Spherical distance metrics applied to protein structure classification

Observed protein structures usually represent energetically favorable conformations. While not all observed structures are necessarily functional, it is generally agreed that protein structure is closely related to protein function. Given a collection of proteins sharing a common global structure, variations in their local structures at specific, critical locations may result in different biological functions. Structural relationships among proteins are important in the study of the evolution of proteins as well as in drug design and development. Analysis of geometrical 3D protein structure has been shown to be effective with respect to classifying proteins. Prior work has shown that the Double Centroid Reduced Representation (DCRR) model is a useful geometric representation for protein structure with respect to visual models, reducing the quantity of modeled information for each amino acid, yet retaining the most important geometrical and chemical features of each: the centroids of the backbone and of the side-chain. DCRR has not yet been applied in the calculation of geometric structural similarity. Meanwhile, multi-dimensional indexing (MDI) of protein structure combines protein structural analysis with distance metrics to facilitate structural similarity queries and is also used for clustering protein structures into related groups. In this respect, the combination of geometric models with MDI has been shown to be effective. Prior work, notably Distance and Density-based Protein Indexing (DDPIn), applies MDI to protein models based on the geometry of the C-alpha backbone. DDPIn\u27s distance metrics are based on radial and density functions that incorporate spherical-based metrics, and the indices are built from metric-tree (M-tree) structures. This work combines DCRR with DDPIn for the development of new DCRR centroid-based metrics: spherical binning distance and inter-centroid spherical distance. The use of DCRR models will provide additional significant structural information via the inclusion of side-chain centroids. Additionally, the newly developed distance metric functions combined with DCRR and M-tree indexing attempt to improve upon the performance of prior work (DDPIn), given the same data set, with respect to both individual k-nearest neighbor (kNN) search queries as well as clustering all proteins in the index

Indexing Metric Spaces for Exact Similarity Search

With the continued digitalization of societal processes, we are seeing an explosion in available data. This is referred to as big data. In a research setting, three aspects of the data are often viewed as the main sources of challenges when attempting to enable value creation from big data: volume, velocity and variety. Many studies address volume or velocity, while much fewer studies concern the variety. Metric space is ideal for addressing variety because it can accommodate any type of data as long as its associated distance notion satisfies the triangle inequality. To accelerate search in metric space, a collection of indexing techniques for metric data have been proposed. However, existing surveys each offers only a narrow coverage, and no comprehensive empirical study of those techniques exists. We offer a survey of all the existing metric indexes that can support exact similarity search, by i) summarizing all the existing partitioning, pruning and validation techniques used for metric indexes, ii) providing the time and storage complexity analysis on the index construction, and iii) report on a comprehensive empirical comparison of their similarity query processing performance. Here, empirical comparisons are used to evaluate the index performance during search as it is hard to see the complexity analysis differences on the similarity query processing and the query performance depends on the pruning and validation abilities related to the data distribution. This article aims at revealing different strengths and weaknesses of different indexing techniques in order to offer guidance on selecting an appropriate indexing technique for a given setting, and directing the future research for metric indexes