AI For Young Learners Pdf

AI For Young Learners Pdf — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

  • Automatic summarization

    Automatic summarization

    Automatic summarization is the process of shortening a set of data computationally, to create a subset (a summary) that represents the most important or relevant information within the original content. Artificial intelligence (AI) algorithms are commonly developed and employed to achieve this, specialized for different types of data. Text summarization is usually implemented by natural language processing methods, designed to locate the most informative sentences in a given document. On the other hand, visual content can be summarized using computer vision algorithms. Image summarization is the subject of ongoing research; existing approaches typically attempt to display the most representative images from a given image collection, or generate a video that only includes the most important content from the entire collection. Video summarization algorithms identify and extract from the original video content the most important frames (key-frames), and/or the most important video segments (key-shots), normally in a temporally ordered fashion. Video summaries simply retain a carefully selected subset of the original video frames and, therefore, are not identical to the output of video synopsis algorithms, where new video frames are being synthesized based on the original video content. == Commercial products == In 2022 Google Docs released an automatic summarization feature. == Approaches == There are two general approaches to automatic summarization: extraction and abstraction. === Extraction-based summarization === Here, content is extracted from the original data, but the extracted content is not modified in any way. Examples of extracted content include key-phrases that can be used to "tag" or index a text document, or key sentences (including headings) that collectively comprise an abstract, and representative images or video segments, as stated above. For text, extraction is analogous to the process of skimming, where the summary (if available), headings and subheadings, figures, the first and last paragraphs of a section, and optionally the first and last sentences in a paragraph are read before one chooses to read the entire document in detail. Other examples of extraction that include key sequences of text in terms of clinical relevance (including patient/problem, intervention, and outcome). === Abstractive-based summarization === Abstractive summarization methods generate new text that did not exist in the original text. This has been applied mainly for text. Abstractive methods build an internal semantic representation of the original content (often called a language model), and then use this representation to create a summary that is closer to what a human might express. Abstraction may transform the extracted content by paraphrasing sections of the source document, to condense a text more strongly than extraction. Such transformation, however, is computationally much more challenging than extraction, involving both natural language processing and often a deep understanding of the domain of the original text in cases where the original document relates to a special field of knowledge. "Paraphrasing" is even more difficult to apply to images and videos, which is why most summarization systems are extractive. === Aided summarization === Approaches aimed at higher summarization quality rely on combined software and human effort. In Machine Aided Human Summarization, extractive techniques highlight candidate passages for inclusion (to which the human adds or removes text). In Human Aided Machine Summarization, a human post-processes software output, in the same way that one edits the output of automatic translation by Google Translate. == Applications and systems for summarization == There are broadly two types of extractive summarization tasks depending on what the summarization program focuses on. The first is generic summarization, which focuses on obtaining a generic summary or abstract of the collection (whether documents, or sets of images, or videos, news stories etc.). The second is query relevant summarization, sometimes called query-based summarization, which summarizes objects specific to a query. Summarization systems are able to create both query relevant text summaries and generic machine-generated summaries depending on what the user needs. An example of a summarization problem is document summarization, which attempts to automatically produce an abstract from a given document. Sometimes one might be interested in generating a summary from a single source document, while others can use multiple source documents (for example, a cluster of articles on the same topic). This problem is called multi-document summarization. A related application is summarizing news articles. Imagine a system, which automatically pulls together news articles on a given topic (from the web), and concisely represents the latest news as a summary. Image collection summarization is another application example of automatic summarization. It consists in selecting a representative set of images from a larger set of images. A summary in this context is useful to show the most representative images of results in an image collection exploration system. Video summarization is a related domain, where the system automatically creates a trailer of a long video. This also has applications in consumer or personal videos, where one might want to skip the boring or repetitive actions. Similarly, in surveillance videos, one would want to extract important and suspicious activity, while ignoring all the boring and redundant frames captured. At a very high level, summarization algorithms try to find subsets of objects (like set of sentences, or a set of images), which cover information of the entire set. This is also called the core-set. These algorithms model notions like diversity, coverage, information and representativeness of the summary. Query based summarization techniques, additionally model for relevance of the summary with the query. Some techniques and algorithms which naturally model summarization problems are TextRank and PageRank, Submodular set function, Determinantal point process, maximal marginal relevance (MMR) etc. === Keyphrase extraction === The task is the following. You are given a piece of text, such as a journal article, and you must produce a list of keywords or key[phrase]s that capture the primary topics discussed in the text. In the case of research articles, many authors provide manually assigned keywords, but most text lacks pre-existing keyphrases. For example, news articles rarely have keyphrases attached, but it would be useful to be able to automatically do so for a number of applications discussed below. Consider the example text from a news article: "The Army Corps of Engineers, rushing to meet President Bush's promise to protect New Orleans by the start of the 2006 hurricane season, installed defective flood-control pumps last year despite warnings from its own expert that the equipment would fail during a storm, according to documents obtained by The Associated Press". A keyphrase extractor might select "Army Corps of Engineers", "President Bush", "New Orleans", and "defective flood-control pumps" as keyphrases. These are pulled directly from the text. In contrast, an abstractive keyphrase system would somehow internalize the content and generate keyphrases that do not appear in the text, but more closely resemble what a human might produce, such as "political negligence" or "inadequate protection from floods". Abstraction requires a deep understanding of the text, which makes it difficult for a computer system. Keyphrases have many applications. They can enable document browsing by providing a short summary, improve information retrieval (if documents have keyphrases assigned, a user could search by keyphrase to produce more reliable hits than a full-text search), and be employed in generating index entries for a large text corpus. Depending on the different literature and the definition of key terms, words or phrases, keyword extraction is a highly related theme. ==== Supervised learning approaches ==== Beginning with the work of Turney, many researchers have approached keyphrase extraction as a supervised machine learning problem. Given a document, we construct an example for each unigram, bigram, and trigram found in the text (though other text units are also possible, as discussed below). We then compute various features describing each example (e.g., does the phrase begin with an upper-case letter?). We assume there are known keyphrases available for a set of training documents. Using the known keyphrases, we can assign positive or negative labels to the examples. Then we learn a classifier that can discriminate between positive and negative examples as a function of the features. Some classifiers make a binary classification for a test example, while others assign a probability of being a keyphrase. For ins

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  • Pushpak Bhattacharyya

    Pushpak Bhattacharyya

    Pushpak Bhattacharyya (3 July 1962 – 5 October 2025) was an Indian computer scientist and professor in the Department of Computer Science and Engineering at the IIT Bombay. He served as the Director of the IIT Patna from 2015 to 2021. He was a past President of the Association for Computational Linguistics (2016–17), and held the Vijay and Sita Vashee Chair Professorship at IIT Bombay. Bhattacharyya led the Natural Language Processing (NLP) research group at the Centre for Indian Language Technology (CFILT) at IIT Bombay until his death. At the inauguration of the Nilekani Centre at AI4Bharat, IIT Madras, Nandan Nilekani, Co-founder and Non-Executive Chairman of Infosys, referred to Bhattacharyya as the "Godfather of Indian NLP". == Early life and education == Bhattacharyya was born in Shillong in 1962. He completed his schooling at Jail Road Boys' High School, Shillong. He obtained a B.Tech. in Computer Science from the IIT Kharagpur, followed by an M.Tech. from the IIT Kanpur, and a Ph.D. in Computer Science from IIT Bombay in 1994. == Research == Bhattacharyya’s research areas includes Natural language processing, Artificial intelligence, Machine learning, Psycholinguistics, Eye tracking, and Information retrieval. He made contributions to the development of multilingual lexical databases such as IndoWordNet and other projects related to machine translation and computational linguistics. He authored and co-authored multiple academic works, including Investigations in Computational Sarcasm (with Aditya Joshi), Cognitively Inspired Natural Language Processing: An Investigation Based on Eye Tracking (with Abhijit Mishra), and Machine Translation and Transliteration of Low Resource Related Languages (with Anoop Kunchukuttan). Over his career, Bhattacharyya published more than 350 research papers in journals and conference proceedings and supervised over 300 undergraduate, master’s, and doctoral students. His projects often addressed computational challenges for Indian languages, such as developing wordnets, building translation systems for low-resource languages, and studying cognitive aspects of language processing. He also led government- and industry-funded research initiatives supported by organizations including IBM, Microsoft, Yahoo, and the United Nations. == Death == Bhattacharyya died on 5 October 2025, at the age of 63. == Awards == Patwardhan Award, IIT Bombay, for Technology Development VNMM Award, IIT Roorkee, for Technology Development Fellow, Indian National Academy of Engineering Eminent Engineer Award, Institution of Engineers (India)

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  • How to Choose an AI Text-to-image Tool

    How to Choose an AI Text-to-image Tool

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

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  • Armin B. Cremers

    Armin B. Cremers

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

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  • Google Vids

    Google Vids

    Google Vids (not to be confused with Google Video) is an online timeline-based video editing application included as part of the Google Workspace suite. It is designed to help users create informational videos for work-related purposes. The app uses Google's Gemini technology to enable users to create video storyboards manually or with AI assistance using simple prompts. Features include uploading media, choosing stock videos, images, background music, and a voiceover feature with script generation using AI. The app is currently in testing with select Google Workspace Labs users. Like Kapwing and Capcut, Google Vids is primarily for creating work-related content like sales training, onboarding videos, vendor outreach, and project updates. It offers various styles and templates, collaborative features, and is not limited to videos without the short integration at the moment. Google Vids was announced on April 9, 2024. In September 2025, Google began to roll out a basic version of the application to Google Workspace users.

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  • Best Conversational AI Platforms in 2026

    Best Conversational AI Platforms in 2026

    Looking for the best conversational AI platform? An conversational AI platform is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right conversational AI platform slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.

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  • Tang Xiao'ou

    Tang Xiao'ou

    Tang Xiao'ou (汤晓鸥; 24 January 1968 – 15 December 2023) was a Chinese businessman and computer scientist. He was the founder and chairman of SenseTime, an AI company. He also served as professor of information engineering, associate dean of engineering, and outstanding fellow of engineering at the Chinese University of Hong Kong. Tang's research primarily focused on areas such as computer vision, pattern recognition, and video processing. Tang was honored with the Best Paper Award at the 2009 IEEE Conference on Computer Vision and Pattern Recognition. He served as the programme chair in 2009 and the general chair in 2019 for the IEEE International Conference on Computer Vision. His editorial contributions include roles as an Associate Editor for both the IEEE Transactions on Pattern Analysis and Machine Intelligence and the International Journal of Computer Vision. Additionally, Tang has been recognised as a Fellow of the IEEE. == Biography == Tang was born in Anshan, Liaoning, northeastern China in 1968. Tang received a Bachelor of Science with a major in computer science from the University of Science and Technology of China in 1990. He received a Master of Science from the University of Rochester in 1991 and a Doctor of Philosophy in ocean engineering from the Massachusetts Institute of Technology in 1996. He worked at MIT and Woods Hole Oceanographic Institution during his doctoral studies. Funders of his research included the Office of Naval Research of the United States Department of the Navy. After graduating from MIT, Tang taught in the Department of Information Engineering of the Chinese University of Hong Kong. In 2001, he founded the Multimedia Laboratory of the Chinese University of Hong Kong. From 2005 to 2008, he worked at Microsoft Research Asia. He served as Associate Dean of the Chinese University of Hong Kong. In 2014, he spearheaded the first facial recognition to beat human accuracy. Tang co-founded SenseTime with Xu Li in 2014. Upon SenseTime's IPO in December 2021, Tang was estimated to have a net worth of approximately $3.4 billion. Tang died on 15 December 2023, at the age of 55. SenseTime made the announcement the next day and changed the colour scheme of its website to black-and-white in mourning. The Chinese University of Hong Kong also changed his faculty page to a black-and-white theme.

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  • Eduard Hovy

    Eduard Hovy

    Eduard Hovy is a Research Professor in the Language Technologies Institute at Carnegie Mellon University. He is one of the original 17 Fellows of the Association for Computational Linguistics. == Biography == Eduard Hovy received M.S. (December 1982) and Ph.D. (May 1987) degrees in Computer Science from Yale University. He was awarded honorary doctorates from the National University of Distance Education (UNED) in Madrid in 2013 and the University of Antwerp in 2015.

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  • Product-family engineering

    Product-family engineering

    Product-family engineering (PFE), also known as product-line engineering (PLE), is based on the ideas of "domain engineering" created by the Software Engineering Institute, a term coined by James Neighbors in his 1980 dissertation at University of California, Irvine. Software product lines are quite common in our daily lives, but before a product family can be successfully established, an extensive process has to be followed. This process is known as product-family engineering. Product-family engineering can be defined as a method that creates an underlying architecture of an organization's product platform. It provides an architecture that is based on commonality as well as planned variabilities. The various product variants can be derived from the basic product family, which creates the opportunity to reuse and differentiate on products in the family. Product-family engineering is conceptually similar to the widespread use of vehicle platforms in the automotive industry. Product-family engineering is a relatively new approach to the creation of new products, recently evolving to Model-Based Product Line Engineering (MBPLE), emphasizing the centrality of a model-centric approach in PLE. It focuses on the process of engineering new products in such a way that it is possible to reuse product components and apply variability with decreased costs and time. Product-family engineering is all about reusing components and structures as much as possible, according to the ISO/IEC 26550/2015 and the latest ISO/IEC 26580/2021 that introduced the concept of feature-based Product Line Engineering. Several studies have proven that using a product-family engineering approach for product development can have several benefits. Here is a list of some of them: Higher productivity Higher quality Faster time-to-market Lower labor needs The Nokia case mentioned below also illustrates these benefits. In 2025 the publishing of the book Model-Based Product Line Engineering (MBPLE): The feature-based path to product lines success by Marco Forlingieri, Tim Weilkiens and Hugo Guillermo Chalé-Gongora formalized the foundation of the discipline, including best practices and new industrial cases. == Overall process == The product family engineering process consists of several phases. The three main phases are: Phase 1: Product management Phase 2: Domain engineering Phase 3: Product engineering The process has been modeled on a higher abstraction level. This has the advantage that it can be applied to all kinds of product lines and families, not only software. The model can be applied to any product family. Figure 1 (below) shows a model of the entire process. Below, the process is described in detail. The process description contains elaborations of the activities and the important concepts being used. All concepts printed in italic are explained in Table 1. === Phase 1: product management === The first phase is the starting up of the whole process. In this phase some important aspects are defined especially with regard to economic aspects. This phase is responsible for outlining market strategies and defining a scope, which tells what should and should not be inside the product family. ==== Evaluate business visioning ==== During this first activity all context information relevant for defining the scope of the product line is collected and evaluated. It is important to define a clear market strategy and take external market information into account, such as consumer demands. The activity should deliver a context document that contains guidelines, constraints and the product strategy. ==== Define product line scope ==== Scoping techniques are applied to define which aspects are within the scope. This is based upon the previous step in the process, where external factors have been taken into account. The output is a product portfolio description, which includes a list of current and future products and also a product roadmap. It can be argued whether phase 1, product management, is part of the product-family-engineering process, because it could be seen as an individual business process that is more focused on the management aspects instead of the product aspect. However phase 2 needs some important input from this phase, as a large piece of the scope is defined in this phase. So from this point of view it is important to include the product-management phase (phase 1) into the entire process as a base for the domain-engineering process. === Phase 2: domain engineering === During the domain-engineering phases, the variable and common requirements are gathered for the whole product line. The goal is to establish a reusable platform. The output of this phase is a set of common and variable requirements for all products in the product line. ==== Analyze domain requirements ==== This activity includes all activities for analyzing the domain with regard to concept requirements. The requirements are categorized and split up into two new activities. The output is a document with the domain analysis. As can be seen in Figure 1 the process of defining common requirements is a parallel process with defining variable requirements. Both activities take place at the same time. ==== Define common requirements ==== Includes all activities for eliciting and documenting the common requirements of the product line, resulting in a document with reusable common requirements. ==== Define variable requirements ==== Includes all activities for eliciting and documenting the variable requirements of the product line, resulting in a document with variable requirements. ==== Design domain ==== This process step consists of activities for defining the reference architecture of the product line. This generates an abstract structure for all products in the product line. ==== Implement domain ==== During this step a detailed design of the reusable components and the implementation of these components are created. ==== Test domain ==== Validates and verifies the reusability of components. Components are tested against their specifications. After successful testing of all components in different use cases and scenarios, the domain engineering phase has been completed. === Phase 3: product engineering === In the final phase a product X is being engineered. This product X uses the commonalities and variability from the domain engineering phase, so product X is being derived from the platform established in the domain engineering phase. It basically takes all common requirements and similarities from the preceding phase plus its own variable requirements. Using the base from the domain engineering phase and the individual requirements of the product engineering phase a complete and new product can be built. After the product has been fully tested and approved, the product X can be delivered. ==== Define product requirements ==== Developing the product requirements specification for the individual product and reuse the requirements from the preceding phase. ==== Design product ==== All activities for producing the product architecture. Makes use of the reference architecture from the step "design domain", it selects and configures the required parts of the reference architecture and incorporates product specific adaptations. ==== Build product ==== During this process the product is built, using selections and configurations of the reusable components. ==== Test product ==== During this step the product is verified and validated against its specifications. A test report gives information about all tests that were carried out, this gives an overview of possible errors in the product. If the product in the next step is not accepted, the process will loop back to "build product", in Figure 1 this is indicated as "[unsatisfied]". ==== Deliver and support product ==== The final step is the acceptance of the final product. If it has been successfully tested and approved to be complete, it can be delivered. If the product does not satisfy to the specifications, it has to be rebuilt and tested again. The next figure shows the overall process of product-family engineering as described above. It is a full process overview with all concepts attached to the different steps. == Process data diagram == On the left side the entire process from the top to bottom has been drawn. All activities on the left side are linked to the concepts on the right side through dotted lines. Every concept has a number, which reflects the association with other concepts. == List of concepts == Below the list with concepts will be explained. Most concept definitions are extracted from Pohl, Bockle, & Linden (2005) and also some new definitions have been added. Table 1: List of concepts == Example == There are some good examples of the use of product family engineering, which were quite successful. The abstract model of product family engineering allows different kinds of uses, most of them are related to the consumer electronics m

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  • Sparse dictionary learning

    Sparse dictionary learning

    Sparse dictionary learning (also known as sparse coding or SDL) is a representation learning method which aims to find a sparse representation of the input data in the form of a linear combination of basic elements as well as those basic elements themselves. These elements are called atoms, and they compose a dictionary. Atoms in the dictionary are not required to be orthogonal, and they may be an over-complete spanning set. This problem setup also allows the dimensionality of the signals being represented to be higher than any one of the signals being observed. These two properties lead to having seemingly redundant atoms that allow multiple representations of the same signal, but also provide an improvement in sparsity and flexibility of the representation. One of the most important applications of sparse dictionary learning is in the field of compressed sensing or signal recovery. In compressed sensing, a high-dimensional signal can be recovered with only a few linear measurements, provided that the signal is sparse or near-sparse. Since not all signals satisfy this condition, it is crucial to find a sparse representation of that signal such as the wavelet transform or the directional gradient of a rasterized matrix. Once a matrix or a high-dimensional vector is transferred to a sparse space, different recovery algorithms like basis pursuit, CoSaMP, or fast non-iterative algorithms can be used to recover the signal. One of the key principles of dictionary learning is that the dictionary has to be inferred from the input data. The emergence of sparse dictionary learning methods was stimulated by the fact that in signal processing, one typically wants to represent the input data using a minimal amount of components. Before this approach, the general practice was to use predefined dictionaries such as Fourier or wavelet transforms. However, in certain cases, a dictionary that is trained to fit the input data can significantly improve the sparsity, which has applications in data decomposition, compression, and analysis, and has been used in the fields of image denoising and classification, and video and audio processing. Sparsity and overcomplete dictionaries have immense applications in image compression, image fusion, and inpainting. == Problem statement == Given the input dataset X = [ x 1 , . . . , x K ] , x i ∈ R d {\displaystyle X=[x_{1},...,x_{K}],x_{i}\in \mathbb {R} ^{d}} we wish to find a dictionary D ∈ R d × n : D = [ d 1 , . . . , d n ] {\displaystyle \mathbf {D} \in \mathbb {R} ^{d\times n}:D=[d_{1},...,d_{n}]} and a representation R = [ r 1 , . . . , r K ] , r i ∈ R n {\displaystyle R=[r_{1},...,r_{K}],r_{i}\in \mathbb {R} ^{n}} such that both ‖ X − D R ‖ F 2 {\displaystyle \|X-\mathbf {D} R\|_{F}^{2}} is minimized and the representations r i {\displaystyle r_{i}} are sparse enough. This can be formulated as the following optimization problem: argmin D ∈ C , r i ∈ R n ∑ i = 1 K ‖ x i − D r i ‖ 2 2 + λ ‖ r i ‖ 0 {\displaystyle {\underset {\mathbf {D} \in {\mathcal {C}},r_{i}\in \mathbb {R} ^{n}}{\text{argmin}}}\sum _{i=1}^{K}\|x_{i}-\mathbf {D} r_{i}\|_{2}^{2}+\lambda \|r_{i}\|_{0}} , where C ≡ { D ∈ R d × n : ‖ d i ‖ 2 ≤ 1 ∀ i = 1 , . . . , n } {\displaystyle {\mathcal {C}}\equiv \{\mathbf {D} \in \mathbb {R} ^{d\times n}:\|d_{i}\|_{2}\leq 1\,\,\forall i=1,...,n\}} , λ > 0 {\displaystyle \lambda >0} C {\displaystyle {\mathcal {C}}} is required to constrain D {\displaystyle \mathbf {D} } so that its atoms would not reach arbitrarily high values allowing for arbitrarily low (but non-zero) values of r i {\displaystyle r_{i}} . λ {\displaystyle \lambda } controls the trade off between the sparsity and the minimization error. The minimization problem above is not convex because of the ℓ0-"norm" and solving this problem is NP-hard. In some cases L1-norm is known to ensure sparsity and so the above becomes a convex optimization problem with respect to each of the variables D {\displaystyle \mathbf {D} } and R {\displaystyle \mathbf {R} } when the other one is fixed, but it is not jointly convex in ( D , R ) {\displaystyle (\mathbf {D} ,\mathbf {R} )} . === Properties of the dictionary === The dictionary D {\displaystyle \mathbf {D} } defined above can be "undercomplete" if n < d {\displaystyle n d {\displaystyle n>d} with the latter being a typical assumption for a sparse dictionary learning problem. The case of a complete dictionary does not provide any improvement from a representational point of view and thus isn't considered. Undercomplete dictionaries represent the setup in which the actual input data lies in a lower-dimensional space. This case is strongly related to dimensionality reduction and techniques like principal component analysis which require atoms d 1 , . . . , d n {\displaystyle d_{1},...,d_{n}} to be orthogonal. The choice of these subspaces is crucial for efficient dimensionality reduction, but it is not trivial. And dimensionality reduction based on dictionary representation can be extended to address specific tasks such as data analysis or classification. However, their main downside is limiting the choice of atoms. Overcomplete dictionaries, however, do not require the atoms to be orthogonal (they will never have a basis anyway) thus allowing for more flexible dictionaries and richer data representations. An overcomplete dictionary which allows for sparse representation of signal can be a famous transform matrix (wavelets transform, fourier transform) or it can be formulated so that its elements are changed in such a way that it sparsely represents the given signal in a best way. Learned dictionaries are capable of giving sparser solutions as compared to predefined transform matrices. == Algorithms == As the optimization problem described above can be solved as a convex problem with respect to either dictionary or sparse coding while the other one of the two is fixed, most of the algorithms are based on the idea of iteratively updating one and then the other. The problem of finding an optimal sparse coding R {\displaystyle R} with a given dictionary D {\displaystyle \mathbf {D} } is known as sparse approximation (or sometimes just sparse coding problem). A number of algorithms have been developed to solve it (such as matching pursuit and LASSO) and are incorporated in the algorithms described below. === Method of optimal directions (MOD) === The method of optimal directions (or MOD) was one of the first methods introduced to tackle the sparse dictionary learning problem. The core idea of it is to solve the minimization problem subject to the limited number of non-zero components of the representation vector: min D , R { ‖ X − D R ‖ F 2 } s.t. ∀ i ‖ r i ‖ 0 ≤ T {\displaystyle \min _{\mathbf {D} ,R}\{\|X-\mathbf {D} R\|_{F}^{2}\}\,\,{\text{s.t.}}\,\,\forall i\,\,\|r_{i}\|_{0}\leq T} Here, F {\displaystyle F} denotes the Frobenius norm. MOD alternates between getting the sparse coding using a method such as matching pursuit and updating the dictionary by computing the analytical solution of the problem given by D = X R + {\displaystyle \mathbf {D} =XR^{+}} where R + {\displaystyle R^{+}} is a Moore-Penrose pseudoinverse. After this update D {\displaystyle \mathbf {D} } is renormalized to fit the constraints and the new sparse coding is obtained again. The process is repeated until convergence (or until a sufficiently small residue). MOD has proved to be a very efficient method for low-dimensional input data X {\displaystyle X} requiring just a few iterations to converge. However, due to the high complexity of the matrix-inversion operation, computing the pseudoinverse in high-dimensional cases is in many cases intractable. This shortcoming has inspired the development of other dictionary learning methods. === K-SVD === K-SVD is an algorithm that performs SVD at its core to update the atoms of the dictionary one by one and basically is a generalization of K-means. It enforces that each element of the input data x i {\displaystyle x_{i}} is encoded by a linear combination of not more than T 0 {\displaystyle T_{0}} elements in a way identical to the MOD approach: min D , R { ‖ X − D R ‖ F 2 } s.t. ∀ i ‖ r i ‖ 0 ≤ T 0 {\displaystyle \min _{\mathbf {D} ,R}\{\|X-\mathbf {D} R\|_{F}^{2}\}\,\,{\text{s.t.}}\,\,\forall i\,\,\|r_{i}\|_{0}\leq T_{0}} This algorithm's essence is to first fix the dictionary, find the best possible R {\displaystyle R} under the above constraint (using Orthogonal Matching Pursuit) and then iteratively update the atoms of dictionary D {\displaystyle \mathbf {D} } in the following manner: ‖ X − D R ‖ F 2 = | X − ∑ i = 1 K d i x T i | F 2 = ‖ E k − d k x T k ‖ F 2 {\displaystyle \|X-\mathbf {D} R\|_{F}^{2}=\left|X-\sum _{i=1}^{K}d_{i}x_{T}^{i}\right|_{F}^{2}=\|E_{k}-d_{k}x_{T}^{k}\|_{F}^{2}} The next steps of the algorithm include rank-1 approximation of the residual matrix E k {\displaystyle E_{k}} , updating d k {\displaystyle d_{k}} and enforcing the s

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  • The Best Free AI Analytics Tool for Beginners

    The Best Free AI Analytics Tool for Beginners

    Trying to pick the best AI analytics tool? An AI analytics tool is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI analytics tool slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.

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  • Best AI Blog Writers in 2026

    Best AI Blog Writers in 2026

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

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  • Concept drift

    Concept drift

    In predictive analytics, data science, machine learning and related fields, concept drift or drift is an evolution of data that invalidates the data model. It happens when the statistical properties of the target variable, which the model is trying to predict, change over time in unforeseen ways. This causes problems because the predictions become less accurate as time passes. Drift detection and drift adaptation are of paramount importance in the fields that involve dynamically changing data and data models. == Predictive model decay == In machine learning and predictive analytics this drift phenomenon is called concept drift. In machine learning, a common element of a data model are the statistical properties, such as probability distribution of the actual data. If they deviate from the statistical properties of the training data set, then the learned predictions may become invalid, if the drift is not addressed. == Data configuration decay == Another important area is software engineering, where three types of data drift affecting data fidelity may be recognized. Changes in the software environment ("infrastructure drift") may invalidate software infrastructure configuration. "Structural drift" happens when the data schema changes, which may invalidate databases. "Semantic drift" is changes in the meaning of data while the structure does not change. In many cases this may happen in complicated applications when many independent developers introduce changes without proper awareness of the effects of their changes in other areas of the software system. For many application systems, the nature of data on which they operate are subject to changes for various reasons, e.g., due to changes in business model, system updates, or switching the platform on which the system operates. In the case of cloud computing, infrastructure drift that may affect the applications running on cloud may be caused by the updates of cloud software. There are several types of detrimental effects of data drift on data fidelity. Data corrosion is passing the drifted data into the system undetected. Data loss happens when valid data are ignored due to non-conformance with the applied schema. Squandering is the phenomenon when new data fields are introduced upstream in the data processing pipeline, but somewhere downstream these data fields are absent. == Inconsistent data == "Data drift" may refer to the phenomenon when database records fail to match the real-world data due to the changes in the latter over time. This is a common problem with databases involving people, such as customers, employees, citizens, residents, etc. Human data drift may be caused by unrecorded changes in personal data, such as place of residence or name, as well as due to errors during data input. "Data drift" may also refer to inconsistency of data elements between several replicas of a database. The reasons can be difficult to identify. A simple drift detection is to run checksum regularly. However the remedy may be not so easy. == Examples == The behavior of the customers in an online shop may change over time. For example, if weekly merchandise sales are to be predicted, and a predictive model has been developed that works satisfactorily. The model may use inputs such as the amount of money spent on advertising, promotions being run, and other metrics that may affect sales. The model is likely to become less and less accurate over time – this is concept drift. In the merchandise sales application, one reason for concept drift may be seasonality, which means that shopping behavior changes seasonally. Perhaps there will be higher sales in the winter holiday season than during the summer, for example. Concept drift generally occurs when the covariates that comprise the data set begin to explain the variation of your target set less accurately — there may be some confounding variables that have emerged, and that one simply cannot account for, which renders the model accuracy to progressively decrease with time. Generally, it is advised to perform health checks as part of the post-production analysis and to re-train the model with new assumptions upon signs of concept drift. == Possible remedies == To prevent deterioration in prediction accuracy because of concept drift, reactive and tracking solutions can be adopted. Reactive solutions retrain the model in reaction to a triggering mechanism, such as a change-detection test or control charts from statistical process control, to explicitly detect concept drift as a change in the statistics of the data-generating process. When concept drift is detected, the current model is no longer up-to-date and must be replaced by a new one to restore prediction accuracy. A shortcoming of reactive approaches is that performance may decay until the change is detected. Tracking solutions seek to track the changes in the concept by continually updating the model. Methods for achieving this include online machine learning, frequent retraining on the most recently observed samples, and maintaining an ensemble of classifiers where one new classifier is trained on the most recent batch of examples and replaces the oldest classifier in the ensemble. Contextual information, when available, can be used to better explain the causes of the concept drift: for instance, in the sales prediction application, concept drift might be compensated by adding information about the season to the model. By providing information about the time of the year, the rate of deterioration of your model is likely to decrease, but concept drift is unlikely to be eliminated altogether. This is because actual shopping behavior does not follow any static, finite model. New factors may arise at any time that influence shopping behavior, the influence of the known factors or their interactions may change. Concept drift cannot be avoided for complex phenomena that are not governed by fixed laws of nature. All processes that arise from human activity, such as socioeconomic processes, and biological processes are likely to experience concept drift. Therefore, periodic retraining, also known as refreshing, of any model is necessary. === Remedy methods === DDM (Drift Detection Method): detects drift by monitoring the model's error rate over time. When the error rate passes a set threshold, it enters a warning phase, and if it passes another threshold, it enters a drift phase. EDDM (Early Drift Detection Method): improves DDM's detection rate by tracking the average distance between two errors instead of only the error rate. ADWIN (Adaptive Windowing): dynamically stores a window of recent data and warns the user if it detects a significant change between the statistics of the window's earlier data compared to more recent data. KSWIN (Kolmogorov–Smirnov Windowing): detects drift based on the Kolmogorov-Smirnov statistical test. DDM and EDDM: Concept Drift Detection online supervised methods that rely on sequential error monitoring to estimate the evolving error rate. ADWIN and KSWIN: Windowing maintain a "window", a subset of the most recent data, of the data stream, which it checks for statistical differences across the window. == Applications in security == Concept drift is a recurring issue in security analytics, especially in malware and intrusion detection. In these systems, models are often trained on past logs, binaries or network traces, but the behaviour of attackers changes over time as new malware families, obfuscation techniques and campaigns appear. When the data no longer resemble the training set, the decision boundaries learned by classifiers or anomaly detectors can become misaligned with the current threat landscape and detection performance can drop unless the models are updated or replaced. Several studies on Windows malware model detection as an evolving data stream and track how performance changes as time passes. They show that classifiers trained on a fixed time window can perform well on nearby data but deteriorate quickly when evaluated on samples collected months or years later, even when large amounts of training data are available. In order to keep up with this, security systems often use sliding or adaptive windows, which restrict training to the most recent portion of the data so that older, less relevant examples are gradually discarded. They also employ drift detectors such as ADWIN and KSWIN that monitor error rates or changes in the distribution of recent observations and signal when the statistics of the incoming stream differ significantly from the past, prompting retraining or model replacement. Related problems appear in spam filtering, fraud detection and intrusion detection, where adversaries change content, patterns of activity or network behavior to evade models trained on historical data. In these settings drift can be gradual, as new types of spam or fraud emerge, or abrupt, after a sudden shift in attack techniques. Common strategies to remain eff

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  • Theano (software)

    Theano (software)

    Theano is a Python library and optimizing compiler for manipulating and evaluating mathematical expressions, especially matrix-valued ones. In Theano, computations are expressed using a NumPy-esque syntax and compiled to run efficiently on either CPU or GPU architectures. == History == Theano is an open source project primarily developed by the Montreal Institute for Learning Algorithms (MILA) at the Université de Montréal. The name of the software references the ancient philosopher Theano, long associated with the development of the golden mean. On 28 September 2017, Pascal Lamblin posted a message from Yoshua Bengio, Head of MILA: major development would cease after the 1.0 release due to competing offerings by strong industrial players. Theano 1.0.0 was then released on 15 November 2017. On 17 May 2018, Chris Fonnesbeck wrote on behalf of the PyMC development team that the PyMC developers will officially assume control of Theano maintenance once the MILA development team steps down. On 29 January 2021, they started using the name Aesara for their fork of Theano. On 29 Nov 2022, the PyMC development team announced that the PyMC developers will fork the Aesara project under the name PyTensor. == Sample code == The following code is the original Theano's example. It defines a computational graph with 2 scalars a and b of type double and an operation between them (addition) and then creates a Python function f that does the actual computation. == Examples == === Matrix Multiplication (Dot Product) === The following code demonstrates how to perform matrix multiplication using Theano, which is essential for linear algebra operations in many machine learning tasks. === Gradient Calculation === The following code uses Theano to compute the gradient of a simple operation (like a neuron) with respect to its input. This is useful in training machine learning models (backpropagation). === Building a Simple Neural Network === The following code shows how to start building a simple neural network. This is a very basic neural network with one hidden layer. === Broadcasting in Theano === The following code demonstrates how broadcasting works in Theano. Broadcasting allows operations between arrays of different shapes without needing to explicitly reshape them.

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  • BFR algorithm

    BFR algorithm

    The BFR algorithm, named after its inventors Bradley, Fayyad and Reina, is a variant of k-means algorithm that is designed to cluster data in a high-dimensional Euclidean space. It makes a very strong assumption about the shape of clusters: they must be normally distributed about a centroid. The mean and standard deviation for a cluster may differ for different dimensions, but the dimensions must be independent. In other words, the data must take the shape of axis-aligned ellipses.

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