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Automatic Clustering Algorithms
Automatic clustering algorithms are algorithms that can perform clustering without prior knowledge of data sets. In contrast with other cluster analysis techniques, automatic clustering algorithms can determine the optimal number of clusters even in the presence of noise and outlier points. Centroid-based Given a set of ''n'' objects, centroid-based algorithms create ''k'' partitions based on a dissimilarity function, such that ''k≤n''. A major problem in applying this type of algorithm is determining the appropriate number of clusters for unlabeled data. Therefore, most research in clustering analysis has been focused on the automation of the process. Automated selection of ''k'' in a ''K''-means clustering algorithm, one of the most used centroid-based clustering algorithms, is still a major problem in machine learning. The most accepted solution to this problem is the elbow method. It consists of running ''k''-means clustering to the data set with a range of values, calcu ... [...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] |
Outlier
In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to a variability in the measurement, an indication of novel data, or it may be the result of experimental error; the latter are sometimes excluded from the data set. An outlier can be an indication of exciting possibility, but can also cause serious problems in statistical analyses. Outliers can occur by chance in any distribution, but they can indicate novel behaviour or structures in the data-set, measurement error, or that the population has a heavy-tailed distribution. In the case of measurement error, one wishes to discard them or use statistics that are robust to outliers, while in the case of heavy-tailed distributions, they indicate that the distribution has high skewness and that one should be very cautious in using tools or intuitions that assume a normal distribution. A frequent cause of outliers is a mixture of two distributions, which may be two dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-means Clustering
''k''-means clustering is a method of vector quantization, originally from signal processing, that aims to partition ''n'' observations into ''k'' clusters in which each observation belongs to the cluster with the nearest mean (cluster centers or cluster centroid), serving as a prototype of the cluster. This results in a partitioning of the data space into Voronoi cells. ''k''-means clustering minimizes within-cluster variances (squared Euclidean distances), but not regular Euclidean distances, which would be the more difficult Weber problem: the mean optimizes squared errors, whereas only the geometric median minimizes Euclidean distances. For instance, better Euclidean solutions can be found using k-medians and k-medoids. The problem is computationally difficult (NP-hard); however, efficient heuristic algorithms converge quickly to a local optimum. These are usually similar to the expectation-maximization algorithm for mixtures of Gaussian distributions via an iterative refine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elbow Method (clustering)
In cluster analysis, the elbow method is a heuristic used in determining the number of clusters in a data set. The method consists of plotting the explained variation as a function of the number of clusters and picking the elbow of the curve as the number of clusters to use. The same method can be used to choose the number of parameters in other data-driven models, such as the number of principal components to describe a data set. The method can be traced to speculation by Robert L. Thorndike in 1953. Intuition Using the "elbow" or "knee of a curve" as a cutoff point is a common heuristic in mathematical optimization to choose a point where diminishing returns are no longer worth the additional cost. In clustering, this means one should choose a number of clusters so that adding another cluster doesn't give much better modeling of the data. The intuition is that increasing the number of clusters will naturally improve the fit (explain more of the variation), since there are mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hierarchical Clustering
In data mining and statistics, hierarchical clustering (also called hierarchical cluster analysis or HCA) is a method of cluster analysis that seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into two categories: * Agglomerative: This is a " bottom-up" approach: Each observation starts in its own cluster, and pairs of clusters are merged as one moves up the hierarchy. * Divisive: This is a "top-down" approach: All observations start in one cluster, and splits are performed recursively as one moves down the hierarchy. In general, the merges and splits are determined in a greedy manner. The results of hierarchical clustering are usually presented in a dendrogram. The standard algorithm for hierarchical agglomerative clustering (HAC) has a time complexity of \mathcal(n^3) and requires \Omega(n^2) memory, which makes it too slow for even medium data sets. However, for some special cases, optimal efficient agglomerative methods (of c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dendrogram
A dendrogram is a diagram representing a tree. This diagrammatic representation is frequently used in different contexts: * in hierarchical clustering, it illustrates the arrangement of the clusters produced by the corresponding analyses. * in computational biology, it shows the clustering of genes or samples, sometimes in the margins of heatmaps. * in phylogenetics, it displays the evolutionary relationships among various biological taxa. In this case, the dendrogram is also called a phylogenetic tree. The name ''dendrogram'' derives from the two ancient greek words (), meaning "tree", and (), meaning "drawing, mathematical figure". Clustering example For a clustering example, suppose that five taxa (a to e) have been clustered by UPGMA based on a matrix of genetic distances. The hierarchical clustering dendrogram would show a column of five nodes representing the initial data (here individual taxa), and the remaining nodes represent the clusters to which the dat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
BIRCH
A birch is a thin-leaved deciduous hardwood tree of the genus ''Betula'' (), in the family Betulaceae, which also includes alders, hazels, and hornbeams. It is closely related to the beech-oak family Fagaceae. The genus ''Betula'' contains 30 to 60 known taxa of which 11 are on the IUCN 2011 Red List of Threatened Species. They are a typically rather short-lived pioneer species widespread in the Northern Hemisphere, particularly in northern areas of temperate climates and in boreal climates. Description Birch species are generally small to medium-sized trees or shrubs, mostly of northern temperate and boreal climates. The simple leaves are alternate, singly or doubly serrate, feather-veined, petiolate and stipulate. They often appear in pairs, but these pairs are really borne on spur-like, two-leaved, lateral branchlets. The fruit is a small samara, although the wings may be obscure in some species. They differ from the alders (''Alnus'', another genus in the family) in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Density-based Clustering
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 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 distances between cluster members, dense areas of the data space, intervals or particular statistical distributions. Clustering can therefore be formulated as a multi-objective optimization problem. The a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
DBSCAN
Density-based spatial clustering of applications with noise (DBSCAN) is a data clustering algorithm proposed by Martin Ester, Hans-Peter Kriegel, Jörg Sander and Xiaowei Xu in 1996. It is a density-based clustering non-parametric algorithm: given a set of points in some space, it groups together points that are closely packed together (points with many nearby neighbors), marking as outliers points that lie alone in low-density regions (whose nearest neighbors are too far away). DBSCAN is one of the most common clustering algorithms and also most cited in scientific literature. In 2014, the algorithm was awarded the test of time award (an award given to algorithms which have received substantial attention in theory and practice) at the leading data mining conference, ACM SIGKDD. , the follow-up paper "DBSCAN Revisited, Revisited: Why and How You Should (Still) Use DBSCAN" appears in the list of the 8 most downloaded articles of the prestigious ACM Transactions on Database System ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
OPTICS Algorithm
Ordering points to identify the clustering structure (OPTICS) is an algorithm for finding density-based clusters in spatial data. It was presented by Mihael Ankerst, Markus M. Breunig, Hans-Peter Kriegel and Jörg Sander. Its basic idea is similar to DBSCAN, but it addresses one of DBSCAN's major weaknesses: the problem of detecting meaningful clusters in data of varying density. To do so, the points of the database are (linearly) ordered such that spatially closest points become neighbors in the ordering. Additionally, a special distance is stored for each point that represents the density that must be accepted for a cluster so that both points belong to the same cluster. This is represented as a dendrogram. Basic idea Like DBSCAN, OPTICS requires two parameters: , which describes the maximum distance (radius) to consider, and , describing the number of points required to form a cluster. A point is a ''core point'' if at least points are found within its -neighborhood N_\vare ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Directed Acyclic Graph
In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it consists of vertices and edges (also called ''arcs''), with each edge directed from one vertex to another, such that following those directions will never form a closed loop. A directed graph is a DAG if and only if it can be topologically ordered, by arranging the vertices as a linear ordering that is consistent with all edge directions. DAGs have numerous scientific and computational applications, ranging from biology (evolution, family trees, epidemiology) to information science (citation networks) to computation (scheduling). Directed acyclic graphs are sometimes instead called acyclic directed graphs or acyclic digraphs. Definitions A graph is formed by vertices and by edges connecting pairs of vertices, where the vertices can be any kind of object that is connected in pairs by edges. In the case of a directed graph, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clustering Criteria
Clustering can refer to the following: In computing: *Computer cluster, the technique of linking many computers together to act like a single computer *Data cluster, an allocation of contiguous storage in databases and file systems *Cluster analysis, the statistical task of grouping a set of objects in such a way that objects in the same group are placed closer together (such as the k-means clustering) *In hash tables, the mapping of keys to nearby slots In economics: *Business cluster, a geographic concentration of interconnected businesses, suppliers, and associated institutions in a particular field In graph theory: *The formation of clusters of linked nodes in a network, measured by the clustering coefficient See also *Cluster (other) may refer to: Science and technology Astronomy * Cluster (spacecraft), constellation of four European Space Agency spacecraft * Asteroid cluster, a small asteroid family * Cluster II (spacecraft), a European Space Agency missio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
