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Correlation Clustering
Clustering is the problem of partitioning data points into groups based on their similarity. Correlation clustering provides a method for clustering a set of objects into the optimum number of clusters without specifying that number in advance. Description of the problem In machine learning, correlation clustering or cluster editing operates in a scenario where the relationships between the objects are known instead of the actual representations of the objects. For example, given a weighted graph G=(V,E) where the edge weight indicates whether two nodes are similar (positive edge weight) or different (negative edge weight), the task is to find a clustering that either maximizes agreements (sum of positive edge weights within a cluster plus the absolute value of the sum of negative edge weights between clusters) or minimizes disagreements (absolute value of the sum of negative edge weights within a cluster plus the sum of positive edge weights across clusters). Unlike other clusteri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Machine Learning
Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence. Machine learning algorithms build a model based on sample data, known as training data, in order to make predictions or decisions without being explicitly programmed to do so. Machine learning algorithms are used in a wide variety of applications, such as in medicine, email filtering, speech recognition, agriculture, and computer vision, where it is difficult or unfeasible to develop conventional algorithms to perform the needed tasks.Hu, J.; Niu, H.; Carrasco, J.; Lennox, B.; Arvin, F.,Voronoi-Based Multi-Robot Autonomous Exploration in Unknown Environments via Deep Reinforcement Learning IEEE Transactions on Vehicular Technology, 2020. A subset of machine learning is closely related to computational statistics, which focuses on making predicti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weighted Graph
This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes or vertices connected in pairs by lines or edges. Symbols A B C D E F G H I K L M N O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Determining The Number Of Clusters In A Data Set
Determining the number of clusters in a data set, a quantity often labelled ''k'' as in the ''k''-means algorithm, is a frequent problem in data clustering, and is a distinct issue from the process of actually solving the clustering problem. For a certain class of clustering algorithms (in particular ''k''-means, ''k''-medoids and expectation–maximization algorithm), there is a parameter commonly referred to as ''k'' that specifies the number of clusters to detect. Other algorithms such as DBSCAN and OPTICS algorithm do not require the specification of this parameter; hierarchical clustering avoids the problem altogether. The correct choice of ''k'' is often ambiguous, with interpretations depending on the shape and scale of the distribution of points in a data set and the desired clustering resolution of the user. In addition, increasing ''k'' without penalty will always reduce the amount of error in the resulting clustering, to the extreme case of zero error if each data point ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polynomial-time Approximation Scheme
In computer science (particularly algorithmics), a polynomial-time approximation scheme (PTAS) is a type of approximation algorithm for optimization problems (most often, NP-hard optimization problems). A PTAS is an algorithm which takes an instance of an optimization problem and a parameter and produces a solution that is within a factor of being optimal (or for maximization problems). For example, for the Euclidean traveling salesman problem, a PTAS would produce a tour with length at most , with being the length of the shortest tour. The running time of a PTAS is required to be polynomial in the problem size for every fixed ε, but can be different for different ε. Thus an algorithm running in time or even counts as a PTAS. Variants Deterministic A practical problem with PTAS algorithms is that the exponent of the polynomial could increase dramatically as ε shrinks, for example if the runtime is . One way of addressing this is to define the efficient polynomial-time a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Approximation Algorithm
In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to optimization problems (in particular NP-hard problems) with provable guarantees on the distance of the returned solution to the optimal one. Approximation algorithms naturally arise in the field of theoretical computer science as a consequence of the widely believed P ≠ NP conjecture. Under this conjecture, a wide class of optimization problems cannot be solved exactly in polynomial time. The field of approximation algorithms, therefore, tries to understand how closely it is possible to approximate optimal solutions to such problems in polynomial time. In an overwhelming majority of the cases, the guarantee of such algorithms is a multiplicative one expressed as an approximation ratio or approximation factor i.e., the optimal solution is always guaranteed to be within a (predetermined) multiplicative factor of the returned solution. However, there are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shuchi Chawla
Shuchi Chawla is an Indian computer scientist who works in the design and analysis of algorithms, and is known for her research on correlation clustering, information privacy, mechanism design, approximation algorithms, hardness of approximation, and algorithmic bias. She works as a professor of computer science at the University of Texas at Austin. Education and career Chawla earned a bachelor's degree from the Indian Institute of Technology Delhi in 2000, and received her Ph.D. from Carnegie Mellon University in 2005. Her dissertation, ''Graph Algorithms for Planning and Partitioning'', was supervised by Avrim Blum. After postdoctoral studies at Stanford University under the mentorship of Tim Roughgarden, and at Microsoft Research, Silicon Valley, she joined the Wisconsin faculty in 2006.. She joined the UT-Austin faculty in 2021. She won a Sloan Research Fellowship The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grigory Yaroslavtsev
Grigory Yaroslavtsev is a Russian-American computer scientist. He is an assistant professor of computer science at George Mason University. Previously he was an assistant professor of computer science at Indiana University and the founding director of the Center for Algorithms and Machine Learning (CAML) at Indiana University. Early education and competitive programing Yaroslavtsev was born in St. Petersburg, then Leningrad, in 1987. He attended the St. Petersburg Classical Gymnasium through 9th grade. In 2004, Yaroslavtsev graduated from the Physics and Technology School in St. Petersburg, a high school founded by Zhores Alferov. Yaroslavtsev completed a B.S. in applied physics at St. Petersburg Polytechnic University in 2008. In 2010, he received his M.S. from St. Petersburg Academic University as the first student in a pilot theoretical computer science program. Yaroslavtsev was active through 2011 in international programming competitions. He was one of 24 world finalis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Optimization
Discrete optimization is a branch of optimization in applied mathematics and computer science. Scope As opposed to continuous optimization, some or all of the variables used in a discrete mathematical program are restricted to be discrete variables—that is, to assume only a discrete set of values, such as the integers. Branches Three notable branches of discrete optimization are:. * combinatorial optimization, which refers to problems on graphs, matroids and other discrete structures * integer programming * constraint programming These branches are all closely intertwined however since many combinatorial optimization problems can be modeled as integer programs (e.g. shortest path) or constraint programs, any constraint program can be formulated as an integer program and vice versa, and constraint and integer programs can often be given a combinatorial interpretation. See also *Diophantine equation In mathematics, a Diophantine equation is an equation, typically a pol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Correlation
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are ''linearly'' related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve. Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. In this example, there is a causal relationship, because extreme weather causes people to use more electricity for heating or cooling. However ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feature Vector
In machine learning and pattern recognition, a feature is an individual measurable property or characteristic of a phenomenon. Choosing informative, discriminating and independent features is a crucial element of effective algorithms in pattern recognition, classification and regression. Features are usually numeric, but structural features such as strings and graphs are used in syntactic pattern recognition. The concept of "feature" is related to that of explanatory variable used in statistical techniques such as linear regression. Classification A numeric feature can be conveniently described by a feature vector. One way to achieve binary classification is using a linear predictor function (related to the perceptron) with a feature vector as input. The method consists of calculating the scalar product between the feature vector and a vector of weights, qualifying those observations whose result exceeds a threshold. Algorithms for classification from a feature vector include ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
High-dimensional Space
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on itfor example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on itfor example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces. In classical mechanics, space and time are different categories and refer to absolute space and time. That conception of the world is a four-dimensional space but not the one that was found necessar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cluster Analysis
Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense) to each other than to those in other groups (clusters). It is a main task of exploratory data analysis, and a common technique for statistics, statistical data analysis, used in many fields, including pattern recognition, image analysis, information retrieval, bioinformatics, data compression, computer graphics and machine learning. Cluster analysis itself is not one specific algorithm, but the general task to be solved. It can be achieved by various algorithms that differ significantly in their understanding of what constitutes a cluster and how to efficiently find them. Popular notions of clusters include groups with small Distance function, distances between cluster members, dense areas of the data space, intervals or particular statistical distributions. Clustering can therefore be formulated as a multi-object ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
