In machine learning, a linear classifier makes a classification decision for each object based on a linear combination of its features. A simpler definition is to say that a linear classifier is one whose decision boundaries are linear. Such classifiers work well for practical problems such as document classification, and more generally for problems with many variables (features), reaching accuracy levels comparable to non-linear classifiers while taking less time to train and use. == Definition == If the input feature vector to the classifier is a real vector x → {\displaystyle {\vec {x}}} , then the output score is y = f ( w → ⋅ x → ) = f ( ∑ j w j x j ) , {\displaystyle y=f({\vec {w}}\cdot {\vec {x}})=f\left(\sum _{j}w_{j}x_{j}\right),} where w → {\displaystyle {\vec {w}}} is a real vector of weights and f is a function that converts the dot product of the two vectors into the desired output. (In other words, w → {\displaystyle {\vec {w}}} is a one-form or linear functional mapping x → {\displaystyle {\vec {x}}} onto R.) The weight vector w → {\displaystyle {\vec {w}}} is learned from a set of labeled training samples. Often f is a threshold function, which maps all values of w → ⋅ x → {\displaystyle {\vec {w}}\cdot {\vec {x}}} above a certain threshold to the first class and all other values to the second class; e.g., f ( x ) = { 1 if w T ⋅ x > θ , 0 otherwise {\displaystyle f(\mathbf {x} )={\begin{cases}1&{\text{if }}\ \mathbf {w} ^{T}\cdot \mathbf {x} >\theta ,\\0&{\text{otherwise}}\end{cases}}} The superscript T indicates the transpose and θ {\displaystyle \theta } is a scalar threshold. A more complex f might give the probability that an item belongs to a certain class. For a two-class classification problem, one can visualize the operation of a linear classifier as splitting a high-dimensional input space with a hyperplane: all points on one side of the hyperplane are classified as "yes", while the others are classified as "no". A linear classifier is often used in situations where the speed of classification is an issue, since it is often the fastest classifier, especially when x → {\displaystyle {\vec {x}}} is sparse. Also, linear classifiers often work very well when the number of dimensions in x → {\displaystyle {\vec {x}}} is large, as in document classification, where each element in x → {\displaystyle {\vec {x}}} is typically the number of occurrences of a word in a document (see document-term matrix). In such cases, the classifier should be well-regularized. == Generative models vs. discriminative models == There are two broad classes of methods for determining the parameters of a linear classifier w → {\displaystyle {\vec {w}}} . They can be generative and discriminative models. Methods of the former model joint probability distribution, whereas methods of the latter model conditional density functions P ( c l a s s | x → ) {\displaystyle P({\rm {class}}|{\vec {x}})} . Examples of such algorithms include: Linear Discriminant Analysis (LDA)—assumes Gaussian conditional density models Naive Bayes classifier with multinomial or multivariate Bernoulli event models. The second set of methods includes discriminative models, which attempt to maximize the quality of the output on a training set. Additional terms in the training cost function can easily perform regularization of the final model. Examples of discriminative training of linear classifiers include: Logistic regression—maximum likelihood estimation of w → {\displaystyle {\vec {w}}} assuming that the observed training set was generated by a binomial model that depends on the output of the classifier. Perceptron—an algorithm that attempts to fix all errors encountered in the training set Fisher's Linear Discriminant Analysis—an algorithm (different than "LDA") that maximizes the ratio of between-class scatter to within-class scatter, without any other assumptions. It is in essence a method of dimensionality reduction for binary classification. Support vector machine—an algorithm that maximizes the margin between the decision hyperplane and the examples in the training set. Note: Despite its name, LDA does not belong to the class of discriminative models in this taxonomy. However, its name makes sense when we compare LDA to the other main linear dimensionality reduction algorithm: principal components analysis (PCA). LDA is a supervised learning algorithm that utilizes the labels of the data, while PCA is an unsupervised learning algorithm that ignores the labels. To summarize, the name is a historical artifact. Discriminative training often yields higher accuracy than modeling the conditional density functions. However, handling missing data is often easier with conditional density models. All of the linear classifier algorithms listed above can be converted into non-linear algorithms operating on a different input space φ ( x → ) {\displaystyle \varphi ({\vec {x}})} , using the kernel trick. === Discriminative training === Discriminative training of linear classifiers usually proceeds in a supervised way, by means of an optimization algorithm that is given a training set with desired outputs and a loss function that measures the discrepancy between the classifier's outputs and the desired outputs. Thus, the learning algorithm solves an optimization problem of the form arg min w R ( w ) + C ∑ i = 1 N L ( y i , w T x i ) {\displaystyle {\underset {\mathbf {w} }{\arg \min }}\;R(\mathbf {w} )+C\sum _{i=1}^{N}L(y_{i},\mathbf {w} ^{\mathsf {T}}\mathbf {x} _{i})} where w is a vector of classifier parameters, L(yi, wTxi) is a loss function that measures the discrepancy between the classifier's prediction and the true output yi for the i'th training example, R(w) is a regularization function that prevents the parameters from getting too large (causing overfitting), and C is a scalar constant (set by the user of the learning algorithm) that controls the balance between the regularization and the loss function. Popular loss functions include the hinge loss (for linear SVMs) and the log loss (for linear logistic regression). If the regularization function R is convex, then the above is a convex problem. Many algorithms exist for solving such problems; popular ones for linear classification include (stochastic) gradient descent, L-BFGS, coordinate descent and Newton methods.
Projection-slice theorem
In mathematics, the projection-slice theorem, central slice theorem or Fourier slice theorem in two dimensions states that the results of the following two calculations are equal: Take a two-dimensional function f(r), project (e.g. using the Radon transform) it onto a (one-dimensional) line, and do a Fourier transform of that projection. Take that same function, but do a two-dimensional Fourier transform first, and then slice the function through its origin, parallel to the projection line. In operator terms, if F1 and F2 are the 1- and 2-dimensional Fourier transform operators mentioned above, P1 is the projection operator (which projects a 2-D function onto a 1-D line), S1 is a slice operator (which extracts a 1-D central slice from a function), then F 1 P 1 = S 1 F 2 . {\displaystyle F_{1}P_{1}=S_{1}F_{2}.} This idea can be extended to higher dimensions. This theorem is used, for example, in the analysis of medical CT scans where a "projection" is an x-ray image of an internal organ. The Fourier transforms of these images are seen to be slices through the Fourier transform of the 3-dimensional density of the internal organ, and these slices can be interpolated to build up a complete Fourier transform of that density. The inverse Fourier transform is then used to recover the 3-dimensional density of the object. This technique was first derived by Ronald N. Bracewell in 1956 for a radio-astronomy problem. == The projection-slice theorem in N dimensions == In N dimensions, the projection-slice theorem states that the Fourier transform of the projection of an N-dimensional function f(r) onto an m-dimensional linear submanifold is equal to an m-dimensional slice of the N-dimensional Fourier transform of that function consisting of an m-dimensional linear submanifold through the origin in the Fourier space which is parallel to the projection submanifold. In operator terms: F m P m = S m F N . {\displaystyle F_{m}P_{m}=S_{m}F_{N}.\,} == The generalized Fourier-slice theorem == In addition to generalizing to N dimensions, the projection-slice theorem can be further generalized with an arbitrary change of basis. For convenience of notation, we consider the change of basis to be represented as B, an N-by-N invertible matrix operating on N-dimensional column vectors. Then the generalized Fourier-slice theorem can be stated as F m P m B = S m B − T | B − T | F N {\displaystyle F_{m}P_{m}B=S_{m}{\frac {B^{-T}}{|B^{-T}|}}F_{N}} where B − T = ( B − 1 ) T {\displaystyle B^{-T}=(B^{-1})^{T}} is the transpose of the inverse of the change of basis transform. == Proof in two dimensions == The projection-slice theorem is easily proven for the case of two dimensions. Without loss of generality, we can take the projection line to be the x-axis. There is no loss of generality because if we use a shifted and rotated line, the law still applies. Using a shifted line (in y) gives the same projection and therefore the same 1D Fourier transform results. The rotated function is the Fourier pair of the rotated Fourier transform, for which the theorem again holds. If f(x, y) is a two-dimensional function, then the projection of f(x, y) onto the x axis is p(x) where p ( x ) = ∫ − ∞ ∞ f ( x , y ) d y . {\displaystyle p(x)=\int _{-\infty }^{\infty }f(x,y)\,dy.} The Fourier transform of f ( x , y ) {\displaystyle f(x,y)} is F ( k x , k y ) = ∫ − ∞ ∞ ∫ − ∞ ∞ f ( x , y ) e − 2 π i ( x k x + y k y ) d x d y . {\displaystyle F(k_{x},k_{y})=\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }f(x,y)\,e^{-2\pi i(xk_{x}+yk_{y})}\,dxdy.} The slice is then s ( k x ) {\displaystyle s(k_{x})} s ( k x ) = F ( k x , 0 ) = ∫ − ∞ ∞ ∫ − ∞ ∞ f ( x , y ) e − 2 π i x k x d x d y {\displaystyle s(k_{x})=F(k_{x},0)=\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }f(x,y)\,e^{-2\pi ixk_{x}}\,dxdy} = ∫ − ∞ ∞ [ ∫ − ∞ ∞ f ( x , y ) d y ] e − 2 π i x k x d x {\displaystyle =\int _{-\infty }^{\infty }\left[\int _{-\infty }^{\infty }f(x,y)\,dy\right]\,e^{-2\pi ixk_{x}}dx} = ∫ − ∞ ∞ p ( x ) e − 2 π i x k x d x {\displaystyle =\int _{-\infty }^{\infty }p(x)\,e^{-2\pi ixk_{x}}dx} which is just the Fourier transform of p(x). The proof for higher dimensions is easily generalized from the above example. == The FHA cycle == If the two-dimensional function f(r) is circularly symmetric, it may be represented as f(r), where r = |r|. In this case the projection onto any projection line will be the Abel transform of f(r). The two-dimensional Fourier transform of f(r) will be a circularly symmetric function given by the zeroth-order Hankel transform of f(r), which will therefore also represent any slice through the origin. The projection-slice theorem then states that the Fourier transform of the projection equals the slice or F 1 A 1 = H , {\displaystyle F_{1}A_{1}=H,} where A1 represents the Abel-transform operator, projecting a two-dimensional circularly symmetric function onto a one-dimensional line, F1 represents the 1-D Fourier-transform operator, and H represents the zeroth-order Hankel-transform operator. == Extension to fan beam or cone-beam CT == The projection-slice theorem is suitable for CT image reconstruction with parallel beam projections. It does not directly apply to fanbeam or conebeam CT. The theorem was extended to fan-beam and conebeam CT image reconstruction by Shuang-ren Zhao in 1995.
Awwwards
Awwwards (Awwwards Online SL) is an organization that hosts web design competitions and conferences across Europe and the United States. Website owners and developers can participate by submitting their websites for review. Submissions are assessed by a jury, and top entries are presented and awarded prizes on a rotational basis. == Nomination process == Web designers submit their websites through Awwwards' platform for consideration for the Site of the Day. A jury, composed of industry professionals, and the Awwwards community evaluate the entries. The best daily sites are published annually in "The 365 Best Websites Around the World" book. == Jury == The jury consists of international designers, developers, and agencies who assess the creativity, technical skills, and insight of the submitted web projects. The panel's expertise ensures a comprehensive review process. === Developer Award === Awwwards, in partnership with Microsoft, created the Developer Award to recognize web developers who demonstrate excellence in creating websites that meet modern standards. The award highlights websites that work seamlessly across various platforms and devices, using best practices in HTML5, JavaScript, and CSS. == Annual winners == Some prominent Site of the Year winners include Mercedes-Benz, Bloomberg L.P., Bose Corporation, Warner Brothers, Volkswagen, Uber, and Google. == Awwwards conference == Awwwards also organizes two-day conferences featuring speakers from major tech companies and industry leaders such as Microsoft, Google, Spotify, Adobe, Opera, and Smashing Magazine. These events focus on the latest trends in web design and development. Speakers at Awwwards conferences have included notable figures in the design and technology industry such as Stefan Sagmeister, Paula Scher, and design leaders from companies including Wix. == Corporate affairs == === Platform === Awwwards operates an online platform where web designers and developers submit websites for evaluation and awards. Submitted projects are reviewed by a jury based on design, usability, creativity, and content. The platform also serves as a community hub for discovering digital trends, showcasing work, and accessing educational resources including talks and interviews. Design professionals from international companies have participated in Awwwards events and platform content. For example, Wix, a cloud-based web development company known for its website builder tools, has featured prominently in Awwwards conferences, with its design leadership contributing to discussions on design trends and creative thinking.
False answer supervision
False answer supervision (FAS) refers to VoIP fraud where the billed duration for the caller is more than the duration of the actual connection duration. The FAS is usually performed by VoIP wholesalers in their softswitches for randomly selected calls. Adding a small amount of extra billed seconds for many calls results in significant revenue for the VoIP wholesaler. == Implementation of FAS == The FAS fraud can be implemented in a softswitch in many different ways. These include: False billing of party A without calling a party B. Usually a fake ringback tone, loopback audio or voicemail message is played Start of billing before actual answer of party B Extra billing after disconnection of party B == Detection of FAS == The FAS can be detected and blocked in a softswitch. Common methods are: Manual verification of call detail records: listening to voice recordings Identification of FAS types and using algorithms to automatically detect the FAS RTP audio signal processing: detection of voice RTP audio signal processing: detection of silence RTP audio signal processing: detection of ringback tone
MIDI Show Control
MIDI Show Control (MSC), is a real-time System Exclusive extension of the international Musical Instrument Digital Interface (MIDI) standard. MSC enables all types of entertainment equipment to communicate with each other through the process of show control. The MIDI Show Control protocol is a technical standard ratified by the MIDI Manufacturers Association in 1991, which allows entertainment control devices to talk with each other and with computers to perform show control functions in live and prerecorded entertainment applications. Just like musical MIDI, MSC does not transmit the actual show media - it simply transmits digital information about a multimedia performance. == How MSC works == When any cue is called by a user (typically a stage manager) and/or preprogrammed timeline in a show control software application, the show controller transmits one or more MSC messages from its 'MIDI Out' port. A typical MSC message sequence is: the user has just called a cue the cue is for lighting device 3 the cue is number 45.8 the cue is in cue list 7 MSC messages are serially transmitted in the same way as musical messages and are fully compatible with all conventional MIDI hardware; however, many modern MSC devices now use Ethernet communications for higher bandwidth and the flexibility afforded by networks. Other performance parameters are also transmitted, such as lighting desk submaster settings using MSC SET messages. All cues that a media control device is capable of playing are assigned MSC messages within the Show Controller's cue list and they are transmitted from its MIDI Out port at the appropriate show time, depending on the actions of the user and the show controller's internally timed sequences. All MSC-compatible instruments follow the MSC specification and thus transmit identical MSC messages for identical MSC events, such as the playing of a certain cue on the media controller. Since they follow a published standard, all MSC devices can communicate with and understand each other, as well as with computers that have been programmed to understand MSC messages using the MSC Command Set. All MSC compatible instruments have a built-in MIDI interface and many now follow one of the various MIDI-over-Ethernet protocols. == History == To create the MSC spec, Charlie Richmond headed the USITT MIDI Forum on their Callboard Network in 1990, which included developers and designers from the theatre sound and lighting industry from around the world. It is believed that this was the first international standard to be developed without a single physical meeting of the participants. This Forum created the MSC standard between January and September 1990. This was ratified by the MIDI Manufacturers Association (MMA) in January 1991, and the Japan MIDI Standards Committee (JMSC) later that year, becoming a part of the standard MIDI specification in August 1991. The first show to fully use the MSC specification was the Magic Kingdom Parade at Walt Disney World's Magic Kingdom in September 1991. == MIDI Show Control software ==
Tandem (app)
Tandem is a mobile language exchange and language learning app. == History == Tandem was founded in Hannover, Germany in 2014 by Arnd Aschentrup, Tobias Dickmeis, and Matthias Kleimann. Prior to founding Tandem, the trio had launched Vive, a members-only mobile video chat platform. Tandem has been criticised for not accepting members into the community immediately, as opposed to competitors including HelloTalk, Speaky or Cafehub. In some countries, there is a waiting list and applicants can wait up to seven days for their application to be processed by human moderators. In 2015, Tandem completed its first funding round (seed funding) of €600,000. Participating investors included business angels such as Atlantic Labs (Christophe Maire), Hannover Beteiligungsfonds, Marcus Englert (Chairman of the Supervisory Board of Rocket Internet SE ), Catagonia, Ludwig zu Salm, Florian Langenscheidt, Heiko Hubertz, Martin Sinner, and Zehden Enterprises. In 2016, the company received a further €2 million from new investors Rubylight and Faber Ventures, as well as from existing investors Hannover Beteiligungsfonds, Atlantic Labs, and Zehden Enterprises. Since 2018, the premium membership Tandem Pro has been available, which offers members unlimited access to all language learning features of the app as well as the removal of advertising for a monthly fee.
Alt TikTok
Alt TikTok (or 2020 Alt) was an online youth subculture and internet community that emerged on TikTok in 2020. Alt TikTok users (also known as alt girls, alt boys, or alt kids) emerged as primarily LGBTQ+ individuals who were in contrast to "Straight TikTok" which was seen as the mainstream and heteronormative side of the platform. The subculture became closely associated with music surrounding the hyperpop scene, particularly 100 gecs and also led to a short-lived fashion style and Internet aesthetic adopted by Generation Z during the COVID-19 lockdowns. Notable artists associated with the movement included Girl in Red, Freddie Dredd, David Shawty, WHOKILLEDXIX, and 645AR. While "alt kid" might imply a general association with traditional alternative fashion, the subculture was more an offshoot of e-girls and e-boys. In 2023, the hashtag #altfashion on TikTok amassed over 1.8 billion views. == History == Around mid-2020, users on TikTok began to group different content on the site into labels like "elite TikTok", "deep TikTok", and "floptok". These categories acted as different "sides of TikTok", deviating from mainstream lip syncing, online trends, and dance videos. Alt TikTok became one of the many subcultural communities to emerge during this period, initially referred to interchangeably with "elite TikTok". The movement quickly identified itself with alternative and queer users, in contrast to "Straight TikTok", also known as the "straight side of TikTok", which was seen as the mainstream and heteronormative side of the platform. Alt TikTok was accompanied by memes with surrealist or supernatural themes (sometimes being described as cursed), such as videos with heavy saturation and humanoid animals. One of the popular videos from Alt TikTok, gaining 18 million likes, shows a llama dancing to a cover of a song from a Russian commercial by the cereal brand Miel Pops, later becoming a viral audio. Some Alt TikTok users personified brands and products in what was referred to as Retail TikTok. In 2020, Rolling Stone described Alt TikTok as "one of the primary countercultures on the app." In 2020, American journalist Taylor Lorenz stated in an article of The New York Times, "Every pop sensation needs its ironic counterpoints. Alt Tiktok gets it done. [...] alt TikTok stars like Mooptopia are mainstays on the more indie side of the app. They aren't the popular crowd, but their cool, quirky content still attracts millions." === Trump rally trolling === In June 2020, alt TikTok and K-pop twitter users coordinated a strategy to ruin a Trump rally in Tulsa, Oklahoma. American politician and activist Alexandria Ocasio-Cortez later saluted the individuals for their "Trump troll". == Alt subculture == In 2020, Alt TikTok was one of many subcultural communities to emerge on TikTok, alongside Deep TikTok (aka DeepTok) and Flop TikTok (aka Floptok). The alt kid subculture emerged from Alt TikTok primarily among young Gen Z women, influenced by online fashion and aesthetics shaped by e-girls and e-boys. The movement was accelerated by the COVID-19 lockdowns, while the subculture itself stood in opposition to mainstream "Straight TikTok" and the VSCO girl movement, primarily adopting aspects of queer and alternative culture. While the phrase might imply a general association with alternative fashion or alternative culture, it is more accurately understood as a specific internet-driven outgrowth of online aesthetic youth subcultures like e-girls and e-boys. The alt subculture's visual style blended influences from goth, punk, emo, and grunge, often expressed through fashion, music taste, and online presence. === Style and music === The style of alt-girls is reminiscent of a myriad of previous alternative fashion trends, often blending these influences with online aesthetics. In 2020, TikTok alt-girls were teens ranging from ages 13 to 16, who tended to wear friendship bracelets, goth boots, Dr. Martens, bunny and frog hats, piercings, and split-dyed hair, as well as iconography lifted from Monster Energy and Hello Kitty. Some alt-girls displayed a love of cosplay, while drawing from Japanese anime and manga, particularly Danganronpa and Haikyu!!, which originally gained traction on the app through Anime TikTok (aka Anitok). Alt TikTok has been noted for being primarily influenced by queer and alternative culture, positioning itself in contrast to "Straight TikTok", which focused on mainstream dances and music. Alt kids frequently intersected with the e-girls and e-boys subculture, in terms of music, style, visual media, and aesthetics. Several musicians and artists were closely associated with the alt subculture, particularly those in the hyperpop scene, while alt tiktok users became important in the wider popularization of artists like 100 gecs. Notable prominent artists associated with Alt Tiktok included Girl in Red, Freddie Dredd, David Shawty, WHOKILLEDXIX, and 645AR, alongside music by YouTubers turned musicians such as Wilbur Soot's "I'm in Love With an E‐Girl" and Corpse Husband's "E-Girls Are Ruining My Life!". == Legacy == In 2020, Pitchfork claimed Alt TikTok as having an influence on wider music trends, stating: "Alt TikTok's music is now a hot zone for major record labels, pushing it even further into the mainstream". After the COVID-19 lockdowns, Alt TikTok, alongside its subculture, fell out of prominence and was taken over by other Gen Z-related internet aesthetics, developments, and online trends.