AI Content Producer

AI Content Producer — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  CPanel

  cPanel is a web hosting control panel software developed by cPanel, L.L.C. It provides a graphical interface (GUI) and automation tools designed to simplify the process of hosting a web site for the website owner or "end user". It enables administration through a standard web browser using a three-tier structure. While cPanel is limited to managing a single hosting account, cPanel & WHM allow the administration of the entire server. In addition to the GUI, cPanel also has command line and API-based access that allows third-party software vendors, web hosting organizations, and developers to automate standard system administration processes. cPanel & WHM is designed to function either as a dedicated server or virtual private server. The latest cPanel & WHM version supports installation on AlmaLinux, Rocky Linux, CloudLinux OS, and Ubuntu. == History == cPanel is currently developed by cPanel, L.L.C., a privately owned company headquartered in Houston, Texas, United States. WebPros is the parent company of cPanel, L.L.C. It was originally designed in 1996 as the control panel for Speed Hosting, a now-defunct web hosting company. The original author of cPanel, J. Nick Koston, had a stake in Speed Hosting. Webking quickly began using cPanel after its merger with Speed Hosting. The new company moved its servers to Virtual Development Inc. (VDI), a now-defunct hosting facility. Following an agreement between Koston and VDI, cPanel was only available to customers hosted directly at VDI. At the time, there was little competition in the control panel market, with the main choices being VDI and Alabanza. Eventually, due to Koston leaving for college, he and William Jensen signed an agreement in which cPanel was split into a separate program called WebPanel; this version was run by VDI. Without the lead programmer, VDI was not able to continue any work on cPanel and eventually stopped supporting it completely. Koston kept working on cPanel while also working at BurstNET. Eventually, he left BurstNET to focus fully on cPanel. cPanel 3 was released in 1999: main additions over cPanel 2 were an automatic upgrade and the Web Host Manager (WHM). The interface was also improved when Carlos Rego of WizardsHosting made what became the default theme of cPanel. With the release of cPanel 11, cPanel adopted a four-tier versioning system, "Parent.Major.Minor.Patch" (e.g., 11.32.0.3). As of version 11.52, the "Parent" representation is deprecated, with 11.54 stylized as "Version 54." cPanel 11.30 is the last major version to support FreeBSD. On August 20, 2018 cPanel L.L.C. announced that it had signed an agreement to be acquired by a group led by Oakley Capital (who also own Plesk and SolusVM). While Koston sold his interest in cPanel, he will continue to be an owner of the company that owns cPanel. In April 2026, a severe vulnerability was discovered that affected all cPanel and WHM versions after 11.40, affectively allowing unauthenticated remote attackers to access the control panel. According to some web hosters the vulnerability was already being actively exploited, with some attempts even dating back to late February 2026. == Add-ons == cPanel provides front-ends for a number of common operations, including the management of PGP keys, crontab tasks, mail and FTP accounts, and mailing lists. Several add-ons exist, some for an additional fee, including auto installers such as Installatron, Fantastico, Softaculous, and WHMSonic (SHOUTcast/radio Control Panel Add-on). The add-ons need to be enabled by the server administrator in WHM to be accessible to the cPanel user. WHM manages some software packages separately from the underlying operating system, applying upgrades to Apache, PHP, MySQL and MariaDB, Exim, FTP, and related software packages automatically. This ensures that these packages are kept up-to-date and compatible with WHM, but makes it more difficult to install newer versions of these packages. It also makes it difficult to verify that the packages have not been tampered with, since the operating system's package management verification system cannot be used to do so. == WHM == WHM, short for WebHost Manager, is a web-based tool which is used for server administration. There are at least two tiers of WHM, often referred to as "root WHM", and non-root WHM (or Reseller WHM). Root WHM is used by server administrators and non-root WHM (with fewer privileges) is used by others, like entity departments, and resellers to manage hosting accounts often referred to as cPanel accounts on a web server. WHM is also used to manage SSL certificates (both server self generated and CA provided SSL certificates), cPanel users, hosting packages, DNS zones, themes, and authentication methods. The default automatic SSL (AutoSSL) provided by cPanel is powered by Let's Encrypt. Additionally, WHM can also be used to manage FTP, Mail (POP, IMAP, and SMTP) and SSH services on the server. As well as being accessible by the root administrator, WHM is also accessible to users with reseller privileges. Reseller users of cPanel have a smaller set of features than the root user, generally limited by the server administrator, to features which they determine will affect their customers' accounts rather than the server as a whole. From root WHM, the server administrator can perform maintenance operations such as upgrading and recompiling Apache and PHP, installing Perl modules, and upgrading RPMs installed on the system. == Enkompass == A version of cPanel & WHM for Microsoft Windows, called Enkompass, was declared end-of-life as of February 2014. Version 3 remained available for download, but without further development or support. In the preceding years, Enkompass had been available for free as product development slowed. == Pricing == On June 27, 2019 cPanel announced a new account-based pricing structure. After backlash from their customers, cPanel issued a second announcement but did not change the new structure.

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  The Best Free AI Logo Maker for Beginners

  Curious about the best AI logo maker? An AI logo maker is software that uses machine learning to help you get more done — it combines speed, accuracy, and an interface that just works. Hands-on testing shows real-world results vary, so a short free trial is the smartest way to decide. Whether you are a beginner or a pro, the right AI logo maker slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.

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  Best AI Clip Makers in 2026

  Trying to pick the best AI clip maker? An AI clip maker is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI clip maker slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.

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  Machine-readable medium and data

  In communications and computing, a machine-readable medium (or computer-readable medium) is a medium capable of storing data in a format easily readable by a digital computer or a sensor. It contrasts with human-readable medium and data. The result is called machine-readable data or computer-readable data, and the data itself can be described as having machine-readability. == Data == Machine-readable data must be structured data. Attempts to create machine-readable data occurred as early as the 1960s. At the same time that seminal developments in machine-reading and natural-language processing were releasing (like Weizenbaum's ELIZA), people were anticipating the success of machine-readable functionality and attempting to create machine-readable documents. One such example was musicologist Nancy B. Reich's creation of a machine-readable catalog of composer William Jay Sydeman's works in 1966. In the United States, the OPEN Government Data Act of 14 January 2019 defines machine-readable data as "data in a format that can be easily processed by a computer without human intervention while ensuring no semantic meaning is lost." The law directs U.S. federal agencies to publish public data in such a manner, ensuring that "any public data asset of the agency is machine-readable". Machine-readable data may be classified into two groups: human-readable data that is marked up so that it can also be read by machines (e.g. microformats, RDFa, HTML), and data file formats intended principally for processing by machines (CSV, RDF, XML, JSON). These formats are only machine readable if the data contained within them is formally structured; exporting a CSV file from a badly structured spreadsheet does not meet the definition. Machine readable is not synonymous with digitally accessible. A digitally accessible document may be online, making it easier for humans to access via computers, but its content is much harder to extract, transform, and process via computer programming logic if it is not machine-readable. Extensible Markup Language (XML) is designed to be both human- and machine-readable, and Extensible Stylesheet Language Transformations (XSLT) is used to improve the presentation of the data for human readability. For example, XSLT can be used to automatically render XML in Portable Document Format (PDF). Machine-readable data can be automatically transformed for human-readability but, generally speaking, the reverse is not true. For purposes of implementation of the Government Performance and Results Act (GPRA) Modernization Act, the Office of Management and Budget (OMB) defines "machine readable format" as follows: "Format in a standard computer language (not English text) that can be read automatically by a web browser or computer system. (e.g.; xml). Traditional word processing documents and portable document format (PDF) files are easily read by humans but typically are difficult for machines to interpret. Other formats such as extensible markup language (XML), (JSON), or spreadsheets with header columns that can be exported as comma separated values (CSV) are machine readable formats. As HTML is a structural markup language, discreetly labeling parts of the document, computers are able to gather document components to assemble tables of contents, outlines, literature search bibliographies, etc. It is possible to make traditional word processing documents and other formats machine readable but the documents must include enhanced structural elements." == Media == Examples of machine-readable media include magnetic media such as magnetic disks, cards, tapes, and drums, punched cards and paper tapes, optical discs, barcodes and magnetic ink characters. Common machine-readable technologies include magnetic recording, processing waveforms, and barcodes. Optical character recognition (OCR) can be used to enable machines to read information available to humans. Any information retrievable by any form of energy can be machine-readable. Examples include: Acoustics Chemical Photochemical Electrical Semiconductor used in volatile RAM microchips Floating-gate transistor used in non-volatile memory cards Radio transmission Magnetic storage Mechanical Tins And Swins Punched card Paper tape Music roll Music box cylinder or disk Grooves (See also: Audio Data) Phonograph cylinder Gramophone record DictaBelt (groove on plastic belt) Capacitance Electronic Disc Optics Optical storage Thermodynamic == Applications == === Documents === === Catalogs === === Dictionaries === === Passports ===

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  TowIt

  "TowIt" is a free, global, cross-platform mobile app, website, and Web API that allows civilians to report parking violations and dangerous driving in real-time. The mission is to remove the barriers required to make cities effectively fight and deter bad parking and dangerous driving habits. The company ultimately aims to better existing social controls in order to drive necessary behavioral change through increased education, real-time reporting, optimized enforcement, as well as the resulting reactivity. == User base and adoption == The application has users reporting vehicular infractions in upwards of 30 countries. The top reporting countries are: Portugal, Canada, United States of America and Australia. Users have adopted TowIt for a variety of reasons, usually central to their geographical location and the prominent offences in those specific areas. For instance, the majority of Portuguese reports are cars parked on sidewalks, footpaths and pedestrian crossings, Australian reports are largely focused on the abuse of disabled parking spaces, and in Toronto or San Francisco users generally capture cars parked in bicycle lanes. == Functions == === Data collection === TowIt gathers data on individual parking offences, the prominence of various offence types, as well as recurring offenders. This allows the company to identify trends and hotspots in order to take action against problem vehicles, as well as to help improve urban planning, traffic congestion and gridlock management. Individuals modify or improve an aspect of their behavior in response to their awareness of being observed, theoretically more so when demonstrating selfishness, egocentrism, narcissism and anti-social behavior. The company states that by becoming a user, one can "help TowIt relieve congestion, reduce collisions, open up economies, improve the environment and enhance the lives of urban residents and suburban commuters alike". The company has acknowledged that there are numerous legislative changes that would be required to integrate with governments at any level in many countries. A simple three-step process allows users to take a photo of an offending vehicle and subsequently verifying the offending vehicle's license plate information before submitting by tapping the TowIt (submit) button. Photographical evidence can only be captured with the camera from within the TowIt application. An Internet connection is required. The company has stated that this was purposefully done for quality control and report validation purposes. Users may only submit and view their own report history on either the iOS or Android applications. Globally submitted reports are displayed uncensored and in aggregate only on the Android application and the TowIt website. The "Global Feed" feature was removed from iOS (see iTunes Connect Acceptance Issues). TowIt's back-end automatically geotags the report and compares it to local parking by-law data, including by-law types, locations, times, side(s) of street, etc.- where available. Valid reports are posted to the global feed, to the TowIt website, and passed on to municipalities and police for enforcement (where connected). === Technologies used under license === TowIt currently utilizes the following software or software libraries under license: AngularJS, Apache Cordova, Apple iTunes Store EULA, Chart.js, Google Play Distribution Agreement, Ionic Framework, MongoDB, Moment.js, Python 2.7, Python Flask, and jQuery. == Company history == The TowIt application was conceived by Michael Duncan McArthur on December 5, 2014, as a response to Toronto Mayor John Tory's election mandate to "get this city moving". The application was announced via TowIt's official Twitter page on January 6, 2015. After the initial public announcement, Michael & Gregory were contacted by members of John Tory's staff on January 8, 2015, and invited to demo a prototype at Toronto City Hall on January 12, 2015. The two were also invited to meet with Toronto Councillor Norm Kelly, in his City Hall office, for a subsequent demo of the live Android application on January 28, 2015. A similar meeting and demo took place with members of the Traffic Services department of Toronto Police Service on February 2, 2015. Michael & Gregory teamed up with friends and Toronto-based developers Dae-Seon Moon, Jesse Malone, and Marcus Veres to complete the prototype in time to meet the city's imposed demo deadline and to launch the initial Android version of the application. TowIt officially launched on the Android platform on January 16, 2015. A subsequent iOS launch took place on March 19, 2015. === iTunes connect acceptance issues === The iOS version of the application was delayed for approximately two months, only after significant deliberation with Apple's iTunes Connect review board around (as then stated) rule: "14.1 - Any App that is defamatory, offensive, mean-spirited, or likely to place the targeted individual or group in harm's way will be rejected." The result was having to remove the "Global Feed" feature from the iOS platform, in which civilian users could view all recent reports from within the application. This feature still exists on the Android platform. === Business and legal === TowIt engaged Wildeboer Dellelce, one of Canada's leading business law and transactional corporate finance law firms, on January 17, 2015. The company filed for incorporation as "TowIt Solutions Inc." by both Michael & Gregory in the Canadian province of Ontario on January 22, 2015. TowIt continues to operate under a Freemium business model. The company is 100% bootstrapped and has received no outside investment to date. TowIt was accepted into the MaRS Discovery District's Venture Services program on March 4, 2015. === Lobbyist registration === After receiving initial press coverage in January and February 2015, an unknown entity reported Michael & Gregory's initial communications with city staff to the City of Toronto's Lobbyist Registrar. This complaint resulted in legal threats of fines received on February 10, 2015, for apparently and unknowingly breaking municipal lobbying by-laws. These fines (of up to $100,000) were eventually withdrawn after Michael & Gregory immediately provided all records of communication with city officials and registered as lobbyists in the City of Toronto on the subjects of By-law / Regulation, Parking, and Technology. Their registration was accepted by the Lobbyist Registrar on March 6, 2015. However, communication with Toronto city staff was reduced greatly as a result, which the company believes may have been the desired intent of the original complaint. === Outreach and activism === TowIt encourages its global user base to reach out to their local government representatives to promote the app at the users' own will. This tactic is used not only to demonstrate grassroots support, but also to avoid future lobbying issues. On June 2, 2015, the company officially partnered with Australian campaign "No Permit No Park" who advocate for the creation of inclusive communities. == Reception == The Best Planning Apps for 2016 by Planetizen, 5 Toronto apps you should be using by Indie88, 12 Best Apps Made In Canada by TechVibes.

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  Kunihiko Fukushima

  Kunihiko Fukushima (Japanese: 福島 邦彦, born 16 March 1936) is a Japanese computer scientist, most noted for his work on artificial neural networks and deep learning. He is currently working part-time as a senior research scientist at the Fuzzy Logic Systems Institute in Fukuoka, Japan. == Notable scientific achievements == In 1980, Fukushima published the neocognitron, the original deep convolutional neural network (CNN) architecture. Fukushima proposed several supervised and unsupervised learning algorithms to train the parameters of a deep neocognitron such that it could learn internal representations of incoming data. Today, however, the CNN architecture is usually trained through backpropagation. This approach is now heavily used in computer vision. In 1969 Fukushima introduced the ReLU (Rectifier Linear Unit) activation function in the context of visual feature extraction in hierarchical neural networks, which he called "analog threshold element". (Though the ReLU was first used by Alston Householder in 1941 as a mathematical abstraction of biological neural networks.) As of 2017 it is the most popular activation function for deep neural networks. == Education and career == In 1958, Fukushima received his Bachelor of Engineering in electronics from Kyoto University. He became a senior research scientist at the NHK Science & Technology Research Laboratories. In 1989, he joined the faculty of Osaka University. In 1999, he joined the faculty of the University of Electro-Communications. In 2001, he joined the faculty of Tokyo University of Technology. From 2006 to 2010, he was a visiting professor at Kansai University. Fukushima acted as founding president of the Japanese Neural Network Society (JNNS). He also was a founding member on the board of governors of the International Neural Network Society (INNS), and president of the Asia-Pacific Neural Network Assembly (APNNA). He was one of the board of governors of the International Neural Network Society (INNS) in 1989-1990 and 1993-2005. == Awards == In 2020, Fukushima received the Bower Award and Prize for Achievement in Science. In 2022, Fukushima became a laureate of the Asian Scientist 100 by the Asian Scientist. He also received the IEICE Achievement Award and Excellent Paper Awards, the IEEE Neural Networks Pioneer Award, the APNNA Outstanding Achievement Award, the JNNS Excellent Paper Award and the INNS Helmholtz Award.

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  Armin B. Cremers

  Armin Bernd Cremers (born June 7, 1946) is a German mathematician and computer scientist. He is a professor in the computer science institute at the University of Bonn, Germany. He is most notable for his contributions to several fields of discrete mathematics including formal languages and automata theory. In more recent years he has been recognized for his work in artificial intelligence, machine learning and robotics as well as in geoinformatics and deductive databases. == Life and work == Armin B. Cremers studied mathematics and physics at the University of Karlsruhe, Germany. After his graduate diploma (1971) and PhD (1972), both in mathematics, both summa cum laude, he received his academic lectureship qualification for computer science (1974), all from the University of Karlsruhe. Following an invitation by Seymour Ginsburg, he joined the University of Southern California (USC), Los Angeles, in 1973 where he worked until 1976 as an assistant professor of electrical engineering and computer science. With Ginsburg he initiated Grammar Forms, a new formalism for grammatical families. In 1976 A. B. Cremers returned to Germany and was appointed to full professor of computer science at the University of Dortmund, where he remained until 1990, holding the chair for information systems. During the same time he continued working as a visiting research professor at USC, where together with Thomas N. Hibbard he developed the concept of Data Spaces, a comprehensive computational model, in theory and applications. At the University of Dortmund A. B. Cremers served as chairman of the computer science department and, since early 1985, as vice president for Research and Junior Scientific Staff. In this position he was liaison for the development of the Technology Center Dortmund Archived 2021-05-09 at the Wayback Machine. He was the initiator and founding director of the Center for Expert Systems Dortmund (ZEDO) and the NRW State Research Collaborative in Artificial Intelligence (KI-NRW). From 1988 to 1996 he was also a member of the supervisory board of the German National Research Center for Mathematics and Data Processing (GMD). Since 1990 A. B. Cremers has been professor and director of computer science and head of the research group in artificial intelligence at the University of Bonn. From Bonn he has contributed fundamentally to artificial intelligence and robotics (with Wolfram Burgard, Dieter Fox, Sebastian Thrun among his students), and to the development of software engineering, particularly in civil engineering, and information systems, particularly in the geosciences. The paper "The Interactive Museum Tour-Guide Robot" won the AAAI Classic Paper award of 2016. Together with Matthias Jarke A. B. Cremers established the Bonn-Aachen International Center for Information Technology (B-IT) in 2001 and led this as Founding Scientific Director from the University of Bonn side until his retirement from teaching in 2014. From 2004 to 2008 Cremers was Dean of the School of Mathematics and Natural Sciences, and from April 2009 to July 2014 University Vice President for Planning and Finance. He is member of advisory boards, e.g., as well as Chairman of the University Council of the University of Koblenz-Landau.

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  Devi Parikh

  Devi Parikh is an American computer scientist. == Career == Parikh earned her PhD in Electrical and Computer Engineering at Carnegie Mellon University. She has served as a professor at Virginia Tech and Georgia Tech, and as of 2022 she is a research director at Meta. == Research == Parikh's research focuses on computer vision and natural language processing. In 2015, Parikh and her students at Virginia Tech worked on AI for Visual Question Answering (VQA). This technology allows users to ask questions about pictures, e.g. "Is this a vegetarian pizza?" Parikh's VQA dataset has been used to evaluate over 30 AI models. In 2017, Parikh published a conversational agent called ParlAI. In 2020, she developed an AI system that generates dance moves in sync with songs. In 2022, Parikh and a team at Meta developed Make-a-Video, a text-to-video AI model that is based on the diffusion algorithm. == Awards == 2017 IJCAI Computers and Thought Award 2011 ICCV Best-Paper Award ("Marr Prize")

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  Quantum machine learning

  Quantum machine learning (QML) is the study of quantum algorithms for machine learning. It often refers to quantum algorithms for machine learning tasks which analyze classical data, sometimes called quantum-enhanced machine learning. QML algorithms use qubits and quantum operations to try to improve the space and time complexity of classical machine learning algorithms. Hybrid QML methods involve both classical and quantum processing, where computationally difficult subroutines are outsourced to a quantum device. These routines can be more complex in nature and executed faster on a quantum computer. Furthermore, quantum algorithms can be used to analyze quantum states instead of classical data. The term "quantum machine learning" is sometimes used to refer classical machine learning methods applied to data generated from quantum experiments (i.e. machine learning of quantum systems), such as learning the phase transitions of a quantum system or creating new quantum experiments. QML also extends to a branch of research that explores methodological and structural similarities between certain physical systems and learning systems, in particular neural networks. For example, some mathematical and numerical techniques from quantum physics are applicable to classical deep learning and vice versa. Furthermore, researchers investigate more abstract notions of learning theory with respect to quantum information, sometimes referred to as "quantum learning theory". == Machine learning with quantum computers == Quantum-enhanced machine learning refers to quantum algorithms that solve tasks in machine learning, thereby improving and often expediting classical machine learning techniques. Such algorithms typically require one to encode the given classical data set into a quantum computer to make it accessible for quantum information processing. Subsequently, quantum information processing routines are applied and the result of the quantum computation is read out by measuring the quantum system. For example, the outcome of the measurement of a qubit reveals the result of a binary classification task. While many proposals of QML algorithms are still purely theoretical and require a full-scale universal quantum computer to be tested, others have been implemented on small-scale or special purpose quantum devices. === Quantum associative memories and quantum pattern recognition === Early work on quantum associative memories has been done by Dan Ventura and Tony Martinez and by Carlo A. Trugenberger in the late 1990s and early 2000s. Associative (or content-addressable) memories are able to recognize stored content on the basis of a similarity measure, while random access memories are accessed by the address of stored information and not its content. As such they must be able to retrieve both incomplete and corrupted patterns, the essential machine learning task of pattern recognition. Typical classical associative memories store p patterns in the O ( n 2 ) {\displaystyle O(n^{2})} interactions (synapses) of a real, symmetric energy matrix over a network of n artificial neurons. The encoding is such that the desired patterns are local minima of the energy functional and retrieval is done by minimizing the total energy, starting from an initial configuration. Unfortunately, classical associative memories are severely limited by the phenomenon of cross-talk. When too many patterns are stored, spurious memories appear which quickly proliferate, so that the energy landscape becomes disordered and no retrieval is anymore possible. The number of storable patterns is typically limited by a linear function of the number of neurons, p ≤ O ( n ) {\displaystyle p\leq O(n)} . Quantum associative memories (in their simplest realization) store patterns in a unitary matrix U acting on the Hilbert space of n qubits. Retrieval is realized by the unitary evolution of a fixed initial state to a quantum superposition of the desired patterns with probability distribution peaked on the most similar pattern to an input. By its very quantum nature, the retrieval process is thus probabilistic. Because quantum associative memories are free from cross-talk, however, spurious memories are never generated. Correspondingly, they have a superior capacity than classical ones. The number of parameters in the unitary matrix U is O ( p n ) {\displaystyle O(pn)} . One can thus have efficient, spurious-memory-free quantum associative memories for any polynomial number of patterns. If the matrix U is encoded as a unique operator (as opposed as to a sequence of gates as in the circuit model), e.g. by an optical interferometer, the retrieval becomes efficient even for an exponential number of patterns. === Linear algebra simulation with quantum amplitudes === A number of quantum algorithms for machine learning are based on the idea of amplitude encoding, that is, to associate the amplitudes of a quantum state with the inputs and outputs of computations. Since a state of n {\displaystyle n} qubits is described by 2 n {\displaystyle 2^{n}} complex amplitudes, this information encoding can allow for an exponentially compact representation. Intuitively, this corresponds to associating a discrete probability distribution over binary random variables with a classical vector. The goal of algorithms based on amplitude encoding is to formulate quantum algorithms whose resources grow polynomially in the number of qubits n {\displaystyle n} , which amounts to a logarithmic time complexity in the number of amplitudes and thereby the dimension of the input. Many QML algorithms in this category are based on variations of the quantum algorithm for linear systems of equations (colloquially called HHL, after the paper's authors) which, under specific conditions, performs a matrix inversion using an amount of physical resources growing only logarithmically in the dimensions of the matrix. One of these conditions is that a Hamiltonian which entry-wise corresponds to the matrix can be simulated efficiently, which is known to be possible if the matrix is sparse or low rank. For reference, any known classical algorithm for matrix inversion requires a number of operations that grows more than quadratically in the dimension of the matrix (e.g. O ( n 2.373 ) {\displaystyle O{\mathord {\left(n^{2.373}\right)}}} ), but they are not restricted to sparse matrices. Quantum matrix inversion can be applied to machine learning methods in which the training reduces to solving a linear system of equations, for example in least-squares linear regression, the least-squares version of support vector machines, and Gaussian processes. A crucial bottleneck of methods that simulate linear algebra computations with the amplitudes of quantum states is state preparation, which often requires one to initialise a quantum system in a state whose amplitudes reflect the features of the entire dataset. Although efficient methods for state preparation are known for specific cases, this step easily hides the complexity of the task. === Variational quantum algorithms (VQAs) === In a variational quantum algorithm, a classical computer optimizes the parameters used to prepare a quantum state, while a quantum computer is used to do the actual state preparation and measurement. VQAs are considered promising candidates for noisy intermediate-scale quantum computers. Variational quantum circuits (or parameterized quantum circuits) are a popular class of VQAs where the parameters are those used in a fixed quantum circuit. Researchers have studied VQCs to solve optimization problems and find the ground state energy of complex quantum systems, which were difficult to solve using a classical computer. === Quantum binary classifier === Pattern reorganization is one of the important tasks of machine learning, binary classification is one of the tools or algorithms to find patterns. Binary classification is used in supervised learning and in unsupervised learning. In QML, classical bits are converted to qubits and they are mapped to Hilbert space; complex value data are used in a quantum binary classifier to use the advantage of Hilbert space. By exploiting the quantum mechanic properties such as superposition, entanglement, interference the quantum binary classifier produces the accurate result in short period of time. === Quantum machine learning algorithms based on Grover search === Another approach to improving classical machine learning with quantum information processing uses amplitude amplification methods based on Grover's search algorithm, which has been shown to solve unstructured search problems with a quadratic speedup compared to classical algorithms. These quantum routines can be employed for learning algorithms that translate into an unstructured search task, as can be done, for instance, in the case of the k-medians and the k-nearest neighbors algorithms. Other applications include quadratic speedups in the training of perceptrons. An e

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  F-score

  In statistical analysis of binary classification and information retrieval systems, the F-score or F-measure is a measure of predictive performance. It is calculated from the precision and recall of the test, where the precision is the number of true positive results divided by the number of all samples predicted to be positive, including those not identified correctly, and the recall is the number of true positive results divided by the number of all samples that should have been identified as positive. Precision is also known as positive predictive value, and recall is also known as sensitivity in diagnostic binary classification. The F1 score is the harmonic mean of the precision and recall. It thus symmetrically represents both precision and recall in one metric. The more generic F β {\displaystyle F_{\beta }} score applies additional weights, valuing one of precision or recall more than the other. The highest possible value of an F-score is 1.0, indicating perfect precision and recall, and the lowest possible value is 0, if the precision or the recall is zero. == Etymology == The name F-measure is believed to be named after a different F function in Van Rijsbergen's book, when introduced to the Fourth Message Understanding Conference (MUC-4, 1992). == Definition == The traditional F-measure or balanced F-score (F1 score) is the harmonic mean of precision and recall: F 1 = 2 r e c a l l − 1 + p r e c i s i o n − 1 = 2 p r e c i s i o n ⋅ r e c a l l p r e c i s i o n + r e c a l l = 2 T P 2 T P + F P + F N {\displaystyle F_{1}={\frac {2}{\mathrm {recall} ^{-1}+\mathrm {precision} ^{-1}}}=2{\frac {\mathrm {precision} \cdot \mathrm {recall} }{\mathrm {precision} +\mathrm {recall} }}={\frac {2\mathrm {TP} }{2\mathrm {TP} +\mathrm {FP} +\mathrm {FN} }}} With precision = TP / (TP + FP) and recall = TP / (TP + FN), it follows that the numerator of F1 is the sum of their numerators and the denominator of F1 is the sum of their denominators. If FP=FN F 1 = 2 T P 2 T P + 2 F P = T P T P + F P {\displaystyle F_{1}={\frac {2\mathrm {TP} }{2\mathrm {TP} +2\mathrm {FP} }}={\frac {\mathrm {TP} }{\mathrm {TP} +\mathrm {FP} }}} or F 1 = 2 T P 2 T P + 2 F N = T P T P + F N {\displaystyle F_{1}={\frac {2\mathrm {TP} }{2\mathrm {TP} +2\mathrm {FN} }}={\frac {\mathrm {TP} }{\mathrm {TP} +\mathrm {FN} }}} So, F1 = precision = recall If TP=FP=FN F 1 = 2 T P 2 T P + 2 F P = 2 T P 4 T P = 1 2 = 0.5 {\displaystyle F_{1}={\frac {2\mathrm {TP} }{2\mathrm {TP} +2\mathrm {FP} }}={\frac {2\mathrm {TP} }{4\mathrm {TP} }}={\frac {1}{2}}=0.5} or F 1 = 2 T P 2 T P + 2 F N = 2 T P 4 T P = 1 2 = 0.5 {\displaystyle F_{1}={\frac {2\mathrm {TP} }{2\mathrm {TP} +2\mathrm {FN} }}={\frac {2\mathrm {TP} }{4\mathrm {TP} }}={\frac {1}{2}}=0.5} To see it as a harmonic mean, note that F 1 − 1 = 1 2 ( r e c a l l − 1 + p r e c i s i o n − 1 ) {\displaystyle F_{1}^{-1}={\frac {1}{2}}(\mathrm {recall} ^{-1}+\mathrm {precision} ^{-1})} . === Fβ score === A more general F score, F β {\displaystyle F_{\beta }} , that uses a positive real factor β {\displaystyle \beta } , where β {\displaystyle \beta } is chosen such that recall is considered β {\displaystyle \beta } times as important as precision, is: F β = β 2 + 1 ( β 2 ⋅ r e c a l l − 1 ) + p r e c i s i o n − 1 = ( 1 + β 2 ) ⋅ p r e c i s i o n ⋅ r e c a l l ( β 2 ⋅ p r e c i s i o n ) + r e c a l l {\displaystyle F_{\beta }={\frac {\beta ^{2}+1}{(\beta ^{2}\cdot \mathrm {recall} ^{-1})+\mathrm {precision} ^{-1}}}={\frac {(1+\beta ^{2})\cdot \mathrm {precision} \cdot \mathrm {recall} }{(\beta ^{2}\cdot \mathrm {precision} )+\mathrm {recall} }}} To see that as a weighted harmonic mean, note that F β − 1 = 1 β + β − 1 ( β ⋅ r e c a l l − 1 + β − 1 ⋅ p r e c i s i o n − 1 ) {\displaystyle F_{\beta }^{-1}={\frac {1}{\beta +\beta ^{-1}}}(\beta \cdot \mathrm {recall} ^{-1}+\beta ^{-1}\cdot \mathrm {precision} ^{-1})} . In terms of Type I and type II errors this becomes: F β = ( 1 + β 2 ) ⋅ T P ( 1 + β 2 ) ⋅ T P + β 2 ⋅ F N + F P = ( 1 + β 2 ) ⋅ T P ( T P + F N ) ⋅ β 2 + ( T P + F P ) {\displaystyle F_{\beta }={\frac {(1+\beta ^{2})\cdot \mathrm {TP} }{(1+\beta ^{2})\cdot \mathrm {TP} +\beta ^{2}\cdot \mathrm {FN} +\mathrm {FP} }}\,={\frac {(1+\beta ^{2})\cdot \mathrm {TP} }{(\mathrm {TP} +\mathrm {FN} )\cdot \beta ^{2}+(\mathrm {TP} +\mathrm {FP} )}}\,} Two commonly used values for β {\displaystyle \beta } are 2, which weighs recall higher than precision, and 1/2, which weighs recall lower than precision. The F-measure was derived so that F β {\displaystyle F_{\beta }} "measures the effectiveness of retrieval with respect to a user who attaches β {\displaystyle \beta } times as much importance to recall as precision". It is based on Van Rijsbergen's effectiveness measure E = 1 − ( α p + 1 − α r ) − 1 {\displaystyle E=1-\left({\frac {\alpha }{p}}+{\frac {1-\alpha }{r}}\right)^{-1}} Their relationship is: F β = 1 − E {\displaystyle F_{\beta }=1-E} where α = 1 1 + β 2 {\displaystyle \alpha ={\frac {1}{1+\beta ^{2}}}} == Diagnostic testing == This is related to the field of binary classification where recall is often termed "sensitivity". == Dependence of the F-score on class imbalance == Precision-recall curve, and thus the F β {\displaystyle F_{\beta }} score, explicitly depends on the ratio r {\displaystyle r} of positive to negative test cases. This means that comparison of the F-score across different problems with differing class ratios is problematic. One way to address this issue (see e.g., Siblini et al., 2020) is to use a standard class ratio r 0 {\displaystyle r_{0}} when making such comparisons. == Applications == The F-score is often used in the field of information retrieval for measuring search, document classification, and query classification performance. It is particularly relevant in applications which are primarily concerned with the positive class and where the positive class is rare relative to the negative class. Earlier works focused primarily on the F1 score, but with the proliferation of large scale search engines, performance goals changed to place more emphasis on either precision or recall and so F β {\displaystyle F_{\beta }} is seen in wide application. The F-score is also used in machine learning. However, the F-measures do not take true negatives into account, hence measures such as the Matthews correlation coefficient, Informedness or Cohen's kappa may be preferred to assess the performance of a binary classifier. The F-score has been widely used in the natural language processing literature, such as in the evaluation of named entity recognition and word segmentation. == Properties == The F1 score is the Dice coefficient of the set of retrieved items and the set of relevant items. The F1-score of a classifier which always predicts the positive class converges to 1 as the probability of the positive class increases. The F1-score of a classifier which always predicts the positive class is equal to 2 proportion_of_positive_class / ( 1 + proportion_of_positive_class ), since the recall is 1, and the precision is equal to the proportion of the positive class. If the scoring model is uninformative (cannot distinguish between the positive and negative class) then the optimal threshold is 0 so that the positive class is always predicted. F1 score is concave in the true positive rate. == Criticism == David Hand and others criticize the widespread use of the F1 score since it gives equal importance to precision and recall. In practice, different types of mis-classifications incur different costs. In other words, the relative importance of precision and recall is an aspect of the problem. According to Davide Chicco and Giuseppe Jurman, the F1 score is less truthful and informative than the Matthews correlation coefficient (MCC) in binary evaluation classification. David M W Powers has pointed out that F1 ignores the True Negatives and thus is misleading for unbalanced classes, while kappa and correlation measures are symmetric and assess both directions of predictability - the classifier predicting the true class and the true class predicting the classifier prediction, proposing separate multiclass measures Informedness and Markedness for the two directions, noting that their geometric mean is correlation. Another source of critique of F1 is its lack of symmetry. It means it may change its value when dataset labeling is changed - the "positive" samples are named "negative" and vice versa. This criticism is met by the P4 metric definition, which is sometimes indicated as a symmetrical extension of F1. Finally, Ferrer and Dyrland et al. argue that the expected cost (or its counterpart, the expected utility) is the only principled metric for evaluation of classification decisions, having various advantages over the F-score and the MCC. Both works show that the F-score can result in wrong conclusions about the absolute and relative quality of systems. == Difference from Fowlkes–Mallows index == While the F-measur

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  Sequential minimal optimization (SMO) is an algorithm for solving the quadratic programming (QP) problem that arises during the training of support-vector machines (SVM). It was invented by John Platt in 1998 at Microsoft Research. SMO is widely used for training support vector machines and is implemented by the popular LIBSVM tool. The publication of the SMO algorithm in 1998 has generated a lot of excitement in the SVM community, as previously available methods for SVM training were much more complex and required expensive third-party QP solvers. == Optimization problem == Consider a binary classification problem with a dataset (x1, y1), ..., (xn, yn), where xi is an input vector and yi ∈ {-1, +1} is a binary label corresponding to it. A soft-margin support vector machine is trained by solving a quadratic programming problem, which is expressed in the dual form as follows: max α ∑ i = 1 n α i − 1 2 ∑ i = 1 n ∑ j = 1 n y i y j K ( x i , x j ) α i α j , {\displaystyle \max _{\alpha }\sum _{i=1}^{n}\alpha _{i}-{\frac {1}{2}}\sum _{i=1}^{n}\sum _{j=1}^{n}y_{i}y_{j}K(x_{i},x_{j})\alpha _{i}\alpha _{j},} subject to: 0 ≤ α i ≤ C , for i = 1 , 2 , … , n , {\displaystyle 0\leq \alpha _{i}\leq C,\quad {\mbox{ for }}i=1,2,\ldots ,n,} ∑ i = 1 n y i α i = 0 {\displaystyle \sum _{i=1}^{n}y_{i}\alpha _{i}=0} where C is an SVM hyperparameter and K(xi, xj) is the kernel function, both supplied by the user; and the variables α i {\displaystyle \alpha _{i}} are Lagrange multipliers. == Algorithm == SMO is an iterative algorithm for solving the optimization problem described above. SMO breaks this problem into a series of smallest possible sub-problems, which are then solved analytically. Because of the linear equality constraint involving the Lagrange multipliers α i {\displaystyle \alpha _{i}} , the smallest possible problem involves two such multipliers. Then, for any two multipliers α 1 {\displaystyle \alpha _{1}} and α 2 {\displaystyle \alpha _{2}} , the constraints are reduced to: 0 ≤ α 1 , α 2 ≤ C , {\displaystyle 0\leq \alpha _{1},\alpha _{2}\leq C,} y 1 α 1 + y 2 α 2 = k , {\displaystyle y_{1}\alpha _{1}+y_{2}\alpha _{2}=k,} and this reduced problem can be solved analytically: one needs to find a minimum of a one-dimensional quadratic function. k {\displaystyle k} is the negative of the sum over the rest of terms in the equality constraint, which is fixed in each iteration. The algorithm proceeds as follows: Find a Lagrange multiplier α 1 {\displaystyle \alpha _{1}} that violates the Karush–Kuhn–Tucker (KKT) conditions for the optimization problem. Pick a second multiplier α 2 {\displaystyle \alpha _{2}} and optimize the pair ( α 1 , α 2 ) {\displaystyle (\alpha _{1},\alpha _{2})} . Repeat steps 1 and 2 until convergence. When all the Lagrange multipliers satisfy the KKT conditions (within a user-defined tolerance), the problem has been solved. Although this algorithm is guaranteed to converge, heuristics are used to choose the pair of multipliers so as to accelerate the rate of convergence. This is critical for large data sets since there are n ( n − 1 ) / 2 {\displaystyle n(n-1)/2} possible choices for α i {\displaystyle \alpha _{i}} and α j {\displaystyle \alpha _{j}} . == Related work == The first approach to splitting large SVM learning problems into a series of smaller optimization tasks was proposed by Bernhard Boser, Isabelle Guyon, and Vladimir Vapnik. It is known as the "chunking algorithm". The algorithm starts with a random subset of the data, solves this problem, and iteratively adds examples which violate the optimality conditions. One disadvantage of this algorithm is that it is necessary to solve QP-problems scaling with the number of SVs. On real world sparse data sets, SMO can be more than 1000 times faster than the chunking algorithm. In 1997, E. Osuna, R. Freund, and F. Girosi proved a theorem which suggests a whole new set of QP algorithms for SVMs. By the virtue of this theorem a large QP problem can be broken down into a series of smaller QP sub-problems. A sequence of QP sub-problems that always add at least one violator of the Karush–Kuhn–Tucker (KKT) conditions is guaranteed to converge. The chunking algorithm obeys the conditions of the theorem, and hence will converge. The SMO algorithm can be considered a special case of the Osuna algorithm, where the size of the optimization is two and both Lagrange multipliers are replaced at every step with new multipliers that are chosen via good heuristics. The SMO algorithm is closely related to a family of optimization algorithms called Bregman methods or row-action methods. These methods solve convex programming problems with linear constraints. They are iterative methods where each step projects the current primal point onto each constraint.

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