Retrieving a contingency table from a correspondence analysis solution

Correspondence analysis (CA) is a dimension reduction technique for categorical data. In particular, CA is typically applied to a contingency matrix in order to visualize the relationships within and between the categories of the two variables as represented by its rows and columns. The CA solution can be obtained by considering a singular value decomposition of the so-called matrix of standardized residuals. Inverse correspondence analysis considers the problem of retrieving the data underlying a given low-dimensional CA solution. Using the specific structure of the CA solutions as well as the characteristics of the original data we formulate the inverse CA problem in an integer linear programming context. Considering various conditions involving the dimensions of the original data matrix, the number of observations, the precision and dimensionality of the CA solution, we show that by solving the integer linear programs, the original data can be retrieved.

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