Bainu ("how are you?") is a Chinese social networking website written in the Mongolian language. As of 2020 it had about 400,000 users, concentrated in Inner Mongolia. == Core features and positioning == Language and Cultural Characteristics Bainu is based on Traditional Mongolian Script and supports social interactions in the Mongolian language, including various message formats such as text, voice, images, and video. This design aims to preserve and promote Mongolian language and culture, particularly appealing to users in Inner Mongolia and other Mongolian-populated areas. Social Features Instant Messaging: Supports one-on-one private chats and group chats. Users can create interest-based groups or join local communities. Life Sharing: Through the "Chomorlig" feature (similar to Moments or a dynamic feed), users can share daily highlights to enhance community interaction. Location-Based Socializing: Recommends nearby users based on location, making it easier to connect with Mongolian friends in the same city or neighboring regions. Multilingual Support The app interface is available in English, Mongolian, and Simplified Chinese. == Technical Features and User Experience == Cross-Platform Compatibility Supports iPhone, iPad, Mac (with M1 chip or above), and Apple Vision Pro devices, covering users across the Apple ecosystem. Pricing Model Free download and basic features are available. Premium services (e.g., ad-free experience, extended social functions) require a subscription, with pricing options including $0.99/month, $2.99/quarter, and $6.99/year. User Feedback Positive Reviews: Some users praise it as the "best Mongolian-language chat app," recognizing its cultural value and social convenience. Negative Feedback: Reports of app crashes and technical issues, with some users calling for improved stability (e.g., frequent crashes in the iOS version). == Privacy and Data Policy == Bainu collects user data such as location, contact information, and device identifiers, which are linked to user identities. Additionally, user behavior may be tracked through third-party services, raising some privacy concerns. == Current Development and Challenges == User Base As of 2020, Bainu had approximately 400,000 users, primarily concentrated in Inner Mongolia. Policy Impact It was reported by Voice of America (VOA) that the Chinese authorities blocked Bainu on 23 August 2020 in order to prohibit Mongolians from discussing the issue of the authorities’ implementation of "bilingual education" in elementary schools. But now, in 2025, this software is completely available for download and use. see:https://bainu.com/
AI-complete
In the field of artificial intelligence (AI), tasks that are hypothesized to require artificial general intelligence to solve are informally known as AI-complete or AI-hard. Calling a problem AI-complete reflects the belief that it cannot be solved by a simple specific algorithm. Prior to 2013, problems supposed to be AI-complete included computer vision, natural language understanding, and dealing with unexpected circumstances while solving any real-world problem. AI-complete tasks were notably considered useful for distinguishing humans from automated agents, as CAPTCHAs aim to do. == History == The term was coined by Fanya Montalvo by analogy with NP-complete and NP-hard in complexity theory, which formally describes the most famous class of difficult problems. Early uses of the term are in Erik Mueller's 1987 PhD dissertation and in Eric Raymond's 1991 Jargon File. Expert systems, that were popular in the 1980s, were able to solve very simple and/or restricted versions of AI-complete problems, but never in their full generality. When AI researchers attempted to "scale up" their systems to handle more complicated, real-world situations, the programs tended to become excessively brittle without commonsense knowledge or a rudimentary understanding of the situation: they would fail as unexpected circumstances outside of its original problem context would begin to appear. When human beings are dealing with new situations in the world, they are helped by their awareness of the general context: they know what the things around them are, why they are there, what they are likely to do and so on. They can recognize unusual situations and adjust accordingly. Expert systems lacked this adaptability and were brittle when facing new situations. DeepMind published a work in May 2022 in which they trained a single model to do several things at the same time. The model, named Gato, can "play Atari, caption images, chat, stack blocks with a real robot arm and much more, deciding based on its context whether to output text, joint torques, button presses, or other tokens." Similarly, some tasks once considered to be AI-complete, like machine translation, are among the capabilities of large language models. == AI-complete problems == AI-complete problems have been hypothesized to include: AI peer review (composite natural language understanding, automated reasoning, automated theorem proving, formalized logic expert system) Bongard problems Computer vision (and subproblems such as object recognition) Natural language understanding (and subproblems such as text mining, machine translation, and word-sense disambiguation) Autonomous driving Dealing with unexpected circumstances while solving any real world problem, whether navigation, planning, or even the kind of reasoning done by expert systems. == Formalization == Computational complexity theory deals with the relative computational difficulty of computable functions. By definition, it does not cover problems whose solution is unknown or has not been characterized formally. Since many AI problems have no formalization yet, conventional complexity theory does not enable a formal definition of AI-completeness. == Research == Roman Yampolskiy suggests that a problem C {\displaystyle C} is AI-Complete if it has two properties: It is in the set of AI problems (Human Oracle-solvable). Any AI problem can be converted into C {\displaystyle C} by some polynomial time algorithm. On the other hand, a problem H {\displaystyle H} is AI-Hard if and only if there is an AI-Complete problem C {\displaystyle C} that is polynomial time Turing-reducible to H {\displaystyle H} . This also gives as a consequence the existence of AI-Easy problems, that are solvable in polynomial time by a deterministic Turing machine with an oracle for some problem. Yampolskiy has also hypothesized that the Turing Test is a defining feature of AI-completeness. Groppe and Jain classify problems which require artificial general intelligence to reach human-level machine performance as AI-complete, while only restricted versions of AI-complete problems can be solved by the current AI systems. For Šekrst, getting a polynomial solution to AI-complete problems would not necessarily be equal to solving the issue of artificial general intelligence, while emphasizing the lack of computational complexity research being the limiting factor towards achieving artificial general intelligence. For Kwee-Bintoro and Velez, solving AI-complete problems would have strong repercussions on society.
Vladimir Batagelj
Vladimir Batagelj (born June 14, 1948 in Idrija, Yugoslavia) is a Slovenian mathematician and an emeritus professor of mathematics at the University of Ljubljana. He is known for his work in discrete mathematics and combinatorial optimization, particularly analysis of social networks and other large networks (blockmodeling). == Education and career == Vladimir Batagelj completed his Ph.D. at the University of Ljubljana in 1986 under the direction of Tomaž Pisanski. He stayed at the University of Ljubljana as a professor until his retirement, where he was a professor of sociology and statistics, while also being a chair of the Department of Sociology of the Faculty of Social Sciences. As visiting professor, he was taught at the University of Pittsburgh (1990-91) and at the University of Konstanz (2002). He was also a member of editorial boards of two journals: Informatica and Journal of Social Structure. His work has been cited over 11000 times. His book Exploratory Social Network Analysis with Pajek on blockmodeling, coauthored with Wouter de Nooy and Andrej Mrvar, is Batagelj's most cited work and has over 3300 citations. The book was translated into Chinese and Japanese. The revised and expanded third edition has been published by Cambridge University Press. In 1975, 11 years before completing his PhD, Batagelj published a solo paper in Communications of the ACM. Batagelj authored more than 20 textbooks in Slovenian, covering topics like TeX, combinatorics and discrete mathematics. He has also written extensively in the Slovenian popular science journal Presek. Batagelj has advised 9 Ph.D. students. == Pajek == Batagelj is particularly known for his work on Pajek, a freely available software for analysis and visualization of large networks. He began work on Pajek in 1996 with Andrej Mrvar, who was then his PhD student. == Awards and honors == First prizes for contributions (with Andrej Mrvar) to Graph Drawing Contests in years: 1995, 1996, 1997, 1998, 1999, 2000 and 2005 / Graph Drawing Hall of Fame. In 2007 the book Generalized blockmodeling was awarded the Harrison White Outstanding Book Award by the Mathematical Sociology Section of American Sociological Association In 2007 he was awarded (together with Anuška Ferligoj) the Simmel Award by INSNA. In 2013, Vladimir Batagelj and Andrej Mrvar received the INSNA's William D. Richards Software award for their work on Pajek. == Selected bibliography == Vladimir Batagelj, Social Network Analysis, Large-Scale [1]. in R.A. Meyers, ed., Encyclopedia of Complexity and Systems Science, Springer 2009: 8245–8265. Vladimir Batagelj, Complex Networks, Visualization of [2]. in R.A. Meyers, ed., Encyclopedia of Complexity and Systems Science, Springer 2009: 1253–1268. Wouter de Nooy, Andrej Mrvar, Vladimir Batagelj, Mark Granovetter (Series Editor), Exploratory Social Network Analysis with Pajek (Structural Analysis in the Social Sciences), Cambridge University Press 2005 (ISBN 0-521-60262-9). ESNA in Japanese, TDU, 2010. Patrick Doreian, Vladimir Batagelj, Anuška Ferligoj, Mark Granovetter (Series Editor), Generalized Blockmodeling (Structural Analysis in the Social Sciences), Cambridge University Press 2004 (ISBN 0-521-84085-6)
Sigmoid function
A sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the logistic function. Other sigmoid functions are given in the Examples section. In some fields, most notably in the context of artificial neural networks, the term "sigmoid function" is used as a synonym for "logistic function". Special cases of sigmoid functions include the Gompertz curve (used in modeling systems that saturate at large values of x) and the ogee curve (used in the spillway of some dams). Sigmoid functions have domain of all real numbers, with return (response) value commonly monotonically increasing but could be decreasing. Sigmoid functions most often show a return value (y axis) in the range 0 to 1. Another commonly used range is from −1 to 1. There is also the Heaviside step function, which instantaneously transitions between 0 and 1. A wide variety of sigmoid functions including the logistic and hyperbolic tangent functions have been used as the activation function of artificial neurons. Sigmoid curves are also common in statistics as cumulative distribution functions (which go from 0 to 1), such as the integrals of the logistic density, the normal density, and Student's t probability density functions. The logistic sigmoid function is invertible, and its inverse is the logit function. == Theory == In mathematics, a unitary sigmoid function is a bounded sigmoid-type function normalized to the unit range, typically with lower and upper asymptotes at 0 and 1. The theory proposed by Grebenc distinguishes three kinds of unitary sigmoid functions according to their asymptotic behavior and the presence or absence of oscillation near the asymptotes. A general form of a unitary sigmoid function is y = A S ( f ( x ) ) + B , {\displaystyle y=A\,S(f(x))+B,} where S {\displaystyle S} is an increasing sigmoid function, f ( x ) {\displaystyle f(x)} is a transformation of the independent variable, and A {\displaystyle A} and B {\displaystyle B} are constants controlling scaling and translation. === Classification === ==== 1st kind ==== A unitary sigmoid function of the first kind is a bounded increasing function that approaches its lower and upper asymptotes monotonically, without oscillation. This class includes many of the standard sigmoid functions used in statistics, biomathematics, and engineering, such as the logistic function and related generalizations. ==== 2nd kind ==== A unitary sigmoid function of the second kind is a bounded increasing function that oscillates near the upper asymptote while preserving an overall sigmoid transition. ==== 3rd kind ==== A unitary sigmoid function of the third kind is a bounded increasing function that oscillates near both the lower and upper asymptotes. These functions retain the global shape of a sigmoid curve but exhibit oscillatory behavior in the vicinity of both limiting states. === Taxonomy === The tables below show the taxonomy of unitary sigmoid functions of all three kinds. Table 1. Taxonomy matrix with examples of sigmoid functions of the 1st kind Table 2. Taxonomy matrix with examples of sigmoid functions of the 2nd kind on the unbounded interval Table 3. Taxonomy matrix with examples of sigmoid functions of the 3rd kind === Construction methods === The same theory presents a list of 30 methods for constructing sigmoid functions.. These include algebraic transformations, integration and convolution methods, constructions from bell-shaped functions, solutions of ordinary and partial differential equations, recursive schemes, stochastic differential equations, feedback systems, and chaotic systems. M0: Construction method for sigmoid functions not evident or intuitive M1: Inverse of singularity functions M2: Sigmoid functions of embedded positive functions M3: Rising a sigmoid function to the power M4: Exponentiating a sigmoid function M5: Symmetric sigmoid functions derived from asymmetric ones M6: Sigmoid functions of the reciprocal independent variable M7: Embedding a sigmoid function into other function M8: Sum of sigmoid functions M9: Multiplication of sigmoid functions M10: Integral of the product of an increasing and a decreasing function M11: Derivation from lambda (bell-shaped) functions M12: Integration of lambda (bell-shaped) function M13: Integration of the sum of lambda (bell-shaped) functions M14: Integration of the product of two lambda (bell-shaped) functions M15: Integration of the difference of two shifted sigmoid functions M16: Integration of the product of two shifted sigmoid functions M17: Convolution of sigmoid functions M18: Integration of the product of lambda and sigmoid function M19: Solutions of ordinary differential equations M20: Solutions of partial differential equation (PDE) M21: Solutions of functional differential equation (FDE) M22: Sum of a sigmoid function and some derivatives M23: Combination of sigmoid functions, its derivative and integral M24: Filtering sigmoid functions M25: Special cases of Gauss hypergeometric functions M26: Feedback closed-loop systems M27: Recursive functions M28: Recursive time-delayed feed-forward loops M29: Solutions of stochastic differential equation M30: Chaotic sigmoid functions Consult reference for more details. == Definition == A sigmoid function is a bounded, differentiable, real function that is defined for all real input values and has a positive derivative at each point. == Properties == In general, a sigmoid function is monotonic, and has a first derivative which is bell shaped. Conversely, the integral of any continuous, non-negative, bell-shaped function (with one local maximum and no local minimum, unless degenerate) will be sigmoidal. Thus the cumulative distribution functions for many common probability distributions are sigmoidal. One such example is the error function, which is related to the cumulative distribution function of a normal distribution; another is the arctan function, which is related to the cumulative distribution function of a Cauchy distribution. A sigmoid function is constrained by a pair of horizontal asymptotes as x → ± ∞ {\displaystyle x\rightarrow \pm \infty } . A sigmoid function is convex for values less than a particular point, and it is concave for values greater than that point: in many of the examples here, that point is 0. == Examples == Logistic function f ( x ) = 1 1 + e − x {\displaystyle f(x)={\frac {1}{1+e^{-x}}}} Hyperbolic tangent (shifted and scaled version of the logistic function, above) f ( x ) = tanh x = e x − e − x e x + e − x {\displaystyle f(x)=\tanh x={\frac {e^{x}-e^{-x}}{e^{x}+e^{-x}}}} Arctangent function f ( x ) = arctan x {\displaystyle f(x)=\arctan x} Gudermannian function f ( x ) = gd ( x ) = ∫ 0 x d t cosh t = 2 arctan ( tanh ( x 2 ) ) {\displaystyle f(x)=\operatorname {gd} (x)=\int _{0}^{x}{\frac {dt}{\cosh t}}=2\arctan \left(\tanh \left({\frac {x}{2}}\right)\right)} Error function f ( x ) = erf ( x ) = 2 π ∫ 0 x e − t 2 d t {\displaystyle f(x)=\operatorname {erf} (x)={\frac {2}{\sqrt {\pi }}}\int _{0}^{x}e^{-t^{2}}\,dt} Generalised logistic function f ( x ) = ( 1 + e − x ) − α , α > 0 {\displaystyle f(x)=\left(1+e^{-x}\right)^{-\alpha },\quad \alpha >0} Smoothstep function f ( x ) = { ( ∫ 0 1 ( 1 − u 2 ) N d u ) − 1 ∫ 0 x ( 1 − u 2 ) N d u , | x | ≤ 1 sgn ( x ) | x | ≥ 1 N ∈ Z ≥ 1 {\displaystyle f(x)={\begin{cases}{\displaystyle \left(\int _{0}^{1}\left(1-u^{2}\right)^{N}du\right)^{-1}\int _{0}^{x}\left(1-u^{2}\right)^{N}\ du},&|x|\leq 1\\\\\operatorname {sgn}(x)&|x|\geq 1\\\end{cases}}\quad N\in \mathbb {Z} \geq 1} Some algebraic functions, for example f ( x ) = x 1 + x 2 {\displaystyle f(x)={\frac {x}{\sqrt {1+x^{2}}}}} and in a more general form f ( x ) = x ( 1 + | x | k ) 1 / k {\displaystyle f(x)={\frac {x}{\left(1+|x|^{k}\right)^{1/k}}}} Up to shifts and scaling, many sigmoids are special cases of f ( x ) = φ ( φ ( x , β ) , α ) , {\displaystyle f(x)=\varphi (\varphi (x,\beta ),\alpha ),} where φ ( x , λ ) = { ( 1 − λ x ) 1 / λ λ ≠ 0 e − x λ = 0 {\displaystyle \varphi (x,\lambda )={\begin{cases}(1-\lambda x)^{1/\lambda }&\lambda \neq 0\\e^{-x}&\lambda =0\\\end{cases}}} is the inverse of the negative Box–Cox transformation, and α < 1 {\displaystyle \alpha <1} and β < 1 {\displaystyle \beta <1} are shape parameters. Smooth transition function normalized to (−1,1): f ( x ) = { 2 1 + e − 2 m x 1 − x 2 − 1 , | x | < 1 sgn ( x ) | x | ≥ 1 = { tanh ( m x 1 − x 2 ) , | x | < 1 sgn ( x ) | x | ≥ 1 {\displaystyle {\begin{aligned}f(x)&={\begin{cases}{\displaystyle {\frac {2}{1+e^{-2m{\frac {x}{1-x^{2}}}}}}-1},&|x|<1\\\\\operatorname {sgn}(x)&|x|\geq 1\\\end{cases}}\\&={\begin{cases}{\displaystyle \tanh \left(m{\frac {x}{1-x^{2}}}\right)},&|x|<1\\\\\operatorname {sgn}(x)&|x|\geq 1\\\end{cases}}\end{aligned}}} using the hyperbolic tangent mentioned above. Here, m {\displaystyle m} is a free parameter encoding the slope at x = 0 {\displaystyle x=0} , which must be great
Apache Mahout
Apache Mahout is a project of the Apache Software Foundation to produce free implementations of distributed or otherwise scalable machine learning algorithms focused primarily on linear algebra. In the past, many of the implementations use the Apache Hadoop platform, however today it is primarily focused on Apache Spark. Mahout also provides Java/Scala libraries for common math operations (focused on linear algebra and statistics) and primitive Java collections. Mahout is a work in progress; a number of algorithms have been implemented. == Features == === Samsara === Apache Mahout-Samsara refers to a Scala domain-specific language (DSL) that allows users to use R-like syntax as opposed to traditional Scala-like syntax. This allows user to express algorithms concisely and clearly. === Backend agnostic === Apache Mahout's code abstracts the domain-specific language from the engine where the code is run. While active development is done with the Apache Spark engine, users are free to implement any engine they choose- H2O and Apache Flink have been implemented in the past and examples exist in the code base. === GPU/CPU accelerators === The JVM has notoriously slow computation. To improve speed, "native solvers" were added which move in-core, and by extension, distributed BLAS operations out of the JVM, offloading to off-heap or GPU memory for processing via multiple CPUs and/or CPU cores, or GPUs when built against the ViennaCL library. ViennaCL is a highly optimized C++ library with BLAS operations implemented in OpenMP, and OpenCL. As of release 14.1, the OpenMP build considered to be stable, leaving the OpenCL build is still in its experimental proof-of-concept phase. === Recommenders === Apache Mahout features implementations of Alternating Least Squares, Co-Occurrence, and Correlated Co-Occurrence, a unique-to-Mahout recommender algorithm that extends co-occurrence to be used on multiple dimensions of data. == History == === Transition from Map Reduce to Apache Spark === While Mahout's core algorithms for clustering, classification and batch based collaborative filtering were implemented on top of Apache Hadoop using the map/reduce paradigm, it did not restrict contributions to Hadoop-based implementations. Contributions that run on a single node or on a non-Hadoop cluster were also welcomed. For example, the 'Taste' collaborative-filtering recommender component of Mahout was originally a separate project and can run stand-alone without Hadoop. Starting with the release 0.10.0, the project shifted its focus to building a backend-independent programming environment, code named "Samsara". The environment consists of an algebraic backend-independent optimizer and an algebraic Scala DSL unifying in-memory and distributed algebraic operators. Supported algebraic platforms are Apache Spark, H2O, and Apache Flink. Support for MapReduce algorithms started being gradually phased out in 2014. === Release history === === Developers === Apache Mahout is developed by a community. The project is managed by a group called the "Project Management Committee" (PMC). The current PMC is Andrew Musselman, Andrew Palumbo, Drew Farris, Isabel Drost-Fromm, Jake Mannix, Pat Ferrel, Paritosh Ranjan, Trevor Grant, Robin Anil, Sebastian Schelter, Stevo Slavić.
Aldus PhotoStyler
Aldus PhotoStyler was a graphics software program developed by the Taiwanese company Ulead. Released in June 1991 as the first 24 bit image editor for Windows, it was bought the same year by the Aldus Prepress group. Its main competition was Adobe Photoshop. Version 2.0 (late 1993) introduced a new user interface and improved color calibration. PhotoStyler SE - lacking some features of the version 2.0 - was bundled with scanners like HP ScanJet. The product disappeared from the Adobe product line after Adobe acquired Aldus in 1994.
Relief (feature selection)
Relief is an algorithm developed by Kenji Kira and Larry Rendell in 1992 that takes a filter-method approach to feature selection that is notably sensitive to feature interactions. It was originally designed for application to binary classification problems with discrete or numerical features. Relief calculates a feature score for each feature which can then be applied to rank and select top scoring features for feature selection. Alternatively, these scores may be applied as feature weights to guide downstream modeling. Relief feature scoring is based on the identification of feature value differences between nearest neighbor instance pairs. If a feature value difference is observed in a neighboring instance pair with the same class (a 'hit'), the feature score decreases. Alternatively, if a feature value difference is observed in a neighboring instance pair with different class values (a 'miss'), the feature score increases. The original Relief algorithm has since inspired a family of Relief-based feature selection algorithms (RBAs), including the ReliefF algorithm. Beyond the original Relief algorithm, RBAs have been adapted to (1) perform more reliably in noisy problems, (2) generalize to multi-class problems (3) generalize to numerical outcome (i.e. regression) problems, and (4) to make them robust to incomplete (i.e. missing) data. To date, the development of RBA variants and extensions has focused on four areas; (1) improving performance of the 'core' Relief algorithm, i.e. examining strategies for neighbor selection and instance weighting, (2) improving scalability of the 'core' Relief algorithm to larger feature spaces through iterative approaches, (3) methods for flexibly adapting Relief to different data types, and (4) improving Relief run efficiency. Their strengths are that they are not dependent on heuristics, they run in low-order polynomial time, and they are noise-tolerant and robust to feature interactions, as well as being applicable for binary or continuous data; however, it does not discriminate between redundant features, and low numbers of training instances fool the algorithm. == Relief Algorithm == Take a data set with n instances of p features, belonging to two known classes. Within the data set, each feature should be scaled to the interval [0 1] (binary data should remain as 0 and 1). The algorithm will be repeated m times. Start with a p-long weight vector (W) of zeros. At each iteration, take the feature vector (X) belonging to one random instance, and the feature vectors of the instance closest to X (by Euclidean distance) from each class. The closest same-class instance is called 'near-hit', and the closest different-class instance is called 'near-miss'. Update the weight vector such that W i = W i − ( x i − n e a r H i t i ) 2 + ( x i − n e a r M i s s i ) 2 , {\displaystyle W_{i}=W_{i}-(x_{i}-\mathrm {nearHit} _{i})^{2}+(x_{i}-\mathrm {nearMiss} _{i})^{2},} where i {\displaystyle i} indexes the components and runs from 1 to p. Thus the weight of any given feature decreases if it differs from that feature in nearby instances of the same class more than nearby instances of the other class, and increases in the reverse case. After m iterations, divide each element of the weight vector by m. This becomes the relevance vector. Features are selected if their relevance is greater than a threshold τ. Kira and Rendell's experiments showed a clear contrast between relevant and irrelevant features, allowing τ to be determined by inspection. However, it can also be determined by Chebyshev's inequality for a given confidence level (α) that a τ of 1/sqrt(αm) is good enough to make the probability of a Type I error less than α, although it is stated that τ can be much smaller than that. Relief was also described as generalizable to multinomial classification by decomposition into a number of binary problems. == ReliefF Algorithm == Kononenko et al. propose a number of updates to Relief. Firstly, they find the near-hit and near-miss instances using the Manhattan (L1) norm rather than the Euclidean (L2) norm, although the rationale is not specified. Furthermore, they found taking the absolute differences between xi and near-hiti, and xi and near-missi to be sufficient when updating the weight vector (rather than the square of those differences). === Reliable probability estimation === Rather than repeating the algorithm m times, implement it exhaustively (i.e. n times, once for each instance) for relatively small n (up to one thousand). Furthermore, rather than finding the single nearest hit and single nearest miss, which may cause redundant and noisy attributes to affect the selection of the nearest neighbors, ReliefF searches for k nearest hits and misses and averages their contribution to the weights of each feature. k can be tuned for any individual problem. === Incomplete data === In ReliefF, the contribution of missing values to the feature weight is determined using the conditional probability that two values should be the same or different, approximated with relative frequencies from the data set. This can be calculated if one or both features are missing. === Multi-class problems === Rather than use Kira and Rendell's proposed decomposition of a multinomial classification into a number of binomial problems, ReliefF searches for k near misses from each different class and averages their contributions for updating W, weighted with the prior probability of each class. == Other Relief-based Algorithm Extensions/Derivatives == The following RBAs are arranged chronologically from oldest to most recent. They include methods for improving (1) the core Relief algorithm concept, (2) iterative approaches for scalability, (3) adaptations to different data types, (4) strategies for computational efficiency, or (5) some combination of these goals. For more on RBAs see these book chapters or this most recent review paper. === RRELIEFF === Robnik-Šikonja and Kononenko propose further updates to ReliefF, making it appropriate for regression. === Relieved-F === Introduced deterministic neighbor selection approach and a new approach for incomplete data handling. === Iterative Relief === Implemented method to address bias against non-monotonic features. Introduced the first iterative Relief approach. For the first time, neighbors were uniquely determined by a radius threshold and instances were weighted by their distance from the target instance. === I-RELIEF === Introduced sigmoidal weighting based on distance from target instance. All instance pairs (not just a defined subset of neighbors) contributed to score updates. Proposed an on-line learning variant of Relief. Extended the iterative Relief concept. Introduced local-learning updates between iterations for improved convergence. === TuRF (a.k.a. Tuned ReliefF) === Specifically sought to address noise in large feature spaces through the recursive elimination of features and the iterative application of ReliefF. === Evaporative Cooling ReliefF === Similarly seeking to address noise in large feature spaces. Utilized an iterative `evaporative' removal of lowest quality features using ReliefF scores in association with mutual information. === EReliefF (a.k.a. Extended ReliefF) === Addressing issues related to incomplete and multi-class data. === VLSReliefF (a.k.a. Very Large Scale ReliefF) === Dramatically improves the efficiency of detecting 2-way feature interactions in very large feature spaces by scoring random feature subsets rather than the entire feature space. === ReliefMSS === Introduced calculation of feature weights relative to average feature 'diff' between instance pairs. === SURF === SURF identifies nearest neighbors (both hits and misses) based on a distance threshold from the target instance defined by the average distance between all pairs of instances in the training data. Results suggest improved power to detect 2-way epistatic interactions over ReliefF. === SURF (a.k.a. SURFStar) === SURF extends the SURF algorithm to not only utilized 'near' neighbors in scoring updates, but 'far' instances as well, but employing inverted scoring updates for 'far instance pairs. Results suggest improved power to detect 2-way epistatic interactions over SURF, but an inability to detect simple main effects (i.e. univariate associations). === SWRF === SWRF extends the SURF algorithm adopting sigmoid weighting to take distance from the threshold into account. Also introduced a modular framework for further developing RBAs called MoRF. === MultiSURF (a.k.a. MultiSURFStar) === MultiSURF extends the SURF algorithm adapting the near/far neighborhood boundaries based on the average and standard deviation of distances from the target instance to all others. MultiSURF uses the standard deviation to define a dead-band zone where 'middle-distance' instances do not contribute to scoring. Evidence suggests MultiSURF performs best in detecting pure 2-way feature interactions. === Reli