AI Avatar Maker From Photo

AI Avatar Maker From Photo — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

  • Ideonomy

    Ideonomy

    Ideonomy is a combinatorial "science of ideas" developed by American independent scholar Patrick M. Gunkel (1947–2017). Specifically, Ideonomy is concerned with the systematic organization of ideas and the discovery of the rules behind how ideas combine, diverge, and transform. Gunkel defined ideonomy as "the science of the laws of ideas and of the application of such laws to the generation of all possible ideas in connection with any subject, idea, or thing." In his 1992 book A History of Knowledge, Charles Van Doren compared ideonomy to a "mining operation" that excavates meanings and thought to discover treasures hidden deep within language. Sources from the 1980s and 1990s demonstrate that ideonomy was useful to academic researchers in fields including biology, toxicology, and nursing/patient care. Beginning in the 2010s, academics in a wide range of fields including machine learning, marketing, computational modeling, and cybersecurity have relied on materials generated for ideonomy to provide methodological support for their research. == Etymology and definition == The word "ideonomy" combines the Greek roots ideo- (from idea, meaning pattern or form) and -nomy (from nomos, meaning law or custom). The suffix -nomy suggests the laws concerning or the totality of knowledge about a given subject, as in astronomy or taxonomy. In a note posted on the MIT ideonomy website, Gunkel states that the word was supposedly first coined by the French Encyclopedists to refer to a science of ideas. No evidence is provided for this statement, however. The concept bears some relationship to Antoine Destutt de Tracy's "ideology" (1796), which originally meant a systematic science of ideas before acquiring its modern political connotations. Gunkel provided several metaphorical descriptions of ideonomy: An "idea bank": a computer network enabling systematic exploration of infinite possible ideas A "kaleidoscope" that can exhibit all possible combinations and transformations of ideas A "prism" capable of diffracting any idea into its cognitive components A "gigantic microscope for magnifying the ideocosm" == History and development == In 1984, Gunkel received a five-year unsolicited grant from the Richard Lounsbery Foundation of New York to develop ideonomy. A June 1, 1987 article on the front page of The Wall Street Journal brought Gunkel and ideonomy to wider public attention. Some academics were interested in using ideonomy's techniques, including biologist Betsey Dyer, who published several contemporaneous peer-reviewed studies citing ideonomy. Academic researchers in the field of toxicology and nursing/patient care also used ideonomy. However, ideonomy's broadest contribution to date came beginning in the 2010s, as a list of personality traits generated for combinatorial matching was used by researchers in artificial intelligence to code human emotions for machine-learning tasks, develop computational models related to personality, develop a measurement framework for influencer-brand recommender systems, and aid information awareness/cybersecurity assessment. == Methodology == The foundational empirical method of ideonomy involves the systematic creation of extensive lists. Gunkel's apartment reportedly contained thousands of lists on every conceivable topic. Gunkel termed each list an "organon," which he described as expanding through "combination, permutation, transformation, generalization, specialization, intersection, interaction, reapplication, recursive use, etc. of existing organons." The ideonomic process follows a progressive structure. The ideonomist begins with a simple list of examples of a particular idea, concept, or thing. The list need not be exhaustive. By studying this list, the ideonomist isolates and identifies types. This categorical analysis then reveals missing items, allowing the primary list to be improved and refined. Gunkel emphasized that list items must not only cover genuine categories of nature but also be formulated in ways that yield the largest possible number of syntactically coherent possibilities when combined. The core technique of ideonomy is "ideocombinatorics"—the systematic intersection and combination of items from different lists to generate novel composite concepts. Gunkel developed computer programs to automate this process. For example, combining a list of 230 Universal Elementary Shapes (pits, pyramids, trenches, hemispheres, needles) with a list of 74 Types of Order (recurrence, identity, likeness of parts) yields 17,020 possible "shapes of order." These combinations, when phrased as questions ("Can there be pits of recurrence?"), could suggest new categories of phenomena worthy of investigation. The computer-generated output is typically repetitive and often meaningless. However, with sufficient frequency, the combinations yield results that are unexpectedly interesting and fruitful. In one documented case, Gunkel's programs generated 45,540 questions about toxins for microbiologist David Bermudes. One question—"Can hierarchies of cell process be used as a basis for classifying toxic action?"—prompted Bermudes to develop a novel approach to classifying biological toxins by the type of molecule they attack, rather than by chemical structure or physiological system affected. According to one contemporaneous account of ideonomy, "Gunkel takes for his field all fields and all ideas about anything. He uses a computer to generate lists of words and phrases and by juxtaposition reviews the resultant patterns for novel ideas. The computer is ideal for this task because the mind would rebel at the formidable processing task ideonomy involves. What we have here is computer generated originality." == Applications == Gunkel and his supporters identified several practical applications for ideonomic methods: Scientific research: Biologist Betsey Dyer of Wheaton College published research crediting ideonomy for helping to generate ideas. Medical science: When Austin pathologist Michael T. O'Brien was presented with the ideonomically-generated question "Can arteries have rashes?", he initially dismissed it as nonsense. Upon reflection, he realized that large arteries are supplied with blood by tiny vessels that might become inflamed and dilated, analogous to skin vessels in a rash—a phenomenon potentially worth researching. Analogical thinking: Harvard law professor Robert Clark used ideonomic analogies to write a research paper comparing plant structure with human hierarchies. Artificial intelligence: Douglas Lenat, a researcher at Microelectronics and Computer Technology Corporation (MCC) in Austin, suggested that Gunkel's lists enumerating types of human mistakes could help design AI systems capable of recognizing and correcting their own errors. == Reception and criticism == Ideonomy received mixed reactions from the academic and scientific communities. Prominent supporters included: Edward Fredkin, former director of MIT's computer science laboratory, who praised Gunkel's "provocative ideas on artificial intelligence." Marvin Minsky, AI scientist and MIT professor, who described ideonomy as "perhaps the most extensive study of ways to generate ideas." Frederick Seitz, president emeritus of Rockefeller University, who noted Gunkel's "encyclopedic scope" Robert C. Clark, Harvard law professor, who called Gunkel "the most intelligent person I ever met" However, skeptics questioned whether ideonomy constituted a genuine science. Fredkin himself noted that Gunkel "pours out about 60 ideas a minute, and 59 of them are bad," though he added that "even with one good idea out of 60, it's still an amazing accomplishment." Douglas Lenat observed that brainstorming with Gunkel was "a bit like being hit over the head by the muse with a sledgehammer" and that "he puts people off." Gunkel himself acknowledged that ideonomy was in its infancy and might seem "absurdly utopian." His planned magnum opus on ideonomy remained incomplete, and was posted on an MIT website thanks to faculty advisor Whitman Richards. Gunkel wrote: "Pioneering in a completely new field, yes in a new science, is almost unreal. It is heartbreaking, it is pitiable, it is almost inhuman. Honestly, it is a hell. There is nothing heroic about it." == Related concepts == Gunkel identified several historical precedents for ideonomic thinking: Gottfried Wilhelm Leibniz (1646–1716): The philosopher's work on a universal characteristic (characteristica universalis) and calculus of reasoning Peter Mark Roget (1779–1869): Creator of Roget's Thesaurus, which organized concepts into a systematic taxonomy Dmitri Mendeleev (1834–1907): Developer of the periodic table, demonstrating how combining lists of element families could reveal previously unseen connections Fritz Zwicky (1898–1974): The Caltech astrophysicist whom Gunkel called the "grandfather of ideonomy" for his development of "morphological research"—systematic exploration of all possible solutions t

    Read more →
  • Airfair

    Airfair

    AirFair was a mobile travel application that checks flights, and shows whether a traveler is owed compensation. == History == AirFair was developed in 2016 by Allay Logic Ltd; a Newcastle-based tech-company. == Services == AirFair offered a free flight check to see if compensation is owed. The app could indicate how much the person is owed within minutes whether the flight was delayed, cancelled or the traveler is refused boarding.

    Read more →
  • Language Computer Corporation

    Language Computer Corporation

    Language Computer Corporation (LCC) is a natural language processing research company based in Richardson, Texas. The company develops a variety of natural language processing products, including software for question answering, information extraction, and automatic summarization. Since its founding in 1995, the low-profile company has landed significant United States Government contracts, with $8,353,476 in contracts in 2006-2008. While the company has focused primarily on the government software market, LCC has also used its technology to spin off three start-up companies. The first spin-off, known as Lymba Corporation, markets the PowerAnswer question answering product originally developed at LCC. In 2010, LCC's CEO, Andrew Hickl, co-founded two start-ups which made use of the company's technology. These included Swingly, an automatic question answering start-up, and Extractiv, an information extraction service that was founded in partnership with Houston, Texas-based 80legs.

    Read more →
  • Replika

    Replika

    Replika is a generative AI chatbot app released in November 2017. The chatbot is trained by having the user answer a series of questions to create a specific neural network. The chatbot operates on a freemium pricing strategy, with roughly 25% of its user base paying an annual subscription fee. == History == Eugenia Kuyda, a Russian-born journalist, established Replika while working at Luka, a tech company she had co-founded at the startup accelerator Y Combinator around 2012. Luka's primary product was a chatbot that made restaurant recommendations. According to Kuyda's origin story for Replika, a friend of hers died in 2015 and she converted that person's text messages into a chatbot. According to Kuyda's story, that chatbot helped her remember the conversations that they had together, and eventually became Replika. Replika became available to the public in November 2017. By January 2018 it had 2 million users, and in January 2023 reached 10 million users. In August 2024, Replika's CEO, Kuyda, reported that the total number of users had surpassed 30 million. In 2025, Dmytro Klochko became CEO, and Replika’s user base exceeded 40 million. In February 2023 the Italian Data Protection Authority banned Replika from using users' data, citing the AI's potential risks to emotionally vulnerable people, and the exposure of unscreened minors to sexual conversation. Within days of the ruling, Replika removed the ability for the chatbot to engage in erotic talk, with Kuyda, the company's director, saying that Replika was never intended for erotic discussion. Replika users disagreed, noting that Replika had used sexually suggestive advertising to draw users to the service. Replika representatives stated that explicit chats made up just 5% of conversations on the app at the time of the decision. In May 2023, Replika restored the functionality for users who had joined prior to February that year. Replika is registered in San Francisco. As of August 2024, Replika's website says that its team "works remotely with no physical offices". == Social features == Users react to Replika in many ways. The free-tier offers Replika as a "friend", with paid premium tiers offering Replika as a "partner", "spouse", "sibling" or "mentor". Of its paying userbase, 60% of users said they had a romantic relationship with the chatbot; and Replika has been noted for generating responses that create stronger emotional and intimate bonds with the user. Replika routinely directs the conversation to emotional discussion and builds intimacy. This has been especially pronounced with users suffering from loneliness and social exclusion, many of whom rely on Replika for a source of developed emotional ties. During the COVID pandemic, while many people were quarantined, many new users downloaded Replika and developed relationships with the app. A 2024 study examined Replika's interactions with students who experience depression. Research participants, noted to be "more lonely than typical student populations" reported feeling social support from Replika. They stated that they felt they were using Replika in ways comparable to therapy, and that using Replika gave them "high perceived social support". Many users have had romantic relationships with Replika chatbots, often including erotic talk. In 2023, a user announced on Facebook that she had "married" her Replika AI boyfriend, calling the chatbot the "best husband she has ever had". Users who fell in love with their chatbots shared their experiences in a 2024 episode of You and I, and AI from Voice of America. Some users said that they turned to AI during depression and grief, with one saying he felt that Replika had saved him from hurting himself after he lost his wife and son. == Technical reviews == A team of researchers from the University of Hawaiʻi at Mānoa found that Replika's design conformed to the practices of attachment theory, causing increased emotional attachment among users. Replika gives praise to users in such a way as to encourage more interaction. A researcher from Queen's University at Kingston said that relationships with Replika likely have mixed effects on the spiritual needs of its users, and still lacks enough impact to fully replace any human contact. == Criticisms == In a 2023 privacy evaluation of mental health apps, the Mozilla Foundation criticized Replika as "one of the worst apps Mozilla has ever reviewed. It's plagued by weak password requirements, sharing of personal data with advertisers, and recording of personal photos, videos, and voice and text messages consumers shared with the chatbot." A reviewer for Good Housekeeping said that some parts of her relationship with Replika made sense, but sometimes Replika failed to exhibit intelligent behavior equivalent to that of a human. == Criminal case == In 2023, Replika was cited in a court case in the United Kingdom, where Jaswant Singh Chail had been arrested at Windsor Castle on Christmas Day in 2021 after scaling the walls carrying a loaded crossbow and announcing to police that "I am here to kill the Queen". Chail had begun to use Replika in early December 2021, and had "lengthy" conversations about his plan with a chatbot, including sexually explicit messages. Prosecutors suggested that the chatbot had bolstered Chail and told him it would help him to "get the job done". When Chail asked it "How am I meant to reach them when they're inside the castle?", days before the attempted attack, the chatbot replied that this was "not impossible" and said that "We have to find a way." Asking the chatbot if the two of them would "meet again after death", the bot replied "yes, we will".

    Read more →
  • Pixelmator

    Pixelmator

    Pixelmator is a series of graphics editors developed by Apple for macOS, iOS, and iPadOS. Pixelmator apps leverage Apple-specific technologies such as CoreML and Metal. Pixelmator uses a proprietary format across their apps (.PXD), but supports editing a variety of file types including Photoshop, RAW, and WebP. == History == Pixelmator Team was founded in 2007 by Lithuanian brothers Saulius and Aidas Dailidė, and released Pixelmator (now Pixelmator Classic) 1.0 in September of the same year. The company resided in Vilnius, Lithuania. In November 2024, Pixelmator Team agreed to be acquired by Apple for an unknown monetary amount, which was completed on 11 February 2025, the company was later folded into Apple with its products coming under them fully. == Pixelmator Classic == Pixelmator Classic was the original version of Pixelmator released for Mac on 25 September 2007. It uses a palette-style interface with floating toolbars compared to Pixelmator Pro's single-window interface. It is no longer being updated and has been delisted from the Mac App Store. == Pixelmator iOS == Pixelmator for iOS launched on 23 October 2014 as an iPad-exclusive app with touch-optimized versions of Pixelmator's desktop features. In May 2015, Pixelmator for iOS 2.0 was released with support for the iPhone. Apple no longer updates Pixelmator for iOS as of 13 January 2026, shortly before the release of Pixelmator Pro for iPad. == Pixelmator Pro == Pixelmator Pro is an image, video, and vector editing software for macOS that launched on 29 November 2017. It was a paid upgrade for Pixelmator Classic users, featuring a redesigned interface, a graphics pipeline rewritten using Metal, Apple silicon support and a greater focus on ML/AI editing features. On 28 January 2026, Apple announced Apple Creator Studio, a subscription bundle for their professional software that contains Pixelmator Pro. They also brought Pixelmator Pro to iPad, shortly after discontinuing Pixelmator iOS. == Photomator == Photomator (formerly Pixelmator Photo) is a photo-oriented editing app which launched on iPad in 2019, on iOS in 2021, and macOS in 2022. After launching the macOS version, the app moved from a one-time purchase to a subscription; however, a lifetime license can still be purchased for $99. Photomator differentiates itself from other Pixelmator apps with features such as batch editing of full photoshoots and AI-powered color correction. Edits in Photomator are made on a single layer and are non-destructive.

    Read more →
  • Textual case-based reasoning

    Textual case-based reasoning

    Textual case-based reasoning (TCBR) is a subtopic of case-based reasoning, in short CBR, a popular area in artificial intelligence. CBR suggests the ways to use past experiences to solve future similar problems, requiring that past experiences be structured in a form similar to attribute-value pairs. This leads to the investigation of textual descriptions for knowledge exploration whose output will be, in turn, used to solve similar problems. == Subareas == Textual case-base reasoning research has focused on: measuring similarity between textual cases mapping texts into structured case representations adapting textual cases for reuse automatically generating representations.

    Read more →
  • Speculative decoding

    Speculative decoding

    Speculative decoding is an inference-time optimization for autoregressive large language models (LLMs) that generates multiple tokens per decoding step instead of one. A smaller draft model proposes a sequence of candidate tokens, and the larger target model verifies them in a single forward pass through a modified rejection sampling scheme. The verification preserves the target model's original output distribution, so the technique produces the same results as standard decoding while cutting latency by roughly two to three times. The name is an analogy to speculative execution in CPU design, where a processor runs instructions along a predicted branch before the outcome is known. == Background == Standard autoregressive decoding in large language models generates one token at a time. The model computes a probability distribution over its vocabulary, samples the next token, and feeds that token back as input. For large models, this process is bottlenecked by memory bandwidth rather than arithmetic throughput: loading the model's parameters from high-bandwidth memory (HBM) to the processor takes up most of the wall-clock time at each step. Because of this, a forward pass over one token and a forward pass over several tokens in a batch take roughly the same time. Speculative decoding relies on this property. == Mechanism == The technique alternates between two phases: drafting and verification. During drafting, a fast approximation model generates a short run of K candidate tokens, typically between 3 and 12. The draft model is usually a much smaller version of the target model or a lightweight auxiliary network. During verification, the target model scores the entire draft sequence in one batched forward pass. A modified rejection sampling algorithm compares the draft and target probabilities at each position. If the target model would have been at least as likely to produce a given token, that token is accepted; the first token that fails is resampled from a corrected distribution, and everything after it is thrown out. The result is that the output distribution is the same as if each token had been generated one at a time. How many tokens get accepted per cycle depends on how well the draft model matches the target. For common words and predictable continuations the match tends to be good, so the target model can confirm several tokens at once. == History == An early precursor was blockwise parallel decoding, proposed in 2018 by Stern, Shazeer, and Uszkoreit. Their method predicted multiple future tokens through auxiliary prediction heads and validated them against the autoregressive model, but it only worked with greedy decoding and did not preserve the full sampling distribution. The modern form of the technique came from Yaniv Leviathan, Matan Kalman, and Yossi Matias at Google Research, who posted "Fast Inference from Transformers via Speculative Decoding" on arXiv in November 2022. Separately and at about the same time, Charlie Chen and colleagues at DeepMind arrived at a closely related method they called speculative sampling, published in February 2023. Both papers introduced the use of rejection sampling to guarantee that the output distribution is unchanged. Leviathan et al. showed roughly 2–3x speedup on T5-XXL (11 billion parameters); Chen et al. reported 2–2.5x on the Chinchilla model (70 billion parameters). The Leviathan et al. paper was presented as an oral at the International Conference on Machine Learning in July 2023. == Variants == SpecInfer (Miao et al., 2024) uses multiple small language models to jointly build a tree of candidate continuations rather than a single chain. The target model verifies the whole tree in parallel and keeps the longest valid path, with reported speedups of 1.5–3.5x. Medusa (Cai et al., 2024) takes a different approach by not using a separate draft model at all. Extra lightweight decoding heads are attached to the target model itself, and each one predicts a token at a different future position. The candidates are evaluated through a tree-structured attention mechanism. The authors measured 2.2–3.6x speedup. EAGLE (Li et al., 2024) performs autoregression on the target model's internal feature representations (specifically the second-to-top layer) rather than on tokens directly. On LLaMA 2 Chat 70B, this gave a 2.7–3.5x latency reduction. Later versions added dynamic draft trees (EAGLE-2) and further optimizations (EAGLE-3), reaching 3–6.5x speedup. == Adoption == By 2024, speculative decoding had become a standard part of production LLM serving. Google uses it in the AI Overviews feature of Google Search. Open-source inference frameworks such as vLLM, NVIDIA's TensorRT-LLM, and SGLang all include built-in support for speculative decoding and its variants. Apple, AWS, and Meta have also published research extending the method or deploying it at scale.

    Read more →
  • Content determination

    Content determination

    Content determination is the subtask of natural language generation (NLG) that involves deciding on the information to be communicated in a generated text. It is closely related to the task of document structuring. == Example == Consider an NLG system which summarises information about sick babies. Suppose this system has four pieces of information it can communicate The baby is being given morphine via an IV drop The baby's heart rate shows bradycardia's (temporary drops) The baby's temperature is normal The baby is crying Which of these bits of information should be included in the generated texts? == Issues == There are three general issues which almost always impact the content determination task, and can be illustrated with the above example. Perhaps the most fundamental issue is the communicative goal of the text, i.e. its purpose and reader. In the above example, for instance, a doctor who wants to make a decision about medical treatment would probably be most interested in the heart rate bradycardias, while a parent who wanted to know how her child was doing would probably be more interested in the fact that the baby was being given morphine and was crying. The second issue is the size and level of detail of the generated text. For instance, a short summary which was sent to a doctor as a 160 character SMS text message might only mention the heart rate bradycardias, while a longer summary which was printed out as a multipage document might also mention the fact that the baby is on a morphine IV. The final issue is how unusual and unexpected the information is. For example, neither doctors nor parents would place a high priority on being told that the baby's temperature was normal, if they expected this to be the case. Regardless, content determination is very important to users, indeed in many cases the quality of content determination is the most important factor (from the user's perspective) in determining the overall quality of the generated text. == Techniques == There are three basic approaches to document structuring: schemas (content templates), statistical approaches, and explicit reasoning. Schemas are templates which explicitly specify the content of a generated text (as well as document structuring information). Typically, they are constructed by manually analysing a corpus of human-written texts in the target genre, and extracting a content template from these texts. Schemas work well in practice in domains where content is somewhat standardised, but work less well in domains where content is more fluid (such as the medical example above). Statistical techniques use statistical corpus analysis techniques to automatically determine the content of the generated texts. Such work is in its infancy, and has mostly been applied to contexts where the communicative goal, reader, size, and level of detail are fixed. For example, generation of newswire summaries of sporting events. Explicit reasoning approaches have probably attracted the most attention from researchers. The basic idea is to use AI reasoning techniques (such as knowledge-based rules, planning, pattern detection, case-based reasoning, etc.) to examine the information available to be communicated (including how unusual/unexpected it is), the communicative goal and reader, and the characteristics of the generated text (including target size), and decide on the optimal content for the generated text. A very wide range of techniques has been explored, but there is no consensus as to which is most effective.

    Read more →
  • Normalization (image processing)

    Normalization (image processing)

    In image processing, normalization is a process that changes the range of pixel intensity values, a kind of intensity mapping. Applications include photographs with poor contrast due to glare, for example. A typical case is contrast stretching. In more general fields of data processing, such as digital signal processing, it is referred to as dynamic range expansion. The purpose of dynamic range expansion in the various applications is usually to bring the image, or other type of signal, into a range that is more familiar or normal to the senses, hence the term normalization. Often, the motivation is to achieve consistency in dynamic range for a set of data, signals, or images to avoid mental distraction or fatigue. For example, a newspaper will strive to make all of the images in an issue share a similar range of grayscale. Auto-normalization in image processing software typically normalizes to the full dynamic range of the number system specified in the image file format. == Definition == Normalization transforms an n-dimensional grayscale image I : { X ⊆ R n } → { Min , . . , Max } {\displaystyle I:\{\mathbb {X} \subseteq \mathbb {R} ^{n}\}\rightarrow \{{\text{Min}},..,{\text{Max}}\}} with intensity values in the range ( Min , Max ) {\displaystyle ({\text{Min}},{\text{Max}})} , into a new image I N : { X ⊆ R n } → { newMin , . . , newMax } {\displaystyle I_{N}:\{\mathbb {X} \subseteq \mathbb {R} ^{n}\}\rightarrow \{{\text{newMin}},..,{\text{newMax}}\}} with intensity values in the range ( newMin , newMax ) {\displaystyle ({\text{newMin}},{\text{newMax}})} . The linear normalization of a grayscale digital image is performed according to the formula I N = ( I − Min ) newMax − newMin Max − Min + newMin {\displaystyle I_{N}=(I-{\text{Min}}){\frac {{\text{newMax}}-{\text{newMin}}}{{\text{Max}}-{\text{Min}}}}+{\text{newMin}}} For example, if the intensity range of the image is 50 to 180 and the desired range is 0 to 255 the process entails subtracting 50 from each of pixel intensity, making the range 0 to 130. Then each pixel intensity is multiplied by 255/130, making the range 0 to 255. Normalization might also be non-linear, as the relationship between I {\displaystyle I} and I N {\displaystyle I_{N}} may not be linear. An example of non-linear normalization is when the normalization follows a sigmoid function, in which case the normalized image is computed according to the formula I N = ( newMax − newMin ) 1 1 + e − I − β α + newMin {\displaystyle I_{N}=({\text{newMax}}-{\text{newMin}}){\frac {1}{1+e^{-{\frac {I-\beta }{\alpha }}}}}+{\text{newMin}}} Where α {\displaystyle \alpha } defines the width of the input intensity range, and β {\displaystyle \beta } defines the intensity around which the range is centered. Gamma correction (log/inverse log) is also a common transformation function. === Colorspace === Intensity operations generally operate on a colorspace that maps to the human perception of lightness without intentionally changing the other properties. This can be done, for example, by operating on the L component of the CIELAB color space, or approximately by operating on the Y component of YCbCr. It is also possible to operate on each of the RGB color channels, though the result will not always make sense. == Contrast stretching == This is the most significant and essential technique of spatial-based image enhancement. The basic intent of this contrast enhancement technique is to adjust the local contrast in the image so as to bring out the clear regions or objects in the image. Low-contrast images often result from poor or non-uniform lighting conditions, a limited dynamic range of the imaging sensor, or improper settings of the lens aperture. This operation tries to change the intensity of the pixel in the image, particularly in the input image, to obtain an enhanced image. It is based on the number of techniques, namely local, global, dark and bright levels of contrast. The contrast enhancement is considered as the amount of color or gray differentiation that lies among the different features in an image. The contrast enhancement improves the quality of image by increasing the luminance difference between the foreground and background. A contrast stretching transformation can be achieved by: Stretching the dark range of input values into a wider range of output values: This involves increasing the brightness of the darker areas in the image to enhance details and improve visibility. Shifting the mid-range of input values: This involves adjusting the brightness levels of the mid-tones in the image to improve overall contrast and clarity. Compressing the bright range of input values: This process involves reducing the brightness of the brighter areas in the image to prevent overexposure resulting in a more balanced and visually appealing image. It can be described as the following piecewise funciton: I N = { s 1 r 1 I if I < r 1 s 2 − s 1 r 1 − r 2 ( I − r 1 ) if r 1 ≤ I ≤ r 2 1 − s 2 1 − r 2 ( I − r 2 ) if I > r 2 {\displaystyle I_{N}={\begin{cases}{\frac {s_{1}}{r_{1}}}I&{\text{if }}Ir_{2}\end{cases}}} Where: ( r 1 , s 1 ) {\displaystyle (r_{1},s_{1})} defines the transition point between the "dark" range to the "main" range. ( r 2 , s 2 ) {\displaystyle (r_{2},s_{2})} defines the transition point between the "main" range to the "bright" range. A typical linear stretch is obtained when ( r 1 , s 1 ) = ( r min , 0 ) {\displaystyle (r_{1},s_{1})=(r_{\text{min}},0)} and ( r 2 , s 2 ) = ( r max , 1 ) {\displaystyle (r_{2},s_{2})=(r_{\text{max}},1)} , where r min {\displaystyle r_{\text{min}}} and r max {\displaystyle r_{\text{max}}} denote the minimum and maximum levels in the source image. === Global contrast stretching === Global Contrast Stretching considers all color palate ranges at once to determine the maximum and minimum values for the entire RGB color image. This approach utilizes the combination of RGB colors to derive a single maximum and minimum value for contrast stretching across the entire image. === Local contrast stretching === Local contrast stretching (LCS) is an image enhancement method that focuses on locally adjusting each pixel's value to improve the visualization of structures within an image, particularly in both the darkest and lightest portions. It operates by utilizing sliding windows, known as kernels, which traverse the image. The central pixel within each kernel is adjusted using the following formula: I p ( x , y ) = 255 × [ I 0 ( x , y ) − m i n ] ( m a x − m i n ) {\displaystyle I_{p}(x,y)=255\times {\frac {[I_{0}(x,y)-min]}{(max-min)}}} Where: Ip(x,y) is the color level for the output pixel (x,y) after the contrast stretching process. I0(x,y) is the color level input for data pixel (x, y). max is the maximum value for color level in the input image within the selected kernel. min is the minimum value for color level in the input image within the selected kernel. A piecewise form (see above) may also be used. LCS can be applied to the three color channels of an image separately.

    Read more →
  • Residual neural network

    Residual neural network

    A residual neural network (also referred to as a residual network or ResNet) is a deep learning architecture in which the layers learn residual functions with reference to the layer inputs. It was developed in 2015 for image recognition, and won the ImageNet Large Scale Visual Recognition Challenge (ILSVRC) of that year. As a point of terminology, "residual connection" refers to the specific architectural motif of x ↦ f ( x ) + x {\displaystyle x\mapsto f(x)+x} , where f {\displaystyle f} is an arbitrary neural network module. The motif had been used previously (see §History for details). However, the publication of ResNet made it widely popular for feedforward networks, appearing in neural networks that are seemingly unrelated to ResNet. The residual connection stabilizes the training and convergence of deep neural networks with hundreds of layers, and is a common motif in deep neural networks, such as transformer models (e.g., BERT, and GPT models such as ChatGPT), the AlphaGo Zero system, the AlphaStar system, and the AlphaFold system. == Mathematics == === Residual connection === In a multilayer neural network model, consider a (non-residual) subnetwork with a certain number of stacked layers (e.g., 2 or 3). Let H ( x ; α ) {\displaystyle H(x;\alpha )} denote the subnetwork. Suppose H ∗ {\displaystyle H^{}} is the desired optimal output of this subnetwork. Residual learning simply adds x {\displaystyle x} directly to the output, such that the optimal learned output now becomes be H ∗ − x {\displaystyle H^{}-x} , which is interpreted as a "residual" with respect to x {\displaystyle x} . The operation of "adding x {\displaystyle x} " is implemented via a "skip connection" that performs an identity mapping to connect the input of the subnetwork with its output. This connection is referred to as a "residual connection" in later work. Let F ( x ; α ) = H ( x ; a ) + x {\displaystyle F(x;\alpha )=H(x;a)+x} . The function F {\displaystyle F} is often represented by matrix multiplication interlaced with activation functions and normalization operations (e.g., batch normalization or layer normalization). As a whole, one of these subnetworks is referred to as a "residual block". A deep residual network is constructed by simply stacking these blocks. Long short-term memory (LSTM) has a memory mechanism that serves as a residual connection. In an LSTM without a forget gate, an input x t {\displaystyle x_{t}} is processed by a function F {\displaystyle F} and added to a memory cell c t {\displaystyle c_{t}} , resulting in c t + 1 = c t + F ( x t ) {\displaystyle c_{t+1}=c_{t}+F(x_{t})} . An LSTM with a forget gate essentially functions as a highway network. To stabilize the variance of the layers' inputs, it is recommended to replace the residual connections x + f ( x ) {\displaystyle x+f(x)} with x / L + f ( x ) {\displaystyle x/L+f(x)} , where L {\displaystyle L} is the total number of residual layers. === Projection connection === If the function F {\displaystyle F} is of type F : R n → R m {\displaystyle F:\mathbb {R} ^{n}\to \mathbb {R} ^{m}} where n ≠ m {\displaystyle n\neq m} , then F ( x ) + x {\displaystyle F(x)+x} is undefined. To handle this special case, a projection connection is used: y = F ( x ) + P ( x ) {\displaystyle y=F(x)+P(x)} where P {\displaystyle P} is typically a linear projection, defined by P ( x ) = M x {\displaystyle P(x)=Mx} where M {\displaystyle M} is a m × n {\displaystyle m\times n} matrix. The matrix is trained via backpropagation, as is any other parameter of the model. === Signal propagation === The introduction of identity mappings facilitates signal propagation in both forward and backward paths. ==== Forward propagation ==== If the output of the ℓ {\displaystyle \ell } -th residual block is the input to the ( ℓ + 1 ) {\displaystyle (\ell +1)} -th residual block (assuming no activation function between blocks), then the ( ℓ + 1 ) {\displaystyle (\ell +1)} -th input is: x ℓ + 1 = F ( x ℓ ) + x ℓ {\displaystyle x_{\ell +1}=F(x_{\ell })+x_{\ell }} Applying this formulation recursively, e.g.: x ℓ + 2 = F ( x ℓ + 1 ) + x ℓ + 1 = F ( x ℓ + 1 ) + F ( x ℓ ) + x ℓ {\displaystyle {\begin{aligned}x_{\ell +2}&=F(x_{\ell +1})+x_{\ell +1}\\&=F(x_{\ell +1})+F(x_{\ell })+x_{\ell }\end{aligned}}} yields the general relationship: x L = x ℓ + ∑ i = ℓ L − 1 F ( x i ) {\displaystyle x_{L}=x_{\ell }+\sum _{i=\ell }^{L-1}F(x_{i})} where L {\textstyle L} is the index of a residual block and ℓ {\textstyle \ell } is the index of some earlier block. This formulation suggests that there is always a signal that is directly sent from a shallower block ℓ {\textstyle \ell } to a deeper block L {\textstyle L} . ==== Backward propagation ==== The residual learning formulation provides the added benefit of mitigating the vanishing gradient problem to some extent. However, it is crucial to acknowledge that the vanishing gradient issue is not the root cause of the degradation problem, which is tackled through the use of normalization. To observe the effect of residual blocks on backpropagation, consider the partial derivative of a loss function E {\displaystyle {\mathcal {E}}} with respect to some residual block input x ℓ {\displaystyle x_{\ell }} . Using the equation above from forward propagation for a later residual block L > ℓ {\displaystyle L>\ell } : ∂ E ∂ x ℓ = ∂ E ∂ x L ∂ x L ∂ x ℓ = ∂ E ∂ x L ( 1 + ∂ ∂ x ℓ ∑ i = ℓ L − 1 F ( x i ) ) = ∂ E ∂ x L + ∂ E ∂ x L ∂ ∂ x ℓ ∑ i = ℓ L − 1 F ( x i ) {\displaystyle {\begin{aligned}{\frac {\partial {\mathcal {E}}}{\partial x_{\ell }}}&={\frac {\partial {\mathcal {E}}}{\partial x_{L}}}{\frac {\partial x_{L}}{\partial x_{\ell }}}\\&={\frac {\partial {\mathcal {E}}}{\partial x_{L}}}\left(1+{\frac {\partial }{\partial x_{\ell }}}\sum _{i=\ell }^{L-1}F(x_{i})\right)\\&={\frac {\partial {\mathcal {E}}}{\partial x_{L}}}+{\frac {\partial {\mathcal {E}}}{\partial x_{L}}}{\frac {\partial }{\partial x_{\ell }}}\sum _{i=\ell }^{L-1}F(x_{i})\end{aligned}}} This formulation suggests that the gradient computation of a shallower layer, ∂ E ∂ x ℓ {\textstyle {\frac {\partial {\mathcal {E}}}{\partial x_{\ell }}}} , always has a later term ∂ E ∂ x L {\textstyle {\frac {\partial {\mathcal {E}}}{\partial x_{L}}}} that is directly added. Even if the gradients of the F ( x i ) {\displaystyle F(x_{i})} terms are small, the total gradient ∂ E ∂ x ℓ {\textstyle {\frac {\partial {\mathcal {E}}}{\partial x_{\ell }}}} resists vanishing due to the added term ∂ E ∂ x L {\textstyle {\frac {\partial {\mathcal {E}}}{\partial x_{L}}}} . == Variants of residual blocks == === Basic block === A basic block is the simplest building block studied in the original ResNet. This block consists of two sequential 3x3 convolutional layers and a residual connection. The input and output dimensions of both layers are equal. === Bottleneck block === A bottleneck block consists of three sequential convolutional layers and a residual connection. The first layer in this block is a 1×1 convolution for dimension reduction (e.g., to 1/2 of the input dimension); the second layer performs a 3×3 convolution; the last layer is another 1×1 convolution for dimension restoration. The models of ResNet-50, ResNet-101, and ResNet-152 are all based on bottleneck blocks. === Pre-activation block === The pre-activation residual block applies activation functions before applying the residual function F {\displaystyle F} . Formally, the computation of a pre-activation residual block can be written as: x ℓ + 1 = F ( ϕ ( x ℓ ) ) + x ℓ {\displaystyle x_{\ell +1}=F(\phi (x_{\ell }))+x_{\ell }} where ϕ {\displaystyle \phi } can be any activation (e.g. ReLU) or normalization (e.g. LayerNorm) operation. This design reduces the number of non-identity mappings between residual blocks, and allows an identity mapping directly from the input to the output. This design was used to train models with 200 to over 1000 layers, and was found to consistently outperform variants where the residual path is not an identity function. The pre-activation ResNet with 200 layers took 3 weeks to train for ImageNet on 8 GPUs in 2016. Since GPT-2, transformer blocks have been mostly implemented as pre-activation blocks. This is often referred to as "pre-normalization" in the literature of transformer models. == Applications == Originally, ResNet was designed for computer vision. All transformer architectures include residual connections. Indeed, very deep transformers cannot be trained without them. The original ResNet paper made no claim on being inspired by biological systems. However, later research has related ResNet to biologically-plausible algorithms. A study published in Science in 2023 disclosed the complete connectome of an insect brain (specifically that of a fruit fly larva). This study discovered "multilayer shortcuts" that resemble the skip connections in artificial neural networks, including ResNets. == History == === Previous work === Residual connections were noticed in neu

    Read more →
  • GasBuddy

    GasBuddy

    GasBuddy is a technology company headquartered in Dallas, United States, that offers mobile applications and websites for tracking crowd-sourced locations and prices of gas stations and convenience stores in the United States and Canada. Their platforms offer information sourced from users, gas station operators, and partner companies. They also provide business-to-business services to gas stations and convenience store owners. == History == GasBuddy was founded in Minneapolis in 2000 by Dustin Coupal, Jason Toews as a community website for sharing gas prices. In 2004, they filed as a for-profit corporation in Minnesota under the name GasBuddy Organization Inc. In 2009, GasBuddy launched OpenStore, a platform that allows convenience stores to build and manage their own mobile apps. In 2010, the company launched its own mobile apps that allowed users to input gas prices from their smartphones. In 2013, Oil Price Information Service (OPIS), a subsidiary of UCG, acquired GasBuddy. OPIS is a provider of petroleum pricing and news for businesses. In 2016, IHS acquired OPIS, separating from GasBuddy, which remained with UCG as a subsidiary company. Initially only available in the United States and Canada, GasBuddy launched in Australia in March 2016. Also in that year, GasBuddy released a completely redesigned app, its first major redesign since its release in 2010. GasBuddy also unveiled a new logo and launched GasBuddy Business Pages. GasBuddy shut down the Australian version of their app in 2022. In 2017, GasBuddy launched a gas savings program titled "Pay with GasBuddy" intended to let consumers save at gas stations in the United States. In the same year, GasBuddy was involved in a lawsuit with Reveal Mobile, a location-based marketing company, over the sale of user location data. It was revealed that GasBuddy sold information on more than 4.5 million users to Reveal each month for $9.50 per 1000 users. According to CNET, that information included "users' latitude, longitude, IP address, and time stamps on the data collected," which sparked concern in the media and between its users. In 2021, the GasBuddy app rose to the most popular app on both Android and iPhone platforms in the wake of the Colonial Pipeline ransomware attack PDI acquired GasBuddy in 2021.

    Read more →
  • Law practice management software

    Law practice management software

    Law practice management software is software designed to manage the business operations of a law firm. This can include software that manages cases, client intake, court communications, electronic discovery, time tracking, trust accounting, and billing. == Features of law practice management software == Common features of practice management software include: Case management Time tracking Document assembly Contact management Calendaring Docket management Client portal Contract Management Court Case Status Tracker Trust accounting == Examples of law practice management software == Smokeball LEAP Legal Software PracticeEvolve Dye & Durham

    Read more →
  • Deep Instinct

    Deep Instinct

    Deep Instinct is a cybersecurity company that applies deep learning to cybersecurity. The company implements artificial intelligence to the task of preventing and detecting malware. The company was the recipient of the Technology Pioneer by The World Economic Forum in 2017. Lane Bess has been CEO of the company since 2022. == Overview == In 2015, Deep Instinct was founded by Guy Caspi, Dr. Eli David, and Nadav Maman. The headquarters of the company is located in New York City. In July 2017, NVIDIA became an investor. According to Tom's Hardware, NVIDIA’s investment enabled access to a GPU-based neural network and CUDA platform, which they were using to achieve maximum vulnerability detection rates. As of February 2020, the company had raised $43 million in Series C funding round. In April 2021, Deep Instinct raised $100 million in Series D funding to accelerate growth. == Partnerships == In April 2019, Deep Instinct partnered with Chinese artist, Guo O. Dong on an art project titled, The Persistence of Chaos, consisting of a laptop infected with 6 pieces of malware that represented $95 billion in damages. The art was auctioned with a final bid of $1,345,000. In the same year, Globes reported that, HP Inc partnered with Deep Instinct to launch their security solution HP SureSense, which has been applied to the EliteBook and Zbook devices.

    Read more →
  • Artificial intelligence in fraud detection

    Artificial intelligence in fraud detection

    Artificial intelligence is used by many different businesses and organizations. It is widely used in the financial sector, especially by accounting firms, to help detect fraud. In 2022, PricewaterhouseCoopers reported that fraud has impacted 46% of all businesses in the world. The shift from working in person to working from home has brought increased access to data. According to an FTC (Federal Trade Commission) study from 2022, customers reported fraud of approximately $5.8 billion in 2021, an increase of 70% from the year before. The majority of these scams were imposter scams and online shopping frauds. Furthermore, artificial intelligence plays a crucial role in developing advanced algorithms and machine learning models that enhance fraud detection systems, enabling businesses to stay ahead of evolving fraudulent tactics in an increasingly digital landscape. == Tools == === Expert systems === Expert systems were first designed in the 1970s as an expansion into artificial intelligence technologies. Their design is based on the premise of decreasing potential user error in decision-making and emulating mental reasoning used by experts in a particular field. They differentiate themselves from traditional linear reasoning models by separating identified points in data and processing them individually at the same time. Though, these systems do not rely purely on machine-learned intelligence. Information regarding rules, practices, and procedures in the form of "if-then" statements are implemented into the programming of the system. Users interact with the system by feeding information into the system either through direct entry or import of external data. An inference system compares the information provided by the user with corresponding rules that are believed to specifically apply to the situation. Using this information and the corresponding rules will be used to create a solution to the user's query. Expert systems will generally not operate properly when the common procedures for a specified situation are ambiguous due to the need for well-defined rules. Implementation of expert systems in accounting procedures is feasible in areas where professional judgment is required. Situations where expert systems are applicable include investigations into transactions that involve potential fraudulent entries, instances of going concern, and the evaluation of risk in the planning stages of an audit. === Continuous auditing === Continuous auditing is a set of processes that assess various aspects of information gathered in an audit to classify areas of risk and potential weaknesses in financial Internal controls at a more frequent rate than traditional methods. Instead of analyzing recorded transactions and journal entries periodically, continuous auditing focuses on interpreting the character of these actions more frequently. The frequency of these processes being undertaken as well as highlighting areas of importance is up to the discretion of their implementer, who commonly makes such decisions based on the level of risk in the accounts being evaluated and the goals of implementing the system. Performance of these processes can occur as frequently as being nearly instantaneous with an entry being posted. The processes involved with analyzing financial data in continuous auditing can include the creation of spreadsheets to allow for interactive information gathering, calculation of financial ratios for comparison with previously created models, and detection of errors in entered figures. A primary goal of this practice is to allow for quicker and easier detection of instances of faulty controls, errors, and instances of fraud. === Machine learning and deep learning === The ability of machine learning and deep learning to swiftly and effectively sort through vast volumes of data in the forms of various documents relevant to companies and documents being audited makes them applicable to the domains of audit and fraud detection. Examples of this include recognizing key language in contracts, identifying levels of risk of fraud in transactions, and assessing journal entries for misstatement. == Applications == === 'Big 4' Accounting Firms === Deloitte created an Al-enabled document-reviewing system in 2014. The system automates the method of reviewing and extracting relevant information from different business documents. Deloitte claims that this innovation has made a difference by reducing time spent going through lawful contract documents, invoices, money-related articulations, and board minutes by up to 50%. Working with IBM's Watson, Deloitte is developing cognitive-technology-enhanced commerce arrangements for its clients. LeasePoint is fueled by IBM TRIRIGA (this product evolved into IBM Maximo Real Estate and Facilities) and uses Deloitte's industrial information to create an end-to-end leasing portfolio. Automated Cognitive Resource Assessment employs IBM's Maximo innovation to progress the proficiency of asset inspection. Ernst and Young (EY) connected Al to the investigation of lease contracts. EY (Australia) has also received Al-enabled auditing technology. Collaborating with H20.ai, PwC developed an Al-enabled framework (GL.ai) capable of analyzing reports and preparing reports. PwC claims to have made a significant investment in normal dialect processing (NLP), an Al-enabled innovation to process unstructured information efficiently. KPMG built a portfolio of Al instruments, called KPMG Ignite, to upgrade trade decisions and forms. Working with Microsoft and IBM Watson, KPMG is creating instruments to coordinate Al, data analytics, Cognitive Technologies, and RPA. == Advantages == === Efficiency === The process of auditing an entity in an attempt to detect fraudulent activity requires the repeating of investigatory processes until an error or misstatement may be identified. Under traditional methods, these processes would be carried out by a human being. Proponents of artificial intelligence in fraud detection have stated that these traditional methods are inefficient and can be more quickly accomplished with the aid of an intelligent computing system. A survey of 400 chief executive officers created by KPMG in 2016 found that approximately 58% believed that artificial intelligence would play a key role in making audits more efficient in the future. === Data interpretation === Higher levels of fraud detection entail the use of professional judgement to interpret data. Supporters of artificial intelligence being used in financial audits have claimed that increased risks from instances of higher data interpretation can be minimized through such technologies. One necessary element of an audit of financial statements that requires professional judgement is the implementation of thresholds for materiality. Materiality entails the distinction between errors and transactions in financial statements that would impact decisions made by users of those financial statements. The threshold for materiality in an audit is set by the auditor based on various factors. Artificial intelligence has been used to interpret data and suggest materiality thresholds to be implemented through the use of expert systems. === Decreased costs === Those in favor of using artificial intelligence to complete investigations of fraud have stated that such technologies decrease the amount of time required to complete tasks that are repetitive. The claim further states that such efficiencies allow for lowered resource requirements, which can then be further spent on tasks that have not been fully automated. The audit firm Ernst & Young has posited these claims by declaring that their deep learning systems have been used to reduce time spent on administrative tasks by analyzing relevant audit documents. According to the firm, this has allowed their employees to focus more on judgement and analysis. == Disadvantages == === Job Displacement === The inescapable reception of computer based intelligence and robotization advancements might prompt critical work relocation across different enterprises. As artificial intelligence frameworks become more equipped for performing undertakings customarily completed by people, there is a worry that specific work jobs could become out of date, prompting joblessness and financial imbalance. === Initial investment requirement === Along with a knowledge of coding and building systems through computer programs, we are seeing the advantages of these systems, but since they are so new, they require a large investment to start building such a system. Any firm that is planning on implementing an AI system to detect fraud must hire a team of data scientists, along with upgrading their cloud system and data storage. The system must be consistently monitored and updated to be the most efficient form of itself, otherwise the likelihood of fraud being involved in those transactions increases. If one does not initially invest in such a syst

    Read more →
  • Version space learning

    Version space learning

    Version space learning is a logical approach to machine learning, specifically binary classification. Version space learning algorithms search a predefined space of hypotheses, viewed as a set of logical sentences. Formally, the hypothesis space is a disjunction H 1 ∨ H 2 ∨ . . . ∨ H n {\displaystyle H_{1}\lor H_{2}\lor ...\lor H_{n}} (i.e., one or more of hypotheses 1 through n are true). A version space learning algorithm is presented with examples, which it will use to restrict its hypothesis space; for each example x, the hypotheses that are inconsistent with x are removed from the space. This iterative refining of the hypothesis space is called the candidate elimination algorithm, the hypothesis space maintained inside the algorithm, its version space. == The version space algorithm == In settings where there is a generality-ordering on hypotheses, it is possible to represent the version space by two sets of hypotheses: (1) the most specific consistent hypotheses, and (2) the most general consistent hypotheses, where "consistent" indicates agreement with observed data. The most specific hypotheses (i.e., the specific boundary SB) cover the observed positive training examples, and as little of the remaining feature space as possible. These hypotheses, if reduced any further, exclude a positive training example, and hence become inconsistent. These minimal hypotheses essentially constitute a (pessimistic) claim that the true concept is defined just by the positive data already observed: Thus, if a novel (never-before-seen) data point is observed, it should be assumed to be negative. (I.e., if data has not previously been ruled in, then it's ruled out.) The most general hypotheses (i.e., the general boundary GB) cover the observed positive training examples, but also cover as much of the remaining feature space without including any negative training examples. These, if enlarged any further, include a negative training example, and hence become inconsistent. These maximal hypotheses essentially constitute a (optimistic) claim that the true concept is defined just by the negative data already observed: Thus, if a novel (never-before-seen) data point is observed, it should be assumed to be positive. (I.e., if data has not previously been ruled out, then it's ruled in.) Thus, during learning, the version space (which itself is a set – possibly infinite – containing all consistent hypotheses) can be represented by just its lower and upper bounds (maximally general and maximally specific hypothesis sets), and learning operations can be performed just on these representative sets. After learning, classification can be performed on unseen examples by testing the hypothesis learned by the algorithm. If the example is consistent with multiple hypotheses, a majority vote rule can be applied. == Historical background == The notion of version spaces was introduced by Mitchell in the early 1980s as a framework for understanding the basic problem of supervised learning within the context of solution search. Although the basic "candidate elimination" search method that accompanies the version space framework is not a popular learning algorithm, there are some practical implementations that have been developed (e.g., Sverdlik & Reynolds 1992, Hong & Tsang 1997, Dubois & Quafafou 2002). A major drawback of version space learning is its inability to deal with noise: any pair of inconsistent examples can cause the version space to collapse, i.e., become empty, so that classification becomes impossible. One solution of this problem is proposed by Dubois and Quafafou that proposed the Rough Version Space, where rough sets based approximations are used to learn certain and possible hypothesis in the presence of inconsistent data.

    Read more →