Canonical Correspondence Analysis

	Canonical Correspondence Analysis In multivariate analysis, canonical correspondence analysis (CCA) is an ordination technique that determines axes from the response data as a linear combination of measured predictors. CCA is commonly used in ecology in order to extract gradients that drive the composition of ecological communities. CCA extends Correspondence Analysis (CA) with regression, in order to incorporate predictor variables. History CCA was developed in 1986 by Cajo ter Braak and implemented in the program CANOCO, an extension of DECORANA. To date, CCA is one of the most popular multivariate methods in ecology, despite the availability of contemporary alternatives. CCA was originally derived and implemented using an algorithm of weighted averaging, though Legendre & Legendre (1998) derived an alternative algorithm. Assumptions The requirements of a CCA are that the samples are random and independent. Also, the data are categorical and that the independent variables are consistent within the sample site ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Ordination (statistics) Ordination or gradient analysis, in multivariate analysis, is a method complementary to data clustering, and used mainly in exploratory data analysis (rather than in hypothesis testing). Ordination orders objects that are characterized by values on multiple variables (multivariate objects) so that similar objects are near each other and dissimilar objects are farther from each other. Such relationships between the objects, on each of several axes (one for each variable), are then characterized numerically and/or graphically. Many ordination techniques exist, including principal components analysis (PCA), non-metric multidimensional scaling (NMDS), correspondence analysis (CA) and its derivatives ( detrended CA (DCA), canonical CA (CCA)), Bray–Curtis ordination, and redundancy analysis (RDA), among others. Contemporary developments for ordination focus on machine learning techniques or using statistical models instead. Applications Ordination can be used on the analysis of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Ecology Ecology () is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms at the individual, population, community, ecosystem, and biosphere level. Ecology overlaps with the closely related sciences of biogeography, evolutionary biology, genetics, ethology, and natural history. Ecology is a branch of biology, and it is not synonymous with environmentalism. Among other things, ecology is the study of: * The abundance, biomass, and distribution of organisms in the context of the environment * Life processes, antifragility, interactions, and adaptations * The movement of materials and energy through living communities * The successional development of ecosystems * Cooperation, competition, and predation within and between species * Patterns of biodiversity and its effect on ecosystem processes Ecology has practical applications in conservation biology, wetland management, natural resource managemen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Correspondence Analysis (CA) Correspondence analysis (CA) is a multivariate statistical technique proposed by Herman Otto Hartley (Hirschfeld) and later developed by Jean-Paul Benzécri. It is conceptually similar to principal component analysis, but applies to categorical rather than continuous data. In a similar manner to principal component analysis, it provides a means of displaying or summarising a set of data in two-dimensional graphical form. Its aim is to display in a biplot any structure hidden in the multivariate setting of the data table. As such it is a technique from the field of multivariate ordination. Since the variant of CA described here can be applied either with a focus on the rows or on the columns it should in fact be called simple (symmetric) correspondence analysis. It is traditionally applied to the contingency table of a pair of nominal variables where each cell contains either a count or a zero value. If more than two categorical variables are to be summarized, a variant called multi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Canonical Correlation In statistics, canonical-correlation analysis (CCA), also called canonical variates analysis, is a way of inferring information from cross-covariance matrices. If we have two vectors ''X'' = (''X''1, ..., ''X''''n'') and ''Y'' = (''Y''1, ..., ''Y''''m'') of random variables, and there are correlations among the variables, then canonical-correlation analysis will find linear combinations of ''X'' and ''Y'' which have maximum correlation with each other. T. R. Knapp notes that "virtually all of the commonly encountered parametric tests of significance can be treated as special cases of canonical-correlation analysis, which is the general procedure for investigating the relationships between two sets of variables." The method was first introduced by Harold Hotelling in 1936, although in the context of angles between flats the mathematical concept was published by Jordan in 1875. Definition Given two column vectors X = (x_1, \dots, x_n)^T and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]