Kernel and Dissimilarity Methods for Exploratory Analysis in a Social Context

While most of the statistical methods for prediction or data mining have been built for data made of independent observations of a common set of p numerical variables, many real-world applications do not fit in this framework. A more common and general situation is the case where a relevant similarity or dissimilarity can be computed between the observations, providing a summary of their relations to each other. This setting is related to the kernel framework that has allowed to extend most of standard statistical supervised and unsupervised methods to any type of data for which a relevant such kernel can be obtained. The present chapter aims at presenting kernel methods in general, with a specific focus on the less studied unsupervised framework. We illustrate its usefulness by describing the extension of self-organizing maps and by proposing an approach to combine kernels in an efficient way. The overall approach is illustrated on categorical time series in a social-science context and allows to illustrate how the choice of a given type of dissimilarity or group of dissimilarities can influence the output of the exploratory analysis.