A class of sets is said to shatter another set if it is possible to "pick out" any element of that set using intersection. The concept of shattered sets plays an important role in Vapnik–Chervonenkis theory, also known as VC-theory. Shattering and VC-theory are used in the study of empirical processes as well as in statistical computational learning theory. == Definition == Suppose A is a set and C is a class of sets. The class C shatters the set A if for each subset a of A, there is some element c of C such that a = c ∩ A . {\displaystyle a=c\cap A.} Equivalently, C shatters A when their intersection is equal to A's power set: P(A) = { c ∩ A | c ∈ C }. We employ the letter C to refer to a "class" or "collection" of sets, as in a Vapnik–Chervonenkis class (VC-class). The set A is often assumed to be finite because, in empirical processes, we are interested in the shattering of finite sets of data points. == Example == We will show that the class of all discs in the plane (two-dimensional space) does not shatter every set of four points on the unit circle, yet the class of all convex sets in the plane does shatter every finite set of points on the unit circle. Let A be a set of four points on the unit circle and let C be the class of all discs. To test where C shatters A, we attempt to draw a disc around every subset of points in A. First, we draw a disc around the subsets of each isolated point. Next, we try to draw a disc around every subset of point pairs. This turns out to be doable for adjacent points, but impossible for points on opposite sides of the circle. Any attempt to include those points on the opposite side will necessarily include other points not in that pair. Hence, any pair of opposite points cannot be isolated out of A using intersections with class C and so C does not shatter A. As visualized below: Because there is some subset which can not be isolated by any disc in C, we conclude then that A is not shattered by C. And, with a bit of thought, we can prove that no set of four points is shattered by this C. However, if we redefine C to be the class of all elliptical discs, we find that we can still isolate all the subsets from above, as well as the points that were formerly problematic. Thus, this specific set of 4 points is shattered by the class of elliptical discs. Visualized below: With a bit of thought, we could generalize that any set of finite points on a unit circle could be shattered by the class of all convex sets (visualize connecting the dots). == Shatter coefficient == To quantify the richness of a collection C of sets, we use the concept of shattering coefficients (also known as the growth function). For a collection C of sets s ⊂ Ω {\displaystyle s\subset \Omega } , Ω {\displaystyle \Omega } being any space, often a sample space, we define the nth shattering coefficient of C as S C ( n ) = max ∀ x 1 , x 2 , … , x n ∈ Ω card { { x 1 , x 2 , … , x n } ∩ s , s ∈ C } {\displaystyle S_{C}(n)=\max _{\forall x_{1},x_{2},\dots ,x_{n}\in \Omega }\operatorname {card} \{\,\{\,x_{1},x_{2},\dots ,x_{n}\}\cap s,s\in C\}} where card {\displaystyle \operatorname {card} } denotes the cardinality of the set and x 1 , x 2 , … , x n ∈ Ω {\displaystyle x_{1},x_{2},\dots ,x_{n}\in \Omega } is any set of n points,. S C ( n ) {\displaystyle S_{C}(n)} is the largest number of subsets of any set A of n points that can be formed by intersecting A with the sets in collection C. For example, if set A contains 3 points, its power set, P ( A ) {\displaystyle P(A)} , contains 2 3 = 8 {\displaystyle 2^{3}=8} elements. If C shatters A, its shattering coefficient(3) would be 8 and S C ( 2 ) {\displaystyle S_{C}(2)} would be 2 2 = 4 {\displaystyle 2^{2}=4} . However, if one of those sets in P ( A ) {\displaystyle P(A)} cannot be obtained through intersections in c, then S C ( 3 ) {\displaystyle S_{C}(3)} would only be 7. If none of those sets can be obtained, S C ( 3 ) {\displaystyle S_{C}(3)} would be 0. Additionally, if S C ( 2 ) = 3 {\displaystyle S_{C}(2)=3} , for example, then there is an element in the set of all 2-point sets from A that cannot be obtained from intersections with C. It follows from this that S C ( 3 ) {\displaystyle S_{C}(3)} would also be less than 8 (i.e. C would not shatter A) because we have already located a "missing" set in the smaller power set of 2-point sets. This example illustrates some properties of S C ( n ) {\displaystyle S_{C}(n)} : S C ( n ) ≤ 2 n {\displaystyle S_{C}(n)\leq 2^{n}} for all n because { s ∩ A | s ∈ C } ⊆ P ( A ) {\displaystyle \{s\cap A|s\in C\}\subseteq P(A)} for any A ⊆ Ω {\displaystyle A\subseteq \Omega } . If S C ( n ) = 2 n {\displaystyle S_{C}(n)=2^{n}} , that means there is a set of cardinality n, which can be shattered by C. If S C ( N ) < 2 N {\displaystyle S_{C}(N)<2^{N}} for some N > 1 {\displaystyle N>1} then S C ( n ) < 2 n {\displaystyle S_{C}(n)<2^{n}} for all n ≥ N {\displaystyle n\geq N} . The third property means that if C cannot shatter any set of cardinality N then it can not shatter sets of larger cardinalities. == Vapnik–Chervonenkis class == If A cannot be shattered by C, there will be a smallest value of n that makes the shatter coefficient(n) less than 2 n {\displaystyle 2^{n}} because as n gets larger, there are more sets that could be missed. Alternatively, there is also a largest value of n for which the S C ( n ) {\displaystyle S_{C}(n)} is still 2 n {\displaystyle 2^{n}} , because as n gets smaller, there are fewer sets that could be omitted. The extreme of this is S C ( 0 ) {\displaystyle S_{C}(0)} (the shattering coefficient of the empty set), which must always be 2 0 = 1 {\displaystyle 2^{0}=1} . These statements lends themselves to defining the VC dimension of a class C as: V C ( C ) = min n { n : S C ( n ) < 2 n } {\displaystyle VC(C)={\underset {n}{\min }}\{n:S_{C}(n)<2^{n}\}\,} or, alternatively, as V C 0 ( C ) = max n { n : S C ( n ) = 2 n } . {\displaystyle VC_{0}(C)={\underset {n}{\max }}\{n:S_{C}(n)=2^{n}\}.\,} Note that V C ( C ) = V C 0 ( C ) + 1. {\displaystyle VC(C)=VC_{0}(C)+1.} . The VC dimension is usually defined as V C 0 {\displaystyle VC_{0}} , the largest cardinality of points chosen that will still shatter A (i.e. n such that S C ( n ) = 2 n {\displaystyle S_{C}(n)=2^{n}} ). Altneratively, if for any n there is a set of cardinality n which can be shattered by C, then S C ( n ) = 2 n {\displaystyle S_{C}(n)=2^{n}} for all n and the VC dimension of this class C is infinite. A class with finite VC dimension is called a Vapnik–Chervonenkis class or VC class. A class C is uniformly Glivenko–Cantelli if and only if it is a VC class.
List of data science software
This is a list of data science software and platforms used in data science, which includes programming languages, programming environments, machine learning frameworks, data engineering tools, statistical software, data analysis, plotting, MLOps systems, and more. == Programming languages == == Development environments == These interactive notebooks, IDEs, and platforms provide specialised development environments. Apache Zeppelin Architect — Eclipse (software) CoCalc Dataiku Data Science Studio FreeMat GNU Octave Google Colab DataSpell Jupyter Notebook / JupyterLab Kaggle Notebooks MATLAB O-Matrix PyCharm RStudio SAS (software) and SAS Studio Spyder Visual Studio Code == Machine and deep learning software == The Machine learning / deep learning tools support development in those fields. == Data engineering == Examples of Data engineering tools. Apache Airflow Apache Flink Apache Hadoop Apache Kafka Apache NiFi Apache Spark Dask Data build tool (dbt) == Data mining == Examples of Data mining tools. === Free and open-source === === Proprietary === == Database management == === List of RDBMS === ==== Proprietary ==== == Data warehouses == Data warehouse environments include: Amazon Redshift Snowflake Google BigQuery Microsoft Azure Synapse Teradata Vertica == Data lakes == Data lake environments include: Apache Hadoop Cloudera Databricks Delta Lake Amazon S3 Google Cloud Storage Azure Data Lake == Algorithms == Apriori algorithm – frequent itemset mining and association rule learning in market basket analysis Backpropagation – algorithm for training artificial neural networks using gradient descent Decision Trees – tree-based algorithm for classification and regression Expectation–maximization algorithm – iterative procedure for maximum likelihood estimation with latent variables Gradient descent – iterative optimization algorithm for minimizing a loss function ID3 algorithm – used to generate a decision tree from a dataset K-Means – clustering algorithm based on minimizing within-cluster distances K-Nearest Neighbors (KNN) – instance-based learning and classification method Linear regression – estimation method for predicting a dependent variable based on independent variables Logistic regression – classification algorithm for predicting a binary outcome Naive Bayes – probabilistic classifier based on Bayes' theorem Ordinary least squares – estimation method for parameters in linear regression PageRank – graph-based algorithm for link analysis and search ranking Principal component analysis – technique to reduce high-dimensional data while preserving variance Q-learning – reinforcement learning algorithm for learning optimal actions Random forest – ensemble of decision trees for improved classification or regression Sequential minimal optimization – solver for training support vector machines Stochastic gradient descent – randomized variant of gradient descent for large-scale machine learning Support Vector Machines (SVM) – algorithm for finding a hyperplane to separate classes == Statistical software == === Open-source === === Public domain === CSPro Dataplot Epi Map X-13ARIMA-SEATS === Freeware === BV4.1 MINUIT WinBUGS Winpepi === Proprietary === == Data processing == Tools for Data processing and analysis: == Data and information visualization == Software for Data visualization: == Plotting software == Software for plotting data to support processing and visualise results. == Maps and geospatial visualization == ArcGIS Carto Epi Map GeoDA Google Earth Engine Leaflet Mapbox MountainsMap QGIS == Machine learning == MLOps and model deployment: BentoML Data Version Control (DVC) Kubeflow MLflow Seldon Core Streamlit TensorFlow Serving Weights & Biases == Data repositories == Kaggle – platform for data science competitions, datasets, and notebooks. OpenML – collaborative platform for sharing datasets, algorithms, and experiments. University of California, Irvine Machine Learning Repository Zenodo – open-access repository supported by CERN and the EU. == Educational data science software == Kaggle – online platform for data science education, competitions, datasets, and collaborative learning. KNIME – open-source data analytics platform used for teaching data science, machine learning, and workflow-based analysis. RapidMiner – used in academic research and education for data mining and machine learning. Statistics Online Computational Resource (SOCR) – online tools and instructional resources for statistics education. Tanagra (machine learning) – data mining software developed for research and teaching purposes. TinkerPlots – explore and analyze data through visual modeling.
System requirements specification
A System Requirements Specification (SysRS) (abbreviated SysRS to be distinct from a software requirements specification (SRS)) is a structured collection of information that embodies the requirements of a system. A business analyst (BA), sometimes titled system analyst, is responsible for analyzing the business needs of their clients and stakeholders to help identify business problems and propose solutions. Within the systems development life cycle domain, the BA typically performs a liaison function between the business side of an enterprise and the information technology department or external service providers.
List of Ada software and tools
This is a list of software and programming tools for the Ada programming language, including IDEs, compilers, libraries, verification and debugging tools, numerical and scientific computing libraries, and related projects. == Compilers == GNAT — GCC Ada compiler and toolchain, maintained by AdaCore AdaCore GNAT Pro — commercial Ada compiler with advanced tooling for high-integrity and real-time systems Green Hills compiler for Ada — Ada compiler for embedded and safety-critical systems ObjectAda — Ada development environment for safety-critical and embedded systems == Integrated development environments (IDEs) and editors == GNAT Studio — IDE developed by AdaCore Emacs — supports Ada editing with Ada mode and syntax checking Eclipse — supports Ada through GNATbench plugin Visual Studio Code — Ada support via Ada Language Server extensions == Libraries and frameworks == See also: Ada Libraries on Wikibooks Ada.Calendar — date and time library Ada Web Services (AWS) — support for RESTful and SOAP web services Ada.Text_IO — standard library for text input/output Florist (POSIX Ada binding) – open-source implementation of the POSIX Ada bindings GNAT – Ada compiler part of GCC, which also provides an extensive runtime and library package hierarchy. GtkAda – Ada bindings for the GTK+ graphical user interface toolkit Matreshka – multipurpose Ada framework supporting Unicode, XML, JSON, and more. XML/Ada – XML and Unicode processing library == Real-time and embedded systems == Ada tasking — built-in concurrency support with tasks, protected objects, and rendezvous. Ada.Real_Time — real-time clocks, delays, and scheduling. ARINC 653 Ada profiles — for avionics real-time applications OpenMP Ada bindings — parallel programming for multi-core embedded systems Ravenscar profile — subset of Ada tasking for real-time and deterministic execution == Numerical and scientific computing == Ada.Numerics — libraries for numerical methods, linear algebra, and mathematical functions. SPARK math libraries — formal-methods-compliant numerical routines == Verification, debugging, and analysis == GNATprove — formal verification and static analysis tool for Ada and SPARK GNATstack — runtime stack analysis and checking GNATcoverage — code coverage measurement for Ada projects AdaControl — style checking and metrics for Ada == Testing frameworks == AUnit — unit testing framework for Ada GNATtest — automated testing framework for Ada == Documentation and code generation == GNATdoc — generates HTML documentation from Ada source code
Toolchain
A toolchain is a set of software development tools used to build and otherwise develop software. Often, the tools are executed sequentially and form a pipeline such that the output of one tool is the input for the next. Sometimes the term is used for a set of related tools that are not necessarily executed sequentially. A relatively common and simple toolchain consists of the tools to build for a particular operating system (OS) and CPU architecture: a compiler, a linker, and a debugger. With a cross-compiler, a toolchain can support cross-platform development. For building more complex software systems, many other tools may be in the toolchain. For example, for a video game, the toolchain may include tools for preparing sound effects, music, textures, 3-dimensional models and animations, and for combining these resources into the finished product.
Software engine
A software engine is a core component of a complex software system. The word "engine" is a metaphor of a car's engine. Thus a software engine is a complex subsystem; not unlike how a car engine functions. Software engines work in conjunction with other components of a process or system. They typically have an input and an output, and the productivity is usually linear to running speed. There is no formal guideline for what should be called an engine, but the term has become widespread in the software industry. == Notable examples == === Multi-engine systems === Mainstream web browsers have both a browser engine and a JavaScript engine. Video games are often based on a game engine. Some of these also have specialized physics or graphics engines.
EyeOS
eyeOS was a web desktop for cloud computing, whose main purpose is to enable collaboration and communication among users. It is mainly written in PHP, XML, and JavaScript. It is a private-cloud application platform with a web-based desktop interface. eyeOS delivers a whole desktop from the cloud with file management, personal management information tools, and collaborative tools, with the integration of the client's applications. == History == The first publicly available eyeOS version was released on August 1, 2005, as eyeOS 0.6.0 in Olesa de Montserrat, Barcelona (Spain). A worldwide community of developers soon took part in the project and helped improve it by translating, testing, and developing it. After two years of development, the eyeOS Team published eyeOS 1.0 on June 4, 2007. Compared with previous versions, eyeOS 1.0 introduced a complete reorganization of the code and some new web technologies, like eyeSoft, a portage-based web software installation system. Moreover, eyeOS also included the eyeOS Toolkit, a set of libraries allowing easy and fast development of new web applications. With the release of eyeOS 1.1 on July 2, 2007, eyeOS changed its license and migrated from GNU GPL Version 2 to Version 3. Version 1.2 was released just a month after the 1.1 version and integrated full compatibility with Microsoft Word files. eyeOS 1.5 Gala was released on January 15, 2008. This version was the first to support both Microsoft Office and OpenOffice.org file formats for documents, presentations, and spreadsheets. With this version, eyeOS also gained the ability to import and export documents in both formats using server-side scripting. eyeOS 1.6 was released on April 25, 2008, and included many improvements such as synchronization with local computers, drag and drop, a mobile version, and more. eyeOS 1.8 Lars was released on January 7, 2009, and featured a completely rewritten file manager and a new sound API to develop media-rich applications. Later, on April 1, 2009, 1.8.5 was released with a new default theme and some rewritten apps, such as the Word Processor and the Address Book. On July 13, 2009, 1.8.6 was released with an interface for the iPhone and a new version of eyeMail with support for POP3 and IMAP. eyeOS 1.9 was released on December 29, 2009. It was followed up with the 1.9.0.1 release with minor fixes on February 18, 2010. These releases were the last of the "classic desktop" interfaces. A major re-work was completed in March 2010, now called eyeOS 2.x. However, a small group of eyeOS developers still maintain the code within the eyeOS forum, where support is provided, but the eyeOS group itself has stopped active 1.x development. It is now available as the On-eye project on GitHub. Active development was halted on 1.x as of February 3, 2010. eyeOS 2.0 release took place on March 3, 2010. This was a total restructure of the operating system. The 2.x stable is the new series of eyeOS, which is in active development and will replace 1.x as stable in a few months. It includes live collaboration and more social capabilities than eyeOS 1.x. eyeOS then released 2.2.0.0 on July 28, 2010. On December 14, 2010, a working group inside the eyeOS open-source development community began the structure development and further upgrade of eyeOS 1.9.x. The group's main goal is to continue the work eyeOS has stopped on 1.9.x. eyeOS released 2.5 on May 17, 2011. This was the last release under an open source license. It is available on SourceForge for download under another project called eyeOS 2.5 Open Source Version. On April 1, 2014, Telefónica announced their acquisition of eyeOS. eyeOS would maintain its headquarters in the Catalonia, Spain, where their staff would continue to work but now as part of Telefónica. After its integration into Telefónica, eyeOS would continue to function as an independent subsidiary under CEO Michel Kisfaludi. == Structure and API == For developers, EyeOS provides the eyeOS Toolkit, a set of libraries and functions to develop applications for eyeOS. Using the integrated Portage-based eyeSoft system, one can create their own repository for eyeOS and distribute applications through it. Each core part of the desktop is its own application, using JavaScript to send server commands as the user interacts. As actions are performed using AJAX (such as launching an application), it sends event information to the server. The server then sends back tasks for the client to do in XML format, such as drawing a widget. On the server, eyeOS uses XML files to store information. This makes it simple for a user to set up on the server, as it requires zero configuration other than the account information for the first user, making it simple to deploy. To avoid bottlenecks that flat files present, each user's information and settings are stored in different files, preventing resource starvation from occurring, though this in turn may create issues in high volume user environments due to host operating system open file descriptor limits. == Professional edition == A Professional Edition of eyeOS was launched on September 15, 2011, as an operating system for businesses. It uses a new version number and was released under version 1.0 instead of continuing with the next version number in the open source project. The Professional Edition retains the web desktop interface used by the open source version while targeting enterprise users. A host of new features designed for enterprises, like file sharing and synchronization (called eyeSync), Active Directory/LDAP connectivity, system-wide administration controls, and a local file execution tool called eyeRun were introduced. A new suite of Web Apps (a mail client, calendar, instant messaging, and collaboration tools) was also introduced, specific to the enterprise edition for the web desktop. With eyeOS Professional Edition 1.1, a to-do task manager tool, Citrix XenApp integration, and a Facebook like 'wall' for collaboration were introduced. == Awards == 2007 – Received the Softpedia's Pick award. 2007 – Finalist at SourceForge's 2007 Community Choice Awards at the "Best Project" category. The winner for that category was 7-Zip. 2007 – Won the Yahoo! Spain Web Revelation award in the Technology category. 2008 – Finalist for the Webware 100 awards by CNET, under the "Browsing" category. 2008 – Finalist at the SourceForge's 2008 Community Choice Awards at the "Most Likely to Change the World" category. The winner for that category was Linux. 2009 – Selected Project of the Month (August 2009) by SourceForge. 2009 – BMW Innovation Award. 2010 – Winner of Accelera (Ernst & Young). 2010 – Asturias & Girona Spanish Prince award “IMPULSA”. 2011 – Winner of MIT's TR35 award as Innovator of the Year in Spain. == Community == eyeOS community is formed with the eyeOS forums, which reached 10,000 members on April 4, 2008; the eyeOS wiki; and the eyeOS Application Communities, available at the eyeOS-Apps website, hosted and provided by openDesktop.org as well as Softpedia.