Categories and Quantities
The rank of a matrix of categorical variables is defined. This may be used as a basis of multivariate methods for approximating categorical data in a similar way that the rank of a quantitative data matrix may be used to define standard methods such as multidimensional scaling, multiple correspondence analysis, principal components analysis and non-linear principal components analysis. Several problems are outlined that depend on the notion of categorical rank. The algorithmic tools for handling categorical rank need to be developed.
KeywordsMultidimensional Scaling Correct Prediction Neighbour Region Multiple Correspondence Analysis Prediction Region
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