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HCS Clustering Algorithm
Th HCS (Highly Connected Subgraphs) clustering algorithm(also known as the HCS algorithm, and other names such as Highly Connected Clusters/Components/Kernels) is an algorithm based on graph connectivity for cluster analysis. It works by representing the similarity data in a similarity graph, and then finding all the highly connected subgraphs. It does not make any prior assumptions on the number of the clusters. This algorithm was published by Erez Hartuv and Ron Shamir in 2000. The HCS algorithm gives a clustering solution, which is inherently meaningful in the application domain, since each solution cluster must have diameter 2 while a union of two solution clusters will have diameter 3. Similarity modeling and preprocessing The goal of cluster analysis is to group elements into disjoint subsets, or clusters, based on similarity between elements, so that elements in the same cluster are highly similar to each other (homogeneity), while elements from different clusters have ... [...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] |
Graph (data Structure)
In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within mathematics. A graph data structure consists of a finite (and possibly mutable) set of ''vertices'' (also called ''nodes'' or ''points''), together with a set of unordered pairs of these vertices for an undirected graph or a set of ordered pairs for a directed graph. These pairs are known as ''edges'' (also called ''links'' or ''lines''), and for a directed graph are also known as ''edges'' but also sometimes ''arrows'' or ''arcs''. The vertices may be part of the graph structure, or may be external entities represented by integer indices or references. A graph data structure may also associate to each edge some ''edge value'', such as a symbolic label or a numeric attribute (cost, capacity, length, etc.). Operations The basic operations provided by a graph data structure ''G'' usually include:See, e.g. , Sectio ... [...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] |
Similarity Graph
Similarity may refer to: In mathematics and computing * Similarity (geometry), the property of sharing the same shape * Matrix similarity, a relation between matrices * Similarity measure, a function that quantifies the similarity of two objects ** Cosine similarity, which uses the angle between vectors ** String metric, also called string similarity ** Semantic similarity, in computational linguistics In linguistics * Lexical similarity * Semantic similarity In other fields * Similitude (model), in engineering, describing the geometric, kinematic and dynamic 'likeness' of two or more systems * Similarity (psychology) * Similarity (philosophy) * Musical similarity * Chemical similarity * Similarity (network science) * Structural similarity * ''Similar'' (film), an upcoming South Korean film See also * * Same (other) * Difference (other) * Equality (mathematics) In mathematics, equality is a relationship between two quantities or, more generally two mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ron Shamir
Ron Shamir (Hebrew: רון שמיר; born 29 November 1953) is an Israeli professor of computer science known for his work in graph theory and in computational biology. He holds the Raymond and Beverly Sackler Chair in Bioinformatics, and is the founder and head of the Edmond J. Safra Center for Bioinformatics at Tel Aviv University. Biography Ron Shamir was born in Jerusalem, Israel in 1953, the eldest son of Varda and Raphael Shamir. His father's Sepharadic family has lived in the old city of Jerusalem for over 400 years. His mother's parents were pioneers who came from Russia to Israel in the Third Aliyah in the early 1920s. He has two younger sisters, Daphna and Gadit. Shamir studied in Gymnasia Rehavia, Jerusalem, for 12 years. In high school, he was active in the scouts and in athletics; among other accomplishments, he won the Jerusalem high school championship in shot put. Shamir started his B.Sc. studies in mathematics and physics at Tel-Aviv University (1973–1975) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimum Cut
In graph theory, a minimum cut or min-cut of a graph is a cut (a partition of the vertices of a graph into two disjoint subsets) that is minimal in some metric. Variations of the minimum cut problem consider weighted graphs, directed graphs, terminals, and partitioning the vertices into more than two sets. The weighted min-cut problem allowing both positive and negative weights can be trivially transformed into a weighted maximum cut problem by flipping the sign in all weights. __TOC__ Without terminal nodes The minimum cut problem in undirected, weighted graphs limited to non-negative weights can be solved in polynomial time by the Stoer-Wagner algorithm. In the special case when the graph is unweighted, Karger's algorithm provides an efficient randomized method for finding the cut. In this case, the minimum cut equals the edge connectivity of the graph. A generalization of the minimum cut problem without terminals is the minimum -cut, in which the goal is to partition the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Highly Connected Subgraph
High may refer to: Science and technology * Height * High (atmospheric), a high-pressure area * High (computability), a quality of a Turing degree, in computability theory * High (tectonics), in geology an area where relative tectonic uplift took or takes place * Substance intoxication, also known by the slang description "being high" * Sugar high, a misconception about the supposed psychological effects of sucrose Music Performers * High (musical group), a 1974–1990 Indian rock group * The High, an English rock band formed in 1989 Albums * ''High'' (The Blue Nile album) or the title song, 2004 * ''High'' (Flotsam and Jetsam album), 1997 * ''High'' (New Model Army album) or the title song, 2007 * ''High'' (Royal Headache album) or the title song, 2015 * ''High'' (EP), by Jarryd James, or the title song, 2016 Songs * "High" (Alison Wonderland song), 2018 * "High" (The Chainsmokers song), 2022 * "High" (The Cure song), 1992 * "High" (David Hallyday song), 1988 * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
HCS Algorithm
HCS may refer to: Education * Hackensack Christian School, in New Jersey, United States * Hallett Cove School, in Adelaide, South Australia * Hampshire Country School, in New Hampshire, United States * Hampton Christian Schools, in Virginia, United States * Hardin County Schools, in Kentucky, United States * Harrisburg Christian School, in Pennsylvania, United States * Hereford Cathedral School, in England * Heritage Christian School (other) * Heritage College Sydney, in New South Wales, Australia * Highland Catholic School, in Minnesota, United States * Hilltop Christian School, in North Carolina, United States * Hinsdale Central School, in New York, United States * Hooghly Collegiate School, in West Bengal, India * Holland Christian Schools, in Michigan, United States * Holy Cross School (other) * Horry County Schools, in South Carolina, United States * Hull Collegiate School, in England Biology and medicine * Hajdu–Cheney syndrome * High-content ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clique Problem
In computer science, the clique problem is the computational problem of finding cliques (subsets of vertices, all adjacent to each other, also called complete subgraphs) in a graph. It has several different formulations depending on which cliques, and what information about the cliques, should be found. Common formulations of the clique problem include finding a maximum clique (a clique with the largest possible number of vertices), finding a maximum weight clique in a weighted graph, listing all maximal cliques (cliques that cannot be enlarged), and solving the decision problem of testing whether a graph contains a clique larger than a given size. The clique problem arises in the following real-world setting. Consider a social network, where the graph's vertices represent people, and the graph's edges represent mutual acquaintance. Then a clique represents a subset of people who all know each other, and algorithms for finding cliques can be used to discover these groups of m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
