Although the protein sequence-structure gap continues to enlarge due to the development of high-throughput sequencing tools, the protein structure universe tends to be complete without proteins with novel structural folds deposited in the protein data bank (PDB) recently. In this work, we identify a protein structural dictionary (Frag-K) composed of a set of backbone fragments ranging from 4 to 20 residues as the structural “keywords” that can effectively distinguish between major protein folds. We firstly apply randomized spectral clustering and random forest algorithms to construct representative and sensitive protein fragment libraries from a large scale of high-quality, non-homologous protein structures available in PDB. We analyze the impacts of clustering cut-offs on the performance of the fragment libraries. Then, the Frag-K fragments are employed as structural features to classify protein structures in major protein folds defined by SCOP (Structural Classification of Proteins). Our results show that a structural dictionary with ~400 4- to 20-residue Frag-K fragments is capable of classifying major SCOP folds with high accuracy.

In recent years, the recommendation systems have become increasingly popular and have been used in a broad variety of applications. Here, we investigate the matrix completion techniques for the recommendation systems that are based on collaborative filtering. The collaborative filtering problem can be viewed as predicting the favorability of a user with respect to new items of commodities. When a rating matrix is constructed with users as rows, items as columns, and entries as ratings, the collaborative filtering problem can then be modeled as a matrix completion problem by filling out the unknown elements in the rating matrix. This article presents a comprehensive survey of the matrix completion methods used in recommendation systems. We focus on the mathematical models for matrix completion and the corresponding computational algorithms as well as their characteristics and potential issues. Several applications other than the traditional user-item association prediction are also discussed.