the USB-C port at a driver/hardware level to avoid exploitation. It deploys exploit mitigations such as hardware-based memory tagging, secure app spawning, restricted dynamic code loading, and more. === Debian-based === Linux Kodachi is a security-focused operating system. Tails is aimed at preserving privacy and anonymity. KickSecure is a security-focused Linux distribution that aims to be "hardened by default". It uses network hardening, kernel hardening, Strong Linux User Account Isolation, better randomness, root access restrictions, and app-specific hardening. Whonix is an anonymity focused operating system based on KickSecure. It consists of two virtual machines, And all communications are routed through Tor. === Other Linux distributions === Alpine Linux is designed to be small, simple, and secure. It uses musl, BusyBox, and OpenRC instead of the more commonly used glibc, GNU Core Utilities, and systemd. Owl - Openwall GNU/Linux, a security-enhanced Linux distribution for servers. Secureblue, a Fedora Silverblue based distro that uses a hardened kernel, custom memory allocator (hardened_malloc), Trivalent, a security-focused, Chromium-based browser inspired by Vanadium, and many other exploit mitigations. == BSD == OpenBSD is a Unix-like operating system that emphasizes portability, standardization, correctness, proactive security, and integrated cryptography. == Xen == Qubes OS aims to provide security through isolation. Isolation is provided through the use of virtualization technology. This allows the segmentation of applications into secure virtual machines.
Read more →
Top 10 AI Logo Makers Compared (2026)

In search of the best AI logo maker? An AI logo maker is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI logo maker slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.
Read more →
Brendan Frey

Brendan John Frey FRSC (born 29 August 1968) is a Canadian computer scientist, entrepreneur, and engineer. He is Founder and CEO of Deep Genomics, Cofounder of the Vector Institute for Artificial Intelligence and Professor of Engineering and Medicine at the University of Toronto. Frey is a pioneer in the development of machine learning and artificial intelligence methods, their use in accurately determining the consequences of genetic mutations, and in designing medications that can slow, stop or reverse the progression of disease. As far back as 1995, Frey co-invented one of the first deep learning methods, called the wake-sleep algorithm, the affinity propagation algorithm for clustering and data summarization, and the factor graph notation for probability models. In the late 1990s, Frey was a leading researcher in the areas of computer vision, speech recognition, and digital communications. == Education == Frey studied computer engineering and physics at the University of Calgary (BSc 1990) and the University of Manitoba (MSc 1993), and then studied neural networks and graphical models as a doctoral candidate at the University of Toronto under the supervision of Geoffrey Hinton (PhD 1997). He was an invited participant of the Machine Learning program at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK (1997) and was a Beckman Fellow at the University of Illinois at Urbana Champaign (1999). == Career == Following his undergraduate studies, Frey worked as a junior research scientist at Bell-Northern Research from 1990 to 1991. After completing his postdoctoral studies at the University of Illinois at Urbana-Champaign, Frey was an assistant professor in the Department of Computer Science at the University of Waterloo, from 1999 to 2001. In 2001, Frey joined the Department of Electrical and Computer Engineering at the University of Toronto and was cross-appointed to the Department of Computer Science, the Banting and Best Department of Medical Research and the Terrence Donnelly Centre for Cellular and Biomolecular Research. From 2008 to 2009, he was a visiting researcher at Microsoft Research (Cambridge, UK) and a visiting professor in the Cavendish Laboratories and Darwin College at Cambridge University. Between 2001 and 2014, Frey consulted for several groups at Microsoft Research and acted as a member of its Technical Advisory Board. In 2002, a personal crisis led Frey to face the fact that there was a tragic gap between our ability to measure a patient's mutations and our ability to understand and treat the consequences. Recognizing that biology is too complex for humans to understand, that in the decades to come there would be an exponential growth in biology data, and that machine learning is the best technology we have for discovering relationships in large datasets, Frey set out to build machine learning systems that could accurately predict genome and cell biology. Frey’s group pioneered much of the early work in the field and over the next 15 years published more papers in leading-edge journals than any other academic or industrial research lab. In 2015, Frey founded Deep Genomics, with the goal of building a company that can produce effective and safe genetic medicines more rapidly and with a higher rate of success than was previously possible. The company has received 240 million dollars in funding to date from leading Bay Area investors, including the backers of SpaceX and Tesla.
Read more →