Spectral Techniques to Explore Point Clouds in Euclidean Space, with Applications to Collective Coordinates in Structural Biology

Abstract

Life sciences, engineering, or telecommunications provide numerous systems whose description requires a large number of variables. Developing insights into such systems, forecasting their evolution, or monitoring them is often based on the inference of correlations between these variables. Given a collection of points describing states of the system, questions such as inferring the effective number of independent parameters of the system (its intrinsic dimensionality) and the way these are coupled are paramount to develop models. In this context, this paper makes two contributions. First, we review recent work on spectral techniques to organize point clouds in Euclidean space, with emphasis on the main difficulties faced. Second, after a careful presentation of the bio-physical context, we present applications of dimensionality reduction techniques to a core problem in structural biology, namely protein folding. Both from the computer science and the structural biology perspective, we expect this survey to shed new light on the importance of non linear computational geometry in geometric data analysis in general, and for protein folding in particular.