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Cophenetic
In the clustering of biological information such as data from microarray experiments, the cophenetic similarity or cophenetic distanceSokal, R. R. and F. J. Rohlf. 1962. The comparison of dendrograms by objective methods. Taxon, 11:33-40 of two objects is a measure of how similar those two objects have to be in order to be grouped into the same cluster. The cophenetic distance between two objects is the height of the dendrogram where the two branches that include the two objects merge into a single branch. Outside the context of a dendrogram, it is the distance between the largest two clusters that contain the two objects individually when they are merged into a single cluster that contains both. See also *Cophenetic correlation In statistics, and especially in biostatistics, cophenetic correlation (more precisely, the cophenetic correlation coefficient) is a measure of how faithfully a dendrogram preserves the pairwise distances between the original unmodeled data points. ... ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cophenetic Correlation
In statistics, and especially in biostatistics, cophenetic correlation (more precisely, the cophenetic correlation coefficient) is a measure of how faithfully a dendrogram preserves the pairwise distances between the original unmodeled data points. Although it has been most widely applied in the field of biostatistics (typically to assess cluster-based models of DNA sequences, or other taxonomic models), it can also be used in other fields of inquiry where raw data tend to occur in clumps, or clusters. This coefficient has also been proposed for use as a test for nested clusters. Calculating the cophenetic correlation coefficient Suppose that the original data have been modeled using a cluster method to produce a dendrogram ; that is, a simplified model in which data that are "close" have been grouped into a hierarchical tree. Define the following distance measures. * x(i,j) = , X_i-X_j, , the Euclidean distance between the ''i''th and ''j''th observations. * t(i,j), the dendrogr ... [...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] |
