Abstract—In the last two decades, a lot of protein 3D shapes have been discovered, characterized, and made available thanks to the Protein Data Bank (PDB), that is nevertheless growing very quickly. New scalable methods are thus urgently required to search through the PDB efficiently. This paper presents an approach entitled LNA (Laplacian Norm Alignment) that performs a structural comparison of two proteins with dynamic programming algorithms. This is achieved by characterizing each residue in the protein with scalar features. The feature values are calculated using a Laplacian operator applied on the graph corresponding to the adjacency matrix of the residues. The weighted Laplacian operator we use estimates, at various scales, local deformations of the topology where each residue is located. On some benchmarks, which are widely shared by the community, we obtain qualitatively similar results compared to other competing approaches, but with an algorithm one or two order of magnitudes faster. 180,000 protein comparisons can be done within 1 second with a single recent Graphical Processing Unit (GPU), which makes our algorithm very scalable and suitable for real-time database querying across the web.

Abstract

This paper proposes a framework dedicated to the construction of what we call discrete elastic inner product allowing one to embed sets of nonuniformly sampled multivariate time series or sequences of varying lengths into inner product space structures. This framework is based on a recursive definition that covers the case of multiple embedded time elastic dimensions. We prove that such inner products exist in our general framework and show how a simple instance of this inner product class operates on some prospective applications, while generalizing the euclidean inner product. Classification experimentations on time series and symbolic sequences data sets demonstrate the benefits that we can expect by embedding time series or sequences into elastic inner spaces rather than into classical euclidean spaces. These experiments show good accuracy when compared to the euclidean distance or even dynamic programming algorithms while maintaining a linear algorithmic complexity at exploitation stage, although a quadratic indexing phase beforehand is required.

No abstract