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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 A dendrogram is a diagram representing a Tree (graph theory), tree graph. This diagrammatic representation is frequently used in different contexts: * in hierarchical clustering, it illustrates the arrangement of the clusters produced by ... 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 ... [...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 data analyzing technique in which task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more Similarity measure, similar (in some specific sense defined by the analyst) 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 refers to a family of algorithms and tasks rather than one specific algorithm. 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 pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microarray
A microarray is a multiplex (assay), multiplex lab-on-a-chip. Its purpose is to simultaneously detect the expression of thousands of biological interactions. It is a two-dimensional array on a Substrate (materials science), solid substrate—usually a glass slide or silicon thin-film cell—that assays (tests) large amounts of biotic material, biological material using high-throughput screening miniaturized, multiplexed and parallel processing and detection methods. The concept and methodology of microarrays was first introduced and illustrated in antibody microarrays (also referred to as antibody matrix) by Tse Wen Chang in 1983 in a scientific publication and a series of patents. The "gene chip" industry started to grow significantly after the 1995 ''Science Magazine'' article by the Ron Davis and Pat Brown labs at Stanford University. With the establishment of companies, such as Affymetrix, Agilent, Applied Microarrays, Arrayjet, Illumina (company), Illumina, and others, the te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dendrogram
A dendrogram is a diagram representing a Tree (graph theory), tree graph. 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 heat map, 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 repre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
