Dissimilarity Analysis And Application To Visual Comparisons

In this chapter, the embedding of a set of data into a vector space is studied when an unconditional pairwise dissimilarity w between data is given. The vector space is endowed with a suitable pseudo-euclidean structure and the data embedding is built by extending the classical kernel principal component analysis. This embedding is unique, up to an isomorphism, and injective if and only if w separates the data. This construction takes advantage of axis corresponding to negative eigenvalues to develop pseudo-euclidean scatterplot matrix representations. This new visual tool is applied to compare various dissimilarities between hidden Markov models built from person's faces.