AI Detection Remover

AI Detection Remover — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

Collabora Online

Collabora Online (often abbreviated as COOL) is an open-source online office suite developed by Collabora, based on LibreOffice Online, the web-based edition of the LibreOffice office suite. It enables real-time collaborative editing of documents, spreadsheets, presentations, and vector graphics in a web browser. Optional applications are available for offline use on Android, ChromeOS, iOS, iPadOS, Linux distributions, macOS, and Windows. It supports the OpenDocument format and is compatible with other major formats, including those used by Microsoft Office. The Document Foundation (TDF), the nonprofit organization behind LibreOffice, states that a majority of the LibreOffice software development is done by its partners like Collabora. Collabora Online is an open-source alternative to proprietary cloud office platforms such as Google Workspace and Microsoft 365. Unlike these services, it can be self-hosted or hosted by third-party providers. The platform is marketed particularly toward enterprises and public institutions seeking greater digital sovereignty and independence from U.S.-based "big tech" companies. Collabora also develops Collabora Office, a standalone desktop and mobile app suite based on LibreOffice. Although Collabora Online has increasingly taken on a central role, both products may be used in parallel, similar to Microsoft Office and Microsoft 365. In November 2025, Collabora released Collabora Office Desktop and renamed the previous product Collabora Office Classic. The new product shares code with Collabora Online and brings the same user interface to the desktop on Linux, Windows and MacOS. A separate version, the Collabora Online Development Edition (CODE), is offered free of charge and is recommended for individuals, small teams, and developers. CODE provides early access to new features and serves as a testing and development platform for open-source community contributors. As TDF does not offer a free version of LibreOffice Online, CODE represents the primary freely available option for organizations and individuals interested in deploying LibreOffice in a web-based, collaborative setting. == Applications == Collabora Online includes several applications for document editing, available through the web-based interface and optional desktop and mobile apps: Collabora Writer – A word processor based on LibreOffice Writer, comparable to Microsoft Word and Google Docs. It supports WYSIWYG editing, styles, formatting tools, comment threads, and change tracking. Collabora Calc – A spreadsheet editor based on LibreOffice Calc, similar to Microsoft Excel and Google Sheets. Features include pivot tables, formulas, data validation, conditional formatting, advanced sorting and filtering, charts, and support for up to 16,000 columns. Compatible with some macros written in VBA. Collabora Impress – A presentation program based on LibreOffice Impress, comparable to Microsoft PowerPoint and Google Slides. It supports master slides, transitions, speaker notes, and multimedia elements. Collabora Draw is not a separate application, most of the functionality of the Draw application is now integrated in Writer and Impress – vector graphics editor based on LibreOffice Draw, comparable to Microsoft Visio and Google Drawings. == Features == Collabora Online can be accessed from modern web browsers without the need for plug-ins or add-ons. It supports real-time collaborative editing of word processing documents, spreadsheets, presentations, and vector graphics. Collaboration features include commenting, version tracking with document comparison and restoration, and integration with communication tools such as chat or video calls. These functions are often enabled through integration with enterprise open-source cloud platforms like Nextcloud, ownCloud, Seafile, EGroupware, GroupOffice and others. Collabora Online can also be embedded or integrated into a variety of third-party applications. Although client apps are not required to use the web-based suite, optional applications are available for offline use on Android, ChromeOS, iOS, iPadOS, Linux distributions, macOS, and Windows. These apps share the same LibreOffice-based core as the server version, ensuring document compatibility across platforms. Development of the LibreOffice core benefits both the online server and the client applications simultaneously. The mobile apps offer touch-optimized interfaces that adapt to different screen sizes and can be used offline, with optional integration into cloud storage services. Collabora Online supports OpenDocument formats (ODF; .odt, .odp, .ods, .odg) in accordance with ISO/IEC 26300. It is also compatible with Microsoft Office formats, including Office Open XML (.docx, .pptx, .xlsx) and legacy binary formats (.doc, .ppt, .xls). Additional supported formats include PDF, PNG, CSV, TSV, RTF, EPUB, and others. The suite can import a range of formats supported by LibreOffice, including Microsoft Visio and Publisher files, Apple Keynote, Numbers, and Pages files, as well as legacy formats used by Lotus 1-2-3, Microsoft Works, and Quattro Pro. The core of Collabora Online is written in C++ and utilizes LibreOfficeKit, a programming interface that enables reuse of much of LibreOffice's existing code for document saving, loading, and rendering. Collabora Online operates on the principle that documents remain on the server, with users viewing tile-rendered images of the document and sending their edits back to the server. The user interface is implemented in JavaScript. For file access and authentication with file hosting services, Collabora Online uses Microsoft's WOPI protocol, allowing compatibility with any service supporting Microsoft 365 integration. == Server == The server component can be self-hosted or deployed through third-party enterprise open-source cloud platforms, allowing organizations to maintain control over data and infrastructure. It is available for various Linux distributions and as a Docker image. The server enables features such as in-browser document editing, file synchronization, and real-time communication. These third-party cloud platforms typically offer additional functionality comparable to services such as Dropbox, Google Workspace, Microsoft 365, or Zoom, including file sharing, calendars, email, contacts, chat, and video conferencing. Collabora Online can be integrated into these applications, as well as with other services such as learning management systems and enterprise content platforms, through open APIs and an SDK. == Reception == Various online and print publications have discussed Collabora Online. In December 2016 the technology website Softpedia mentioned the availability of collaborative editing in version 2.0 and the integration with ownCloud, Nextcloud, and other file synchronization and sharing solutions. In June 2020, ZDNET reported that Collabora Online would be included as the standard office suite in Nextcloud version 19, noting that direct document editing was added to the native video conferencing software Talk. The technology blog OMG! Ubuntu! covered the release of Collabora's Android and iOS apps, emphasizing their offline functionality. In September 2020, Linux Magazine compared Collabora Online with OnlyOffice, noting the flexibility and platform independence of both tools and highlighting Collabora's extensive feature set derived from LibreOffice. === Digital sovereignty === Collabora Online's open-source design and support for self-hosting have made it notable in discussions about digital sovereignty—the ability of users and organizations to control their own data. This is particularly relevant in Europe, where concerns about dependence on U.S.-based "big tech" companies and data privacy have grown in recent years. On 10th June 2025, Microsoft executives under oath in the French Senate admitted that they cannot guarantee data sovereignty and would be compelled to pass French (and by implication the wider European Union) information to the US administration if requested via a warrant or subpoena. The Cloud Act is a law that gives the US government authority to obtain digital data held by US-based tech corporations, irrespective of whether that data is stored on servers at home or on foreign soil. A 2020 briefing by the European Parliament highlighted risks associated with reliance on major technology companies that collect and exploit user data. Legal decisions such as the Schrems II ruling have further underscored these concerns. Several European government agencies have adopted private cloud solutions using Collabora Online and related platforms to enhance data security and maintain control over sensitive information. == History == The former LibreOffice development team from SUSE joined Collabora in September 2013, forming the subsidiary Collabora Productivity. In 2015 Collabora and IceWarp announced the development of an enterprise-ready version of LibreOffice Online to compete wi
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Python (programming language)

Python is a high-level, general-purpose programming language that emphasizes code readability, simplicity, and ease-of-writing with the use of significant indentation, "plain English" naming, an extensive ("batteries-included") standard library, and garbage collection. Python supports multiple programming paradigms but with an emphasis on object-oriented programming and dynamic typing. Guido van Rossum began working on Python in the late 1980s as a successor to the ABC programming language. Python 3.0, released in 2008, was a major revision and not completely backward-compatible with earlier versions. Beginning with Python 3.5, capabilities and keywords for typing were added to the language, allowing optional static typing. As of 2026, the Python Software Foundation supports Python 3.10, 3.11, 3.12, 3.13, and 3.14, following the project's annual release cycle and five-year support policy. Python 3.15 is currently in the alpha development phase, and the stable release is expected to launch in October 2026. Earlier versions in the 3.x series have reached end-of-life and no longer receive security updates. Python has gained extensive use in the machine learning community. It is widely taught as an introductory programming language. Since 2003, Python has consistently ranked among the top ten most popular programming languages in the TIOBE Programming Community Index, which ranks programming languages based on searches across 24 platforms. == History == Python was conceived in the late 1980s by Guido van Rossum at Centrum Wiskunde & Informatica (CWI) in the Netherlands. It was designed as a successor to the ABC programming language, which was inspired by SETL, capable of exception handling and interfacing with the Amoeba operating system. Python implementation began in December 1989. Van Rossum first released it in 1991 as Python 0.9.0. Van Rossum assumed sole responsibility for the project, as the lead developer, until 12 July 2018, when he announced his "permanent vacation" from responsibilities as Python's "benevolent dictator for life" (BDFL); this title was bestowed on him by the Python community to reflect his long-term commitment as the project's chief decision-maker. (He has since come out of retirement and is self-titled "BDFL-emeritus".) In January 2019, active Python core developers elected a five-member Steering Council to lead the project. The name Python derives from the British comedy series Monty Python's Flying Circus. (See § Naming.) Python 2.0 was released on 16 October 2000, featuring many new features such as list comprehensions, cycle-detecting garbage collection, reference counting, and Unicode support. Python 2.7's end-of-life was initially set for 2015, and then postponed to 2020 out of concern that a large body of existing code could not easily be forward-ported to Python 3. It no longer receives security patches or updates. While Python 2.7 and older versions are officially unsupported, a different unofficial Python implementation, PyPy, continues to support Python 2, i.e., "2.7.18+" (plus 3.11), with the plus signifying (at least some) "backported security updates". Python 3.0 was released on 3 December 2008, and was a major revision and not completely backward-compatible with earlier versions, with some new semantics and changed syntax. Python 2.7.18, released in 2020, was the last release of Python 2. Several releases in the Python 3.x series have added new syntax to the language, and made a few (considered very minor) backward-incompatible changes. As of May 2026, Python 3.14.5 is the latest stable release. All older 3.x versions had a security update down to Python 3.9.24 then again with 3.9.25, the final version in 3.9 series. Python 3.10 is, since November 2025, the oldest supported branch. Python 3.15 has an alpha released, and Android has an official downloadable executable available for Python 3.14. Releases receive two years of full support followed by three years of security support. == Design philosophy and features == Python is a multi-paradigm programming language. Object-oriented programming and structured programming are fully supported, and many of their features support functional programming and aspect-oriented programming – including metaprogramming and metaobjects. Many other paradigms are supported via extensions, including design by contract and logic programming. Python is often referred to as a 'glue language' because it is purposely designed to be able to integrate components written in other languages. Python uses dynamic typing and a combination of reference counting and a cycle-detecting garbage collector for memory management. It uses dynamic name resolution (late binding), which binds method and variable names during program execution. Python's design offers some support for functional programming in the "Lisp tradition". It has filter, map, and reduce functions; list comprehensions, dictionaries, sets, and generator expressions. The standard library has two modules (itertools and functools) that implement functional tools borrowed from Haskell and Standard ML. Python's core philosophy is summarized in the Zen of Python (PEP 20) written by Tim Peters, which includes aphorisms such as these: Explicit is better than implicit. Simple is better than complex. Readability counts. Special cases aren't special enough to break the rules. Although practicality beats purity, errors should never pass silently, unless explicitly silenced. There should be one-- and preferably only one --obvious way to do it. However, Python has received criticism for violating these principles and adding unnecessary language bloat. Responses to these criticisms note that the Zen of Python is a guideline rather than a rule. The addition of some new features had been controversial: Guido van Rossum resigned as Benevolent Dictator for Life after conflict about adding the assignment expression operator in Python 3.8. Nevertheless, rather than building all functionality into its core, Python was designed to be highly extensible through modules. This compact modularity has made it particularly popular as a means of adding programmable interfaces to existing applications. Van Rossum's vision of a small core language with a large standard library and an easily extensible interpreter stemmed from his frustrations with ABC, which represented the opposite approach. Python claims to strive for a simpler, less-cluttered syntax and grammar, while giving developers a choice in their coding methodology. Python lacks do .. while loops, which Rossum considered harmful. In contrast to Perl's motto "there is more than one way to do it", Python advocates an approach where "there should be one – and preferably only one – obvious way to do it". In practice, however, Python provides many ways to achieve a given goal. There are at least three ways to format a string literal, with no certainty as to which one a programmer should use. Alex Martelli is a Fellow at the Python Software Foundation and Python book author; he wrote that "To describe something as 'clever' is not considered a compliment in the Python culture." Python's developers typically prioritize readability over performance. For example, they reject patches to non-critical parts of the CPython reference implementation that would offer increases in speed that do not justify the cost of clarity and readability. Execution speed can be improved by moving speed-critical functions to extension modules written in languages such as C, or by using a just-in-time compiler like PyPy. Also, it is possible to transpile to other languages. However, this approach either fails to achieve the expected speed-up, since Python is a very dynamic language, or only a restricted subset of Python is compiled (with potential minor semantic changes). Python is meant to be a fun language to use. This goal is reflected in the name – a tribute to the British comedy group Monty Python – and in playful approaches to some tutorials and reference materials. For instance, some code examples use the terms "spam" and "eggs" (in reference to a Monty Python sketch), rather than the typical terms "foo" and "bar". A common neologism in the Python community is pythonic, which has a broad range of meanings related to program style: Pythonic code may use Python idioms well; be natural or show fluency in the language; or conform with Python's minimalist philosophy and emphasis on readability. === Enhancement Proposals === Python Enhancement Proposals are a design document for either providing information to the Python community, or proposal for new feature in Python. PEPs are intented to explain new processes in Python, provide naming conventions or document the processes in the language. PEPs are overseen by Python Steering Council. There are 3 kinds of PEPs, with those are being standards track PEP, Informational PEP and Process PEPs which has their own unique meanings. They were firstly introduced in 2000, in
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FastTrack Automation Studio

FastTrack Automation Studio (formerly known as FastTrack Scripting Host), often referred to as just FastTrack, is a scripting language for Windows IT System Administrators. The product’s goal is to handle any kind of scripting that might be required to automate processes with Microsoft Windows networks. == Manufacturer == FastTrack is produced by FastTrack Software, which is headquartered in Aalborg, Denmark. The product is promoted by the manufacturer as a one-stop shop for Windows script writers and its development paradigm is “one operation = one script line”. Script writers use a purpose-built editor to create scripts, inserting script lines via menus, drag’n drop, or simply typing them in. Scripts may be used out of the box, created from scratch, imported from forums or other users, or customized from product documentation. == Types of scripts == Simple scripts include: Outlook Signatures Login scripts Backup and replication scripts Inventory and asset management Automated Windows OS installation and deployment Automated application software deployment Active Directory scripts More advanced scripts include: SCCM task sequences Citrix ICA and RDP Clients built-in Deploying applications to server farms Deploying GPO MSI files SQL Server scripts == Basic structure == Under the hood, scripts comprise commands, functions, collections, and conditions. When a script is executed these components are converted into many lines of C# code, sometimes hundreds of lines, depending on the particular script operation. Scripts can be compiled into EXE files or MSI packages and treated as standalone Windows applications. == History == FastTrack Scripting Host (FastTrack) was first developed around 2006 to ease the administration burden of IT System Administrators on Windows networks. === Product idea === The idea for the product came from founder and President of FastTrack Software, Lars Pedersen, who has a background in systems administration. Previously with Telenor, Denmark’s major telephone company, Pedersen performed various roles in systems administration, programming and web development. He also worked as a consultant and developer on several major projects at various companies in Europe. Dissatisfied from his own experiences and frustrations administering Windows networks, Pederson looked for a way to make life easier for system administrators. In particular, he wanted something that could minimize the amount of time needed each day to perform routine and mundane tasks, which was a waste of time and expertise that should have been committed to other projects. === Development === Leading a small team of developers, Pedersen developed FastTrack Scripting Host to simplify and automate the routine tasks of system administrators. The resulting product is definitely a scripting language, but it can be used intuitively like a programming language, without requiring users to learn syntax or other concepts typically associated with programming languages. === Marketing === In April 2010, FastTrack Software entered into an agreement with Binary Research International Archived 2008-10-15 at the Wayback Machine, based in the city of Milwaukee, United States to market and sell the product globally. === Awards === FSH received a Windows IT Pro Community Choice award in 2012. == Versions == The first version was produced in June 2006 and contained 51 components, which are the commands, functions, conditions and collections making up FastTrack. The following table summarizes dates and components for major releases. Companies and organizations such as NOAA, Kawasaki, and Goodyear have used and implemented the FastTrack Scripting Host. == Comparison with other scripting software == FastTrack Scripting Host Kixtart PowerShell ScriptLogic VBScript
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Scripped

Scripped was an online screenplay services company offering three services: script writing, script registration, and script coverage. Scripped did not facilitate collaboration among screenwriters. It combined with Zhura in 2010. According to Techcrunch, Scripped had more than 60,000 writers as of March 2010. Scripped was administered by Sunil Rajaraman, Ryan Buckley and Zak Freer. Actor, writer, and director Edward Burns and screenwriter Steven E. de Souza joined Scripped's Board of Advisers in May 2008. In 2008, the company formed a partnership with Write Brothers, makers of Movie Magic Screenwriter software. On March 29, 2010, Scripped announced that it closed $250,000 in private investment and merged with competitor Zhura. Scripped's CEO, Sunil Rajaraman, remains the merged company's Chief Executive Officer. On April 1, 2015, citing a serious technical failure, Scripped shuttered its service. As part of the announcement, it was disclosed that their backup servers had failed as well, losing all of its users' stored scripts. The website URL currently redirects to WriterDuet's website, another online scriptwriting service; Scripped had advertised WriterDuet in Scripped's shutdown open letter. == Features == The Scripped Writer provided a built-in screenplay template which formatted the document to a standard for scripts as recommended by the AMPAS. The screenplay document was composed of seven elements: scene, action, character, dialog, parenthetical, transition and general. Each element had a specific style to which the Scripped Writer conformed as text was entered. Like other client-side screenplay software, Scripped offered Tab-Enter toggling between screenplay elements, making the writing process much faster. Text files could be imported into the Scripped Writer and automatically conformed to the screenplay template. Completed scripts could be exported as PDF files. In May 2011 the administrators of Scripped launched Scripted.com - a sister site focused on freelance writing jobs. Subsequent to the service's launch, the company was renamed to Scripted, Inc.
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Hint (app)

Hint (hint.app) is an American software platform that provides astrological content, personality assessments, and relationship compatibility tools. The application was launched in 2018 and is based in Claymont, Delaware. The platform has been described in media coverage as part of a broader trend of astrology-based and self-reflection applications, particularly among younger users. As of 2026, the company reports that it has reached more than 25 million users worldwide. == History == Hint was founded in 2018 and is headquartered in Claymont, Delaware. The platform was developed to address a growing demand among Millennials and Gen Z for structured self-reflection tools that deviate from traditional religious or clinical psychological frameworks. The app has become a prominent figure in the "emotional technology" sector, reaching over 25 million global users by 2026. The platform is frequently cited by sociologists and media outlets as a primary driver of the Open-source intelligence trend, where individuals use digital tools to vet and analyze personal relationships in the dating economy. Media coverage has described the platform as part of a broader trend in which digital tools incorporate astrology and symbolic frameworks into wellness and relationship advice. == Reception == Coverage of Hint has appeared alongside reporting on changing attitudes toward dating and relationships, particularly among younger adults. Surveys reported by media outlets have described shifts in dating behavior, including reduced interest in casual relationships and increased reliance on digital tools for emotional reflection and compatibility assessment. Additional reporting has linked the use of astrology apps to broader trends in emotional fatigue and changing relationship expectations. Lifestyle and culture publications have described Hint, as an example of applications that integrate astrology into digital self-reflection and relationship analysis.
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Amazon Kinesis

Amazon Kinesis is a family of services provided by Amazon Web Services (AWS) for processing and analyzing real-time streaming data at a large scale. Launched in November 2013, it offers developers the ability to build applications that can consume and process data from multiple sources simultaneously. Kinesis supports multiple use cases, including real-time analytics, log and event data collection, and real-time processing of data generated by IoT devices. == History == Amazon Kinesis was launched by Amazon Web Services (AWS) in November 2013 as a managed service for processing and analyzing real-time streaming data at a large scale. The service was introduced to address the growing need for businesses to process and analyze data as it was generated, rather than in batches, allowing for real-time insights and decision-making. Since its launch, the Amazon Kinesis family of services has expanded to include four main components: Kinesis Data Streams, Kinesis Data Firehose, Kinesis Data Analytics, and Kinesis Video Streams. Each of these components serves a specific purpose in the processing and analysis of real-time streaming data. In August 2015, AWS announced the availability of Kinesis Data Firehose, a fully managed service for delivering real-time streaming data to destinations such as Amazon S3, Amazon Redshift, and Amazon Elasticsearch. A year later in August 2016, AWS launched Kinesis Data Analytics, enabling customers to analyze streaming data in real time using standard SQL queries. AWS introduced Kinesis Video Streams, a fully managed service for securely capturing, processing, and storing video streams for analytics and machine learning applications, was introduced by AWS in November 2017. == Components == Amazon Kinesis is composed of four main services: Kinesis Data Streams, Kinesis Data Firehose, Kinesis Data Analytics, and Kinesis Video Streams. === Kinesis Data Streams === Kinesis Data Streams is a scalable and durable real-time data streaming service that captures and processes gigabytes of data per second from multiple sources. It enables the storage and processing of data in real time, making it useful for applications that require immediate insights, such as monitoring and alerting. === Kinesis Data Firehose === Kinesis Data Firehose is a fully managed service for delivering real-time streaming data to destinations such as Amazon S3, Amazon Redshift, Amazon Elasticsearch, and AWS-partner data stores. With Data Firehose, users can configure and scale data delivery without manual intervention. === Kinesis Data Analytics === Kinesis Data Analytics enables the analysis of streaming data in real time using standard SQL or Apache Flink. === Kinesis Video Streams === Kinesis Video Streams is a fully managed service for securely capturing, processing, and storing video streams for analytics and machine learning. It supports multiple video codecs and streaming protocols, making it suitable for various use cases, such as security and surveillance, video-enabled IoT devices, and live event broadcasting. == Integration == Amazon Kinesis can be easily integrated with other AWS services, such as AWS Lambda, Amazon S3, Amazon Redshift, and Amazon OpenSearch. This integration enables developers to build end-to-end streaming data processing applications, taking advantage of the extensive AWS ecosystem. == Use cases == Some common use cases for Amazon Kinesis include: Real-time analytics: Analyzing streaming data in real time to provide immediate insights and make data-driven decisions. Log and event data collection: Collecting, processing, and analyzing log and event data generated by applications, infrastructure, and devices. IoT data processing: Processing and analyzing large volumes of data generated by IoT devices in real time. Machine learning: Ingesting and processing video streams for machine learning applications, such as object recognition, facial recognition, and sentiment analysis. == Pricing == Amazon Kinesis follows a pay-as-you-go pricing model, with costs depending on the chosen service, data volume, and processing power required. AWS provides a free tier for Kinesis Data Streams and Kinesis Data Firehose, allowing users to get started with the services at no cost.
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MyPoolin

Mypoolin is a mobile peer-to-peer and group payment application. Their software allows the settling of debts and group-expenditure for events and activities. The software utilizes Unified Payment Interface of India to collect and settle daily expenses with friends. Users can also plan and pay together for group-gifting, movies, vacations, concerts, events, and parties. == Service == Mypoolin is a mobile payment provider that lets its users transfer money to other users via their mobile number. A user can create an account by verifying an OTP code which is sent to his mobile phone. It also allows the users to track their friends’ activities on the app. == History == Mypoolin was founded by Rohit Taneja (IIT Delhi) and Ankit Singh (FMS Delhi) in 2014 as a medium to aggregate money for various purposes in a hassle free and quick manner. Prior to the mobile app launch, Mypoolin was initially launched as a web application. == Funding == Mypoolin has been seed funded by angel investors. As winners of the QPrize 2015, Mypoolin jointly received an additional funding of $250,000 from Qualcomm Ventures. == Growth == Mypoolin reached INR 10 lakhs in revenue during its first four months of the web application launch, and was listed in the "Top ten free apps" in its category within the first 5 days of the Android app launch. It was one of the Top 50 start-ups in Asia at the Echelon Asia Summit held in Singapore. And among the top 3 start-ups in 1776 Cup Challenge 2016. Apple Inc also featured the app on their app store in India. == Features == Users are able to collect and share money on the app for daily uses like movies, events and trips. The money collected can then be redeemed in the form of an online voucher redeemable across several e-commerce sites. The amount can be redeemed also in the form of an offline debit card delivered to the address or in the form of a wire transfer. == Media coverage == Mypoolin was featured in The Economic Times and The Hindu Business Line after winning the Qualcomm Ventures' QPrize 2015. Digit magazine featured them recently as the app of the week. The app has mostly grown organically so far in the Indian urban millennial space.
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Gemini Enterprise Agent Platform

Gemini Enterprise Agent Platform (formerly known as Vertex AI) is a managed machine learning (ML) and artificial intelligence (AI) platform developed by Google Cloud. It provides a unified environment for building, training, deploying, and scaling ML models and generative AI applications. The platform integrates tools for the full ML lifecycle, including data preparation, model training, evaluation, deployment, and monitoring, under a single API and user interface. Vertex AI was announced at Google I/O and released as a generally available product on May 18, 2021. At launch, Google described Vertex AI as unifying its AutoML offerings with its prior Cloud AI Platform capabilities, and as adding operational features intended to help teams move models from experimentation into production use. On April 22, 2026, Google announced Gemini Enterprise Agent Platform as the replacement evolution of Vertex AI. == History == Google Cloud announced the general availability of Vertex AI on May 18, 2021, at the Google I/O developer conference. The platform was designed to consolidate Google Cloud's previously separate ML offerings, including AutoML and the legacy AI Platform, into a single system. At launch, Google claimed that Vertex AI required roughly 80% fewer lines of code to train a model compared to competing platforms. In June 2023, Google made generative AI support in Vertex AI generally available, giving developers access to foundation models including PaLM 2, Imagen, and Codey through the platform's Model Garden and the newly launched Generative AI Studio. At the time of this launch, Model Garden included over 60 models from Google and its partners. In August 2023, at the Google Cloud Next conference, Google announced further updates to Vertex AI, including the addition of third-party models such as Claude 2 from Anthropic and Llama 2 from Meta to the Model Garden, as well as new tools called Vertex AI Extensions for connecting models to APIs for real-time data retrieval. At the same event, Vertex AI Search and Conversation were made generally available, providing enterprise search and chatbot capabilities powered by foundation models. In April 2024, at Google Cloud Next, the company introduced Vertex AI Agent Builder, a no-code tool for creating AI-powered conversational agents built on top of Gemini large language models. This brought together the existing Vertex AI Search and Conversation products with new developer tools for building generative AI experiences. == Features == === Model training === Vertex AI supports both AutoML, which enables code-free model training on tabular, image, text, or video data, and custom training, which gives users full control over the ML framework, training code, and hyperparameter tuning. The platform provides serverless training as well as dedicated training clusters with GPU and TPU accelerators. Vertex AI Vizier handles automatic hyperparameter tuning, and Vertex AI Experiments allows comparison and tracking of training runs. === Model Garden === The Vertex AI Model Garden is a curated catalog of over 200 enterprise-ready models, including Google's own foundation models (such as Gemini, Imagen, and Veo), third-party models (such as Anthropic's Claude and Mistral AI models), and popular open-source models (such as Llama and Gemma). Models are accessible as fully managed model-as-a-service APIs. === Pipelines (workflow orchestration) === Vertex AI Pipelines provides managed orchestration of ML workflows and supports pipelines built with the Kubeflow Pipelines SDK, among other options described in Google Cloud documentation. === Vertex AI Studio === Vertex AI Studio provides tools for prompt design, testing, and model management, allowing developers to prototype and build generative AI applications using natural language, code, images, or video. === Agent Builder and Agent Engine === Vertex AI Agent Builder is a suite of products for building, deploying, and governing AI agents in production environments. It supports development with the open-source Agent Development Kit (ADK) and other frameworks. Vertex AI Agent Engine provides the underlying infrastructure for deploying and scaling agents, with support for enterprise security features including HIPAA compliance, customer-managed encryption keys (CMEK), and VPC Service Controls. === Generative AI tooling and model access === Google markets Vertex AI as providing access to Google foundation models (including the Gemini family) and developer tools such as Vertex AI Studio, along with a model catalog that includes Google and selected open source models (marketed as "Model Garden"). Google has also offered products within Vertex AI aimed at building generative search and conversational applications, including offerings named "Vertex AI Search" and "Vertex AI Conversation" as reported in 2023 coverage of platform updates. === MLOps tools === The platform includes a range of MLOps capabilities: Vertex AI Pipelines for orchestrating and automating ML workflows as reusable pipelines. Vertex AI Feature Store for serving, sharing, and reusing ML features across projects. Vertex AI Model Registry for storing, versioning, and managing trained models. Vertex AI Model Monitoring for detecting training-serving skew and inference drift in deployed models. Vertex Explainable AI for interpreting model predictions. Vertex AI Workbench for managed JupyterLab notebook environments integrated with Google Cloud Storage and BigQuery. == Industry recognition == Google was named a Leader for the fifth consecutive year in the 2024 Gartner Magic Quadrant for Cloud AI Developer Services, a recognition that encompasses Vertex AI and its related offerings. Google was also recognized as a Leader in the 2024 Gartner Magic Quadrant for Data Science and Machine Learning Platforms and was named a Leader in the Forrester Wave for AI/ML Platforms, Q3 2024. In October 2025, Google was also named a Leader in the 2025 IDC (International Data Corporation) MarketScape for Worldwide GenAI Life-Cycle Foundation Model Software. == Pricing == Vertex AI uses a pay-as-you-go pricing model, with costs determined by the specific services consumed, including model training, prediction serving, and data storage. For generative AI tasks, pricing is based on a per-token model, with rates varying depending on the specific model used and whether tokens are input or output. Google offers a free tier for new users, which includes limited custom training hours and online prediction usage, along with an introductory US$300 in Google Cloud credits valid for 90 days. == Adoption == In the year following its 2021 launch, Google reported that usage of Vertex AI and BigQuery had driven 2.5 times more machine learning predictions compared to the prior year, and that active customers of Vertex AI Workbench had grown 25-fold over a six-month period. Early enterprise adopters included Ford, Wayfair, and Seagate, among others. Wayfair reported that it was able to run large model training jobs 5 to 10 times faster using the platform.
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MobileNet

MobileNet is a family of convolutional neural network (CNN) architectures designed for image classification, object detection, and other computer vision tasks. They are designed for small size, low latency, and low power consumption, making them suitable for on-device inference and edge computing on resource-constrained devices like mobile phones and embedded systems. They were originally designed to be run efficiently on mobile devices with TensorFlow Lite. The need for efficient deep learning models on mobile devices led researchers at Google to develop MobileNet. As of June 2025, the family has five versions, each improving upon the previous one in terms of performance and efficiency. == Features == === V1 === MobileNetV1 was published in April 2017. Its main architectural innovation was incorporation of depthwise separable convolutions. It was first developed by Laurent Sifre during an internship at Google Brain in 2013 as an architectural variation on AlexNet to improve convergence speed and model size. The depthwise separable convolution decomposes a single standard convolution into two convolutions: a depthwise convolution that filters each input channel independently and a pointwise convolution ( 1 × 1 {\displaystyle 1\times 1} convolution) that combines the outputs of the depthwise convolution. This factorization significantly reduces computational cost. The MobileNetV1 has two hyperparameters: a width multiplier α {\displaystyle \alpha } that controls the number of channels in each layer. Smaller values of α {\displaystyle \alpha } lead to smaller and faster models, but at the cost of reduced accuracy, and a resolution multiplier ρ {\displaystyle \rho } , which controls the input resolution of the images. Lower resolutions result in faster processing but potentially lower accuracy. === V2 === MobileNetV2 was published in March 2019. It uses inverted residual layers and linear bottlenecks. Inverted residuals modify the traditional residual block structure. Instead of compressing the input channels before the depthwise convolution, they expand them. This expansion is followed by a 1 × 1 {\displaystyle 1\times 1} depthwise convolution and then a 1 × 1 {\displaystyle 1\times 1} projection layer that reduces the number of channels back down. This inverted structure helps to maintain representational capacity by allowing the depthwise convolution to operate on a higher-dimensional feature space, thus preserving more information flow during the convolutional process. Linear bottlenecks removes the typical ReLU activation function in the projection layers. This was rationalized by arguing that that nonlinear activation loses information in lower-dimensional spaces, which is problematic when the number of channels is already small. === V3 === MobileNetV3 was published in 2019. The publication included MobileNetV3-Small, MobileNetV3-Large, and MobileNetEdgeTPU (optimized for Pixel 4). They were found by a form of neural architecture search (NAS) that takes mobile latency into account, to achieve good trade-off between accuracy and latency. It used piecewise-linear approximations of swish and sigmoid activation functions (which they called "h-swish" and "h-sigmoid"), squeeze-and-excitation modules, and the inverted bottlenecks of MobileNetV2. === V4 === MobileNetV4 was published in September 2024. The publication included a large number of architectures found by NAS. Inspired by Vision Transformers, the V4 series included multi-query attention. It also unified both inverted residual and inverted bottleneck from the V3 series with the "universal inverted bottleneck", which includes these two as special cases. === V5 === MobileNetV5's architecture was published shortly after the release of Gemma 3n in June 2025. While the announcement stated a technical report on MobileNetV5 would be available soon, this has not yet materialised. The network is 10 times larger than the largest V4 variant.
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Visual Expert

Visual Expert is a static code analysis tool, extracting design and technical information from software source code by reverse-engineering, used by programmers for software maintenance, modernization or optimization. It is designed to parse several programming languages at the same time (PL/SQL, Transact-SQL, PowerBuilder...) and analyze cross-language dependencies, in addition to each language's source code. Visual Expert checks source code against hundreds of code inspection rules for vulnerability assessment, bug fix, and maintenance issues. == Features == Cross-references exploration: Impact Analysis, E/R diagrams, call graphs, CRUD matrix, dependency graphs. Software documentation: a documentation generator produces technical documentation and low-level design descriptions. Inspect the code to detect bugs, security vulnerabilities and maintainability issues. Native integration with Jenkins. Reports on duplicate code, unused objects and methods and naming conventions. Calculates software metrics and source lines of code. Code comparison: finds differences between several versions of the same code. Performance analysis: identifies code parts that slow down the application because of their syntax - it extracts statistics about code execution from the database and combines it with the static analysis of the code. == Usage == Visual Expert is used in several contexts: Change impact analysis: evaluating the consequences of a change in the code or in a database. Avoiding negative side effects when evolving a system. Static Application Security Testing (SAST): detecting and removing security issues. Continuous Integration / Continuous Inspection : adding a static code analysis job in a CI/CD workflow to automatically verify the quality and security of a new build when it is released. Program comprehension: helping programmers understand and maintain existing code, or modernize legacy systems. Transferring knowledge of the code, from one programmer to another. Software sizing: calculating the size of an application, or a piece of code, in order to estimate development efforts. Code review: improving the code by finding and removing code smells, dead code, code causing poor performances or violations of coding conventions. == Limitations == As a static code analyzer, Visual Expert is limited to the programming languages supported by its code parsers - Oracle PL/SQL, SQL Server Transact-SQL, PowerBuilder. A preliminary reverse engineering is required. Visual Expert does it automatically, but its duration depends on the size of the code parsed. Users must wait for the parsing completion prior to using the features, or schedule it in advance. They must also allocate sufficient hardware resources to support their volume of code. Visual Expert is based on a client/server architecture: the code analysis is running on a Windows PC - preferably a server. The information extracted from the code is stored in a RDBMS, communicating with a client application installed on the programmer's computer - no web client is available. This requires that the code, the parsers, the RDBMS and the programmers’ computers are connected to the same LAN or VPN. == History == 1995- 1998 - Prog and Doc - Initial version distributed on the French market 2001 - Visual Expert 4.5 2003 - Visual Expert 5 2007 - Visual Expert 5.7 2010 - Visual Expert 6.0 2015 - Visual Expert 2015 - Server component added to schedule code analyses 2016 - Visual Expert 2016 - Oracle PL/SQL code parser, code inventory (lines of code, number of objects…) 2017 - Visual Expert 2017 - SQL Server T-SQL code parser, Code comparison, CRUD matrix 2018 - Visual Expert 2018 - DB Code Performance Analysis, integration with TFS 2019 - Visual Expert 2019 - Generation of E/R diagrams from the code 2020 - Visual Expert 2020 - Object dependency matrix, naming consistency verification, integration with GIT and SVN 2021 - Visual Expert 2021 - Continuous Code Inspection, integration with Jenkins 2022 - Visual Expert 2022 - Support for cloud-based repositories and large volumes of code 2023 - Visual Expert 2023 - Performance tuning for PowerBuilder 2024 - Visual Expert 2024 - New web UI to simplify deployment and use among large teams. 2025 - Visual Expert 2025 - AI-based features to explain code, generate comments, and optimize queries
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Bright Computing

Bright Computing, Inc. was a developer of software for deploying and managing high-performance (HPC) clusters, Kubernetes clusters, and OpenStack private clouds in on-premises data centers as well as in the public cloud. In 2022, it was acquired by Nvidia. == History == Bright Computing was founded by Matthijs van Leeuwen in 2009, who spun the company out of ClusterVision, which he had co-founded with Alex Ninaber and Arijan Sauer. Alex and Matthijs had worked together at UK’s Compusys, which was one of the first companies to commercially build HPC clusters. They left Compusys in 2002 to start ClusterVision in the Netherlands, after determining there was a growing market for building and managing supercomputer clusters using off-the-shelf hardware components and open source software, tied together with their own customized scripts. ClusterVision also provided delivery and installation support services for HPC clusters at universities and government entities. In 2004, Martijn de Vries joined ClusterVision and began development of cluster management software. The software was made available to customers in 2008, under the name ClusterVisionOS v4. In 2009, Bright Computing was spun out of ClusterVision. ClusterVisionOS was renamed Bright Cluster Manager, and van Leeuwen was named Bright Computing’s CEO. In February 2016, Bright appointed Bill Wagner as chief executive officer. Matthijs van Leeuwen became chief strategy officer, and then left the company and board of directors in 2018. In January 2022 Bright was acquired by Nvidia. Nvidia cited using Bright's Amsterdam facility as a development center. The acquisition occurred after several layoffs under Bill Wagner. == Customers == Early customers included Boeing, Sandia National Laboratories, Virginia Tech, Hewlett Packard, NSA, and Drexel University. Many early customers were introduced through resellers, including SICORP, Cray, Dell, and Advanced HPC. As of 2019, the company had more than 700 customers, including more than fifty Fortune 500 Companies. == Products and services == Bright Cluster Manager for HPC lets customers deploy and manage complete clusters. It provides management for the hardware, the operating system, the HPC software, and users. In 2014, the company announced Bright OpenStack, software to deploy, provision, and manage OpenStack-based private cloud infrastructures. In 2016, Bright started bundling several machine learning frameworks and associated tools and libraries with the product, to make it very easy to get machine learning workload up and running on a Bright cluster. In December 2018, version 8.2 was released, which introduced support for the ARM64 architecture, edge capabilities to build clusters spread out over many different geographical locations, improved workload accounting & reporting features, as well as many improvements to Bright's integration with Kubernetes. Bright Cluster Manager software was frequently sold through original equipment manufacturer (OEM) resellers, including Dell and HPE. In version 10, Bright Cluster Manager was merged into the NVIDIA Base Command Manager. Bright Computing was covered by Software Magazine and Yahoo! Finance, among other publications. == Awards == In 2016, Bright Computing was awarded a €1.5M Horizon 2020 SME Instrument grant from the European Commission. Bright Computing was one of only 33 grant recipients from 960 submitted proposals. In its category only 5 out of 260 grants were awarded. 2015 HPCwire Editor’s Choice Award for “Best HPC Cluster Solution or Technology" Main Software 50 “Highest Growth” award winner, 2013 Deloitte Technology Fast50 “Rising Star 2013” award winner Bio-IT World Conference & Expo ‘13, Boston, MA, winner of “IT Hardware & Infrastructure” category of the “Best of Show Award” program Red Herring Top 100 Global Award, 2013
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Anaconda (Python distribution)

Anaconda is an open source data science and artificial intelligence distribution platform for the Python programming language. Developed by Anaconda, Inc., an American company founded in 2012, the platform is used to develop and manage data science and AI projects. In 2024, Anaconda Inc. has about 300 employees and 45 million users. == History == Co-founded in Austin, Texas in 2012 as Continuum Analytics by Peter Wang and Travis Oliphant, Anaconda Inc. operates from the United States and Europe. Anaconda Inc. developed Conda, a cross-platform, language-agnostic binary package manager. It also launched PyData community workshops and the Jupyter Cloud Notebook service (Wakari.io). In 2013, it received funding from DARPA. In 2015, the company had two million users including 200 of the Fortune 500 companies and raised $24 million in a Series A funding round led by General Catalyst and BuildGroup. Anaconda secured an additional $30 million in funding in 2021. Continuum Analytics rebranded as Anaconda in 2017. That year, it announced the release of Anaconda Enterprise 5, an integration with Microsoft Azure, and had over 13 million users by year's end. In 2022, it released Anaconda Business; new integrations with Snowflake and others; and the open-source PyScript. It also acquired PythonAnywhere, while Anaconda's user base exceeded 30 million in 2022. In 2023, Anaconda released Python in Excel, a new integration with Microsoft Excel, and launched PyScript.com. The company made a series of investments in AI during 2024. That February, Anaconda partnered with IBM to import its repository of Python packages into Watsonx, IBM's generative AI platform. The same year, Anaconda joined IBM's AI Alliance and released an integration with Teradata and Lenovo. In 2024, Anaconda's user base reached 45 million users and Barry Libert was named company CEO, after serving on Anaconda's board of directors. He was succeeded as CEO in October 2025 by David DeSanto, who also became a company director. In May 2025, the company introduced the first unified AI platform for Open Source, Anaconda AI Platform, a central control for AI workflows that enables customization in Python-based enterprise AI development. That July, after reaching over $150 million in a Series C funding round, Anaconda was evaluated at about $1.5 billion. == Overview == Anaconda distribution comes with over 300 packages automatically installed, and over 7,500 additional open-source packages can be installed from the Anaconda repository as well as the Conda package and virtual environment manager. It also includes a GUI, Anaconda Navigator, as a graphical alternative to the command-line interface (CLI). Conda was developed to address dependency conflicts native to the pip package manager, which would automatically install any dependent Python packages without checking for conflicts with previously installed packages (until its version 20.3, which later implemented consistent dependency resolution). The Conda package manager's historical differentiation analyzed and resolved these installation conflicts. Anaconda is a distribution of the Python programming language (and previously also R) for scientific computing (data science, machine learning applications, large-scale data processing, predictive analytics, etc.), that aims to simplify package management and deployment. Anaconda distribution includes data-science packages suitable for Windows, Linux, and macOS. Other company products include Anaconda Free, and subscription-based Starter, Business and Enterprise. Anaconda's business tier offers Package Security Manager. Package versions in Anaconda are managed by the package management system Conda, which was spun out as a separate open-source package as useful both independently and for applications other than Python. There is also a small, bootstrap version of Anaconda called Miniconda, which includes only Conda, Python, the packages they depend on, and a small number of other packages. Open source packages can be individually installed from the Anaconda repository, Anaconda Cloud (anaconda.org), or the user's own private repository or mirror, using the conda install command. Anaconda, Inc. compiles and builds the packages available in the Anaconda repository itself, and provides binaries for Windows 32/64 bit, Linux 64 bit and MacOS 64-bit (Intel, Apple Silicon). Anything available on PyPI may be installed into a Conda environment using pip, and Conda will keep track of what it has installed and what pip has installed. Custom packages can be made using the conda build command, and can be shared with others by uploading them to Anaconda Cloud, PyPI or other repositories. The default installation of Anaconda2 includes Python 2.7 and Anaconda3 includes Python 3.7. However, it is possible to create new environments that include any version of Python packaged with Conda. === Anaconda Navigator === Anaconda Navigator is a desktop graphical user interface (GUI) included in Anaconda distribution that allows users to launch applications and manage Conda packages, environments and channels without using command-line commands. Navigator can search for packages on Anaconda Cloud or in a local Anaconda Repository, install them in an environment, run the packages and update them. It is available for Windows, macOS and Linux. The following applications are available by default in Navigator: JupyterLab Jupyter Notebook QtConsole Spyder Glue Orange RStudio Visual Studio Code === Conda === Conda is an open source, cross-platform, language-agnostic package manager and environment management system that installs, runs, and updates packages and their dependencies. It was created for Python programs, but it can package and distribute software for any language, including multi-language projects. The Conda package and environment manager is included in all versions of Anaconda, Miniconda, and Anaconda Repository. == Anaconda.org == Anaconda Cloud is a package management service by Anaconda where users can find, access, store and share public and private notebooks, environments, and Conda and PyPI packages. Cloud hosts useful Python packages, notebooks and environments for a wide variety of applications. Users do not need to log in or to have a Cloud account, to search for public packages, download and install them. Users can build new Conda packages using Conda-build and then use the Anaconda Client CLI to upload packages to Anaconda.org. Notebooks users can be aided with writing and debugging code with Anaconda's AI Assistant.
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Tuber (app)

Tuber (Chinese: Tuber浏览器) was a web browser mobile app developed by Shanghai Fengxuan Information Technology that allowed users within mainland China to view filtered versions of certain websites normally blocked by the Great Firewall. Filtered versions of websites such as Google, Facebook, Instagram, YouTube, Twitter, Netflix, IMDb, and Wikipedia could be viewed. The app was backed by cybersecurity company Qihoo 360 which served as the parent company. The app required phone number registration. Sensitive keywords were blocked by the app. On October 9, 2020, Global Times editor Rita Bai Yunyi tweeted that the move represented "a great step for China's opening up". The app was removed from China domestic app stores and operations ceased as of October 10, 2020. On October 12, when questioned by a Bloomberg News reporter on the topic, Foreign Ministry spokesperson Zhao Lijian replied, "This is not a diplomatic issue, and I do not have the relevant information you mentioned. China has always managed the Internet in accordance with the law. I suggest you ask the competent department for the specific situation."
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Azure Stream Analytics

Microsoft Azure Stream Analytics is a serverless scalable complex event processing engine by Microsoft that enables users to develop and run real-time analytics on multiple streams of data from sources such as devices, sensors, web sites, social media, and other applications. Users can set up alerts to detect anomalies, predict trends, trigger necessary workflows when certain conditions are observed, and make data available to other downstream applications and services for presentation, archiving, or further analysis. == Query Language == Users can author real-time analytics using a simple declarative SQL-like language with embedded support for temporal logic. Callouts to custom code with JavaScript user defined functions extend the streaming logic written in SQL. Callouts to Azure Machine Learning helps with predictive scoring on streaming data. == Scalability == Azure Stream Analytics is a serverless job service on Azure that eliminates the need for infrastructure, servers, virtual machines, or managed clusters. Users only pay for the processing used for the running jobs. == IoT applications == Azure Stream Analytics integrates with Azure IoT Hub to enable real-time analytics on data from IoT devices and applications. == Real-time Dashboards == Users can build real-time dashboards with Power BI for a live command and control view. Real-time dashboards help transform live data into actionable and insightful visuals. == Data Input Sources == Stream Analytics supports three different types of input sources - Azure Event Hubs, Azure IoT Hubs, and Azure Blob Storage. Additionally, stream analytics supports Azure Blob storage as the input reference data to help augment fast moving event data streams with static data. Stream analytics supports a wide variety of output targets. Support for Power BI allows for real-time dashboarding. Event Hub, Service bus topics and queues help trigger downstream workflows. Support for Azure Table Storage, Azure SQL Databases, Azure SQL Data Warehouse, Azure SQL, Document DB, Azure Data Lake Store enable a variety of downstream analysis and archiving capabilities.
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Model-based clustering

In statistics, cluster analysis is the algorithmic grouping of objects into homogeneous groups based on numerical measurements. Model-based clustering based on a statistical model for the data, usually a mixture model. This has several advantages, including a principled statistical basis for clustering, and ways to choose the number of clusters, to choose the best clustering model, to assess the uncertainty of the clustering, and to identify outliers that do not belong to any group. == Model-based clustering == Suppose that for each of n {\displaystyle n} observations we have data on d {\displaystyle d} variables, denoted by y i = ( y i , 1 , … , y i , d ) {\displaystyle y_{i}=(y_{i,1},\ldots ,y_{i,d})} for observation i {\displaystyle i} . Then model-based clustering expresses the probability density function of y i {\displaystyle y_{i}} as a finite mixture, or weighted average of G {\displaystyle G} component probability density functions: p ( y i ) = ∑ g = 1 G τ g f g ( y i ∣ θ g ) , {\displaystyle p(y_{i})=\sum _{g=1}^{G}\tau _{g}f_{g}(y_{i}\mid \theta _{g}),} where f g {\displaystyle f_{g}} is a probability density function with parameter θ g {\displaystyle \theta _{g}} , τ g {\displaystyle \tau _{g}} is the corresponding mixture probability where ∑ g = 1 G τ g = 1 {\displaystyle \sum _{g=1}^{G}\tau _{g}=1} . Then in its simplest form, model-based clustering views each component of the mixture model as a cluster, estimates the model parameters, and assigns each observation to cluster corresponding to its most likely mixture component. === Gaussian mixture model === The most common model for continuous data is that f g {\displaystyle f_{g}} is a multivariate normal distribution with mean vector μ g {\displaystyle \mu _{g}} and covariance matrix Σ g {\displaystyle \Sigma _{g}} , so that θ g = ( μ g , Σ g ) {\displaystyle \theta _{g}=(\mu _{g},\Sigma _{g})} . This defines a Gaussian mixture model. The parameters of the model, τ g {\displaystyle \tau _{g}} and θ g {\displaystyle \theta _{g}} for g = 1 , … , G {\displaystyle g=1,\ldots ,G} , are typically estimated by maximum likelihood estimation using the expectation-maximization algorithm (EM); see also EM algorithm and GMM model. Bayesian inference is also often used for inference about finite mixture models. The Bayesian approach also allows for the case where the number of components, G {\displaystyle G} , is infinite, using a Dirichlet process prior, yielding a Dirichlet process mixture model for clustering. === Choosing the number of clusters === An advantage of model-based clustering is that it provides statistically principled ways to choose the number of clusters. Each different choice of the number of groups G {\displaystyle G} corresponds to a different mixture model. Then standard statistical model selection criteria such as the Bayesian information criterion (BIC) can be used to choose G {\displaystyle G} . The integrated completed likelihood (ICL) is a different criterion designed to choose the number of clusters rather than the number of mixture components in the model; these will often be different if highly non-Gaussian clusters are present. === Parsimonious Gaussian mixture model === For data with high dimension, d {\displaystyle d} , using a full covariance matrix for each mixture component requires estimation of many parameters, which can result in a loss of precision, generalizabity and interpretability. Thus it is common to use more parsimonious component covariance matrices exploiting their geometric interpretation. Gaussian clusters are ellipsoidal, with their volume, shape and orientation determined by the covariance matrix. Consider the eigendecomposition of a matrix Σ g = λ g D g A g D g T , {\displaystyle \Sigma _{g}=\lambda _{g}D_{g}A_{g}D_{g}^{T},} where D g {\displaystyle D_{g}} is the matrix of eigenvectors of Σ g {\displaystyle \Sigma _{g}} , A g = diag { A 1 , g , … , A d , g } {\displaystyle A_{g}={\mbox{diag}}\{A_{1,g},\ldots ,A_{d,g}\}} is a diagonal matrix whose elements are proportional to the eigenvalues of Σ g {\displaystyle \Sigma _{g}} in descending order, and λ g {\displaystyle \lambda _{g}} is the associated constant of proportionality. Then λ g {\displaystyle \lambda _{g}} controls the volume of the ellipsoid, A g {\displaystyle A_{g}} its shape, and D g {\displaystyle D_{g}} its orientation. Each of the volume, shape and orientation of the clusters can be constrained to be equal (E) or allowed to vary (V); the orientation can also be spherical, with identical eigenvalues (I). This yields 14 possible clustering models, shown in this table: It can be seen that many of these models are more parsimonious, with far fewer parameters than the unconstrained model that has 90 parameters when G = 4 {\displaystyle G=4} and d = 9 {\displaystyle d=9} . Several of these models correspond to well-known heuristic clustering methods. For example, k-means clustering is equivalent to estimation of the EII clustering model using the classification EM algorithm. The Bayesian information criterion (BIC) can be used to choose the best clustering model as well as the number of clusters. It can also be used as the basis for a method to choose the variables in the clustering model, eliminating variables that are not useful for clustering. Different Gaussian model-based clustering methods have been developed with an eye to handling high-dimensional data. These include the pgmm method, which is based on the mixture of factor analyzers model, and the HDclassif method, based on the idea of subspace clustering. The mixture-of-experts framework extends model-based clustering to include covariates. == Example == We illustrate the method with a dateset consisting of three measurements (glucose, insulin, sspg) on 145 subjects for the purpose of diagnosing diabetes and the type of diabetes present. The subjects were clinically classified into three groups: normal, chemical diabetes and overt diabetes, but we use this information only for evaluating clustering methods, not for classifying subjects. The BIC plot shows the BIC values for each combination of the number of clusters, G {\displaystyle G} , and the clustering model from the Table. Each curve corresponds to a different clustering model. The BIC favors 3 groups, which corresponds to the clinical assessment. It also favors the unconstrained covariance model, VVV. This fits the data well, because the normal patients have low values of both sspg and insulin, while the distributions of the chemical and overt diabetes groups are elongated, but in different directions. Thus the volumes, shapes and orientations of the three groups are clearly different, and so the unconstrained model is appropriate, as selected by the model-based clustering method. The classification plot shows the classification of the subjects by model-based clustering. The classification was quite accurate, with a 12% error rate as defined by the clinical classification. Other well-known clustering methods performed worse with higher error rates, such as single-linkage clustering with 46%, average link clustering with 30%, complete-linkage clustering also with 30%, and k-means clustering with 28%. == Outliers in clustering == An outlier in clustering is a data point that does not belong to any of the clusters. One way of modeling outliers in model-based clustering is to include an additional mixture component that is very dispersed, with for example a uniform distribution. Another approach is to replace the multivariate normal densities by t {\displaystyle t} -distributions, with the idea that the long tails of the t {\displaystyle t} -distribution would ensure robustness to outliers. However, this is not breakdown-robust. A third approach is the "tclust" or data trimming approach which excludes observations identified as outliers when estimating the model parameters. == Non-Gaussian clusters and merging == Sometimes one or more clusters deviate strongly from the Gaussian assumption. If a Gaussian mixture is fitted to such data, a strongly non-Gaussian cluster will often be represented by several mixture components rather than a single one. In that case, cluster merging can be used to find a better clustering. A different approach is to use mixtures of complex component densities to represent non-Gaussian clusters. == Non-continuous data == === Categorical data === Clustering multivariate categorical data is most often done using the latent class model. This assumes that the data arise from a finite mixture model, where within each cluster the variables are independent. === Mixed data === These arise when variables are of different types, such as continuous, categorical or ordinal data. A latent class model for mixed data assumes local independence between the variable. The location model relaxes the local independence assumption. The clustMD approach assumes that the observed variables are manifestations of underlying continuous Gaussian latent
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