Correlation-based embedding of pairwise score data

Protein Sequence Analysis by Proximities

Sequence data are widely used to get a deeper insight into biological systems. From a data analysis perspective they are given as a set of sequences of symbols with varying length. In general they are compared using nonmetric score functions. In this form the data are nonstandard, because they do not provide an immediate metric vector space and their analysis using standard methods is complicated. In this chapter we provide various strategies for how to analyze these type of data in a mathematically accurate way instead of the often seen ad hoc solutions. Our approach is based on the scoring values from protein sequence data although be applicable in a broader sense. We discuss potential recoding concepts of the scores and discuss algorithms to solve clustering, classification and embedding tasks for score data for a protein sequence application.

Indefinite Proximity Learning: A Review

Efficient learning of a data analysis task strongly depends on the data representation. Most methods rely on (symmetric) similarity or dissimilarity representations by means of metric inner products or distances, providing easy access to powerful mathematical formalisms like kernel or branch-and-bound approaches. Similarities and dissimilarities are, however, often naturally obtained by nonmetric proximity measures that cannot easily be handled by classical learning algorithms. Major efforts have been undertaken to provide approaches that can either directly be used for such data or to make standard methods available for these types of data. We provide a comprehensive survey for the field of learning with nonmetric proximities. First, we introduce the formalism used in nonmetric spaces and motivate specific treatments for nonmetric proximity data. Second, we provide a systematization of the various approaches. For each category of approaches, we provide a comparative discussion of the individual algorithms and address complexity issues and generalization properties. In a summarizing section, we provide a larger experimental study for the majority of the algorithms on standard data sets. We also address the problem of large-scale proximity learning, which is often overlooked in this context and of major importance to make the method relevant in practice. The algorithms we discuss are in general applicable for proximity-based clustering, one-class classification, classification, regression, and embedding approaches. In the experimental part, we focus on classification tasks.