STATISTICAL INDEPENDENCE AND NOVELTY DETECTION WITH INFORMATION PRESERVING NONLINEAR MAPS

According to Barlow (1989), feature extraction can be understood as fi nding a statistically independent representation of the probability di stribution underlying the measured signals. The search for a statistic ally independent representation can be formulated by the criterion of minimal mutual information, which reduces to decorrelation in the case of gaussian distributions. If nongaussian distributions are to be con sidered, minimal mutual information is the appropriate generalization of decorrelation as used in linear Principal Component Analyses (PCA). We also generalize to nonlinear transformations by only demanding per fect transmission of information. This leads to a general class of non linear transformations, namely symplectic maps. Conservation of inform ation allows us to consider only the statistics of single coordinates. The resulting factorial representation of the joint probability distr ibution gives a density estimation. We apply this concept to the real world problem of electrical motor fault detection treated as a novelty detection task.