Correspondence analysis with least absolute residuals

Three different ways to characterize correspondence analysis as a minimum norm technique are distinguished: an optimal correlation problem, a dual pair of distance approximation problems, and a reciprocal location problem. The consequences of switching from the usual least squares concepts to least absolute residual loss functions are discussed for each of these. The reciprocal location approach gets most attention. Algorithms based on iterative majorization are proposed which are sufficiently general to be adapted to loss functions that are built upon mixtures of least squares and least absolute residuals. A remarkable clustering phenomenon is observed in applications of the new procedure. For the other two approaches no explicit algorithms are given; their development could proceed along the same line.