Spatial anti-aliasing

Spatial anti-aliasing

In digital signal processing, spatial anti-aliasing is a technique for minimizing the distortion artifacts (aliasing) when representing a high-resolution image at a lower resolution. Anti-aliasing is used in digital photography, computer graphics, digital audio, and many other applications. Anti-aliasing means removing signal components that have a higher frequency than is able to be properly resolved by the recording (or sampling) device. This removal is done before (re)sampling at a lower resolution. When sampling is performed without removing this part of the signal, it causes undesirable artifacts such as black-and-white noise. In signal acquisition and audio, anti-aliasing is often done using an analog anti-aliasing filter to remove the out-of-band component of the input signal prior to sampling with an analog-to-digital converter. In digital photography, optical anti-aliasing filters made of birefringent materials smooth the signal in the spatial optical domain. The anti-aliasing filter essentially blurs the image slightly in order to reduce the resolution to or below that achievable by the digital sensor (the larger the pixel pitch, the lower the achievable resolution at the sensor level). == Examples == In computer graphics, anti-aliasing improves the appearance of "jagged" polygon edges, or "jaggies", so they are smoothed out on the screen. However, it incurs a performance cost for the graphics card and uses more video memory. The level of anti-aliasing determines how smooth polygon edges are (and how much video memory it consumes). Near the top of an image with a receding checker-board pattern, the image is difficult to recognise and often not considered aesthetically pleasing. In contrast, when anti-aliased the checker-board near the top blends into grey, which is usually the desired effect when the resolution is insufficient to show the detail. Even near the bottom of the image, the edges appear much smoother in the anti-aliased image. Multiple methods exist, including the sinc filter, which is considered a better anti-aliasing algorithm. When magnified, it can be seen how anti-aliasing interpolates the brightness of the pixels at the boundaries to produce grey pixels since the space is occupied by both black and white tiles. These help make the sinc filter antialiased image appear much smoother than the original. In a simple diamond image, anti-aliasing blends the boundary pixels; this reduces the aesthetically jarring effect of the sharp, step-like boundaries that appear in the aliased graphic. Anti-aliasing is often applied in rendering text on a computer screen, to suggest smooth contours that better emulate the appearance of text produced by conventional ink-and-paper printing. Particularly with fonts displayed on typical LCD screens, it is common to use subpixel rendering techniques like ClearType. Sub-pixel rendering requires special colour-balanced anti-aliasing filters to turn what would be severe colour distortion into barely-noticeable colour fringes. Equivalent results can be had by making individual sub-pixels addressable as if they were full pixels, and supplying a hardware-based anti-aliasing filter as is done in the OLPC XO-1 laptop's display controller. Pixel geometry affects all of this, whether the anti-aliasing and sub-pixel addressing are done in software or hardware. == Simplest approach to anti-aliasing == The most basic approach to anti-aliasing a pixel is determining what percentage of the pixel is occupied by a given region in the vector graphic - in this case a pixel-sized square, possibly transposed over several pixels - and using that percentage as the colour. A Python program producing a basic plot of a single, white-on-black anti-aliased point using the method is as follows: This method is generally best suited for simple graphics, such as basic lines or curves, and applications that would otherwise have to convert absolute coordinates to pixel-constrained coordinates, such as 3D graphics. It is a fairly fast function, but it is relatively low-quality, and gets slower as the complexity of the shape increases. For purposes requiring very high-quality graphics or very complex vector shapes, this will probably not be the best approach. Note: The plot_antialiased_point routine above cannot blindly set the colour value to the percent calculated. It must add the new value to the existing value at that location up to a maximum of 1. Otherwise, the brightness of each pixel will be equal to the darkest value calculated in time for that location which produces a very bad result. For example, if one point sets a brightness level of 0.90 for a given pixel and another point calculated later barely touches that pixel and has a brightness of 0.05, the final value set for that pixel should be 0.95, not 0.05. For more sophisticated shapes, the algorithm may be generalized as rendering the shape to a pixel grid with higher resolution than the target display surface (usually a multiple that is a power of 2 to reduce distortion), then using bicubic interpolation to determine the average intensity of each real pixel on the display surface. == Signal processing approach to anti-aliasing == In this approach, the ideal image is regarded as a signal. The image displayed on the screen is taken as samples, at each (x,y) pixel position, of a filtered version of the signal. Ideally, one would understand how the human brain would process the original signal, and provide an on-screen image that will yield the most similar response by the brain. The most widely accepted analytic tool for such problems is the Fourier transform; this decomposes a signal into basis functions of different frequencies, known as frequency components, and gives us the amplitude of each frequency component in the signal. The waves are of the form: cos ⁡ ( 2 j π x ) cos ⁡ ( 2 k π y ) {\displaystyle \ \cos(2j\pi x)\cos(2k\pi y)} where j and k are arbitrary non-negative integers. There are also frequency components involving the sine functions in one or both dimensions, but for the purpose of this discussion, the cosine will suffice. The numbers j and k together are the frequency of the component: j is the frequency in the x direction, and k is the frequency in the y direction. The goal of an anti-aliasing filter is to greatly reduce frequencies above a certain limit, known as the Nyquist frequency, so that the signal will be accurately represented by its samples, or nearly so, in accordance with the sampling theorem; there are many different choices of detailed algorithm, with different filter transfer functions. Current knowledge of human visual perception is not sufficient, in general, to say what approach will look best. == Two dimensional considerations == The previous discussion assumes that the rectangular mesh sampling is the dominant part of the problem. The filter usually considered optimal is not rotationally symmetrical, as shown in this first figure; this is because the data is sampled on a square lattice, not using a continuous image. This sampling pattern is the justification for doing signal processing along each axis, as it is traditionally done on one dimensional data. Lanczos resampling is based on convolution of the data with a discrete representation of the sinc function. If the resolution is not limited by the rectangular sampling rate of either the source or target image, then one should ideally use rotationally symmetrical filter or interpolation functions, as though the data were a two dimensional function of continuous x and y. The sinc function of the radius has too long a tail to make a good filter (it is not even square-integrable). A more appropriate analog to the one-dimensional sinc is the two-dimensional Airy disc amplitude, the 2D Fourier transform of a circular region in 2D frequency space, as opposed to a square region. One might consider a Gaussian plus enough of its second derivative to flatten the top (in the frequency domain) or sharpen it up (in the spatial domain), as shown. Functions based on the Gaussian function are natural choices, because convolution with a Gaussian gives another Gaussian whether applied to x and y or to the radius. Similarly to wavelets, another of its properties is that it is halfway between being localized in the configuration (x and y) and in the spectral (j and k) representation. As an interpolation function, a Gaussian alone seems too spread out to preserve the maximum possible detail, and thus the second derivative is added. As an example, when printing a photographic negative with plentiful processing capability and on a printer with a hexagonal pattern, there is no reason to use sinc function interpolation. Such interpolation would treat diagonal lines differently from horizontal and vertical lines, which is like a weak form of aliasing. == Practical real-time anti-aliasing approximations == There are only a handful of primitives used at the lowest level in a real-time rend

I Am Rich

I Am Rich is a discontinued 2008 mobile app for iPhones which had minimal function and was priced at US$999.99 (equivalent to $1,495 in 2025). The app was pulled from the App Store less than 24 hours after its launch. Receiving negative reviews from critics, only eight copies were sold. In the years since, several similar applications have been released at lower prices. == Overview == I Am Rich was developed as a joke by German software developer, Armin Heinrich, after he saw iPhone users complaining about software priced above $0.99. The app only showed a glowing red gem and an icon that, when pressed, displayed the following mantra in large text: I am richI deserv [sic] itI am good,healthy & successful Heinrich told The New York Times that "I regard it as art. I did not expect many people to buy it and did not expect all the fuss about it." The application is described as "a work of art with no hidden function at all", with its only purpose being to show other people that they were able to afford it. Vox writer Zachary Crockett called it "the ultimate Veblen good in app form". == Release == Heinrich released and distributed I Am Rich through the App Store on 5 August 2008. The app was sold for US$999.99 (equivalent to $1,495 in 2025), €799.99 (equivalent to €1,078 in 2023), and £599.99 (equivalent to £978.12 in 2025)—the highest prices Apple allowed for App Store content. Without explanation, the application was removed from the App Store by Apple less than a day after its release. === Purchases === Eight people bought the application, at least one of whom claimed to have done so accidentally. Six US sales and two European sales netted $5,600 for Heinrich and $2,400 for Apple (respectively equivalent to $8,374 and $3,589 in 2025). In correspondence with the Los Angeles Times, Heinrich told the newspaper that Apple had refunded two purchasers of his app, and that he was happy to not have dissatisfied customers. == Reception == Discussing the app on the website Silicon Alley Insider, Dan Frommer described the program as a "scam", "worthless", and finally "a joke that smells like a scammy rip-off" on August 5, 6, and 8, respectively. Without purchasing the app, Fox News's Paul Wagenseil guessed that the secret mantra was "German for 'Sucker!'" (Heinrich is German). Wired's Brian X. Chen described I Am Rich as a waste of money to "prove you're a jerk", and contrasted the expenditure with donating to cancer foundations and Third World countries. Heinrich told the Los Angeles Times's Mark Milian that he had received correspondence from satisfied customers: "I've got e-mails from customers telling me that they really love the app [... and that they had] no trouble spending the money". In an interview with The New York Times, though, he told of receiving many insulting emails and telephone messages. == Similar applications == The next year, Heinrich released I Am Rich LE. Priced at US$9.99 (equivalent to $14.99 in 2025), the new app has several new features (including a calculator, "help system", and the "famous mantra without the spelling mistakes") to meet Apple's requirement that apps have "definable content". Some customers were disappointed by the new functionality, poorly rating the app due to its ostensible improvements. On 23 February 2009, CNET Asia reported on the "conceptually similar" app, I Am Richer, developed by Mike DG for Google's Android. The app was released on the Android Market for US$200 (equivalent to $300.14 in 2025), a limit imposed by Google, who had no objection to the application. With the same name, the I Am Rich that was released on the Windows Phone Marketplace on 22 December 2010, was developed by DotNetNuzzi. Described by MobileCrunch as equally useless as the original, this app cost US$499.99 (equivalent to $738.2 in 2025), the price cap imposed by Microsoft.

Lexalytics

Lexalytics, Inc. provides sentiment and intent analysis to an array of companies using SaaS and cloud based technology. Salience 6, the engine behind Lexalytics, was built as an on-premises, multi-lingual text analysis engine. It is leased to other companies who use it to power filtering and reputation management programs. In July, 2015 Lexalytics acquired Semantria to be used as a cloud option for its technology. In September, 2021 Lexalytics was acquired by CX company InMoment. == History == Lexalytics spun into existence in January 2003 out of a content management startup called Lightspeed. Lightspeed consolidated on America's West Coast. Jeff Catlin, a Lightspeed General Manager, and Mike Marshall, a Lighstpeed Principal Engineer, convinced investors to give them the East Coast company so as to avoid shutdown costs. Catlin and Marshall renamed the operation Lexalytics. Catlin took on the role of chief executive officer with Marshall working as Chief Technology Officer. Lexalytics opted to not accept venture cash. Instead, the company initially shared sales and marketing expenses with U.K. based document management company Infonic. The partner companies soon formed a joint venture in July 2008, which was later dissolved. Since then, Lexalytics has worked with many other companies, like Bottlenose, Salesforce, Thomson Reuters, Oracle and DataSift. Relationships with social media monitoring companies like Datasift tend to find Lexalytics’ Salience engine baked into the product itself. Lexalytics is used similarly to monitor sentiment as it relates to stock trading. In December 2014, Lexalytics announced the latest iteration to its sentiment analysis engine, Salience 6. Earlier that year Lexalytics acquired Semantria in a bid to appeal to a wider variety of business models. Created by former Lexalytics Marketing Director Oleg Rogynskyy, Semantria is a SaaS text mining service offered as an API and Excel based plugin that measures sentiment. The goal of the acquisition, which cost Lexalytics less than US$10 million, was to expand the customer base both within the United States and abroad with multilingual support. The engine that powers Semantria, Salience, is grounded in its deep learning ability. An example of this is its concept matrix, which allows Salience an understanding of concepts and relationship between concepts based on a detailed reading of the entire repository of Wikipedia. This matrix allows Salience to use Wikipedia for automatic categorization. Along with features like the concept matrix, Salience supports 16 international languages. The engine has earned Lexalytics a spot on EContent's “Top 100 Companies in the Digital Content Industry” List for 2014–2015. In September 2018, Lexalytics launched document data extraction market using natural language processing (NLP).

SmarterChild

SmarterChild was a chatbot available on AOL Instant Messenger and Windows Live Messenger (previously MSN Messenger) networks. == History == SmarterChild was an apparently intelligent agent or "bot" developed by ActiveBuddy, Inc., with offices in New York and Sunnyvale. It was widely distributed across global instant messaging networks. SmarterChild became very popular, attracting over 30 million Instant Messenger "buddies" on AIM (AOL), MSN and Yahoo Messenger over the course of its lifetime. Founded in 2000, ActiveBuddy was the brainchild of Robert Hoffer and Timothy Kay, who later brought seasoned advertising executive Peter Levitan on board as CEO. The concept for conversational instant messaging bots came from the founder's vision to add natural language comprehension functionality to the increasingly popular AIM instant messaging application. The original implementation took shape as a demo that Kay programmed in Perl in his Los Altos garage to connect a single buddy name, "ActiveBuddy", to look up stock symbols, and later allow AIM users to play Colossal Cave Adventure, a word-based adventure game, and MIT's Boris Katz Start Question Answering System but quickly grew to include a wide range of database applications the company called 'knowledge domains' including instant access to news, weather, stock information, movie times, yellow pages listings, and detailed sports data, as well as a variety of tools (personal assistant, calculators, translator, etc.). None of the individual domains which the company had named “stocksBuddy”, “sportsBuddy”, etc. ever launched publicly. When Stephen Klein came on board as COO — and eventually CEO — he insisted that all of the disparate test “buddies” be launched together with the company’s highly-developed colloquial chat domain. He suggested using “SmarterChild”, a username coined by Tim Kay which Tim was using to test various things. The bundled domains were launched publicly as SmarterChild (on AIM initially) in June 2001. SmarterChild provided information wrapped in fun and quirky conversation. The company generated no revenue from SmarterChild, but used it as a demonstration of the power of what Klein called “conversational computing”. The company subsequently marketed Automated Service Agents—delivering immediate answers to customer service inquiries—-to large corporations, like Comcast, Cingular, TimeWarner Cable, etc. SmarterChild's popularity spawned targeted marketing-oriented bots for Radiohead, Austin Powers, Intel, Keebler, The Sporting News and others. ActiveBuddy co-founders, Kay and Hoffer, as co-inventors, were issued two controversial U.S. patents in 2002. ActiveBuddy changed its name to Colloquis (briefly Conversagent) and targeted development of consumer-facing enterprise customer service agents, which the company marketed as Automated Service Agents. Microsoft acquired Colloquis in October 2006 and proceeded to de-commission SmarterChild and kill off the Automated Service Agent business as well. Robert Hoffer, ActiveBuddy co-founder, licensed the technology from Microsoft after Microsoft abandoned the Colloquis technology.

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

Clapper (service)

Clapper is an American short-form video-hosting service headquartered in Dallas, Texas. It was founded in 2020 by Edison Chen as an alternative for TikTok for mature audiences. The app is functionally similar to TikTok and includes tipping and e-commerce features. Following an influx of far-right content in early 2021, Clapper strengthened its moderation practices. It achieved 2 million monthly active users by 2023, and the number of downloads increased after a U.S. bill that would potentially ban TikTok in the country was signed in 2024. == History == With its offices in Dallas, Texas, Clapper was founded in July 2020 by Chinese-American entrepreneur Edison Chen. Chen considered that most online platforms, such as TikTok, were being targeted to young generations, such as Generation Z. He then concepted Clapper as a service with short-form content for mature audiences among Generation X and millennials, while not intending to compete directly with TikTok. Clapper averaged fewer than ten thousand daily active users during 2020, reaching 500 thousand downloads in the next year. Initially without paying for external advertising, the company raised about $3 million during a 2021 seed funding round. In 2023, the app reportedly reached about 300 to 400 thousand daily active users and 2 million monthly active users. The average user was between the ages of 35 and 55. Following the April 2024 signing of the Protecting Americans from Foreign Adversary Controlled Applications Act, which would potentially enact a ban on TikTok in the U.S. in January 2025, Clapper averaged 200 thousand weekly downloads. In 2025, before the day scheduled for the ban (January 19), TikTok users migrated to other apps. As a result, Clapper received 1.4 million new downloads in a week preceding the date. It was listed as the third most-downloaded free app on Apple's App Store on January 14, behind Xiaohongshu and Lemon8, and the term "TikTok refugee" became a trending term. == Features == Clapper presents similarities with TikTok in its layout, including "Following" and "For You" tabs with videos up to three minutes long that can be liked, commented on or shared. A "Clapback" feature allows users to create responses to videos from others. Users can create livestreams and chat rooms in the app. Users can tip Clapper creators through its Clapper Fam monetization feature, in place of in-app advertisements. The Clapper Shop allows for e-commerce between users. The service had distributed $10 million to its users in total by 2023, according to Clapper CEO Chen. == Content == Clapper includes a policy requiring users to be at least 17 years of age, although Clapper CEO Chen described that "there is no adult content" on the platform. Lindsay Dodgson of Business Insider described the content as generally outdated and "reminiscent of 'getting owned' compilations of the earlier internet." The Washington Post's Tatum Hunter characterized Clapper as including sexual or engagement baiting content more prevalently than TikTok. === Moderation === Clapper's team, which had fifteen employees in early 2021, initially stated it would not moderate content as strictly as TikTok and would mostly rely on user reports. Following that year's January 6 United States Capitol attack, far-right conservative videos promoting QAnon and anti-vaccine conspiracy theories appeared on Clapper's "For You" page to a substantial degree for weeks. The videos were made in protest against decisions by platforms, particularly TikTok, to ban such content. Clapper's team stated in January 10 that its rules prohibiting incitements to violence would be strictly enforced. By February, videos and accounts promoting the conspiracy theories had been removed, and QAnon-related content was banned permanently. Clapper's team hired more content auditors and implemented moderation by artificial intelligence for further community guideline violations.

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