For similarity-based clustering, we propose modeling the entries of a given similarity matrix as the inner products of the unknown cluster probabilities. To estimate the cluster probabilities from the given similarity matrix, we introduce a left-stochastic non-negative matrix factorization problem. A rotation-based algorithm is proposed for the matrix factorization. Conditions for unique matrix...

The degree of similarity or dissimilarity between the objects under study plays an important role. In vector space, especially, the cosine similarity measure is often used in information retrieval, citation analysis, and automatic classification. However, it scarcely deals with trapezoidal fuzzy information and multicriteria decision-making problems. For this purpose, a cosine similarity measur...

Similarity Matrix of Proteins (SIMAP) (http://mips.gsf.de/simap) provides a database based on a pre-computed similarity matrix covering the similarity space formed by >4 million amino acid sequences from public databases and completely sequenced genomes. The database is capable of handling very large datasets and is updated incrementally. For sequence similarity searches and pairwise alignments...

Tf-idf weighting scheme is adopted by state-ofthe-art object retrieval systems to reflect the difference in discriminability between visual words. However, we argue it is only suboptimal by noting that tf-idf weighting scheme does not take quantization error into account and exploit word correlation. We view tf-idf weights as an example of diagonal Mahalanobis-type similarity matrix and general...

Protein sequence similarity searching programs like BLASTP, SSEARCH (UNIT 3.10), and FASTA use scoring matrices that are designed to identify distant evolutionary relationships (BLOSUM62 for BLAST, BLOSUM50 for SEARCH and FASTA). Different similarity scoring matrices are most effective at different evolutionary distances. "Deep" scoring matrices like BLOSUM62 and BLOSUM50 target alignments with...

A molecular similarity measure has been developed using molecular topological graphs and atomic partial charges. Two kinds of topological graphs were used. One is the ordinary adjacency matrix and the other is a matrix which represents the minimum path length between two atoms of the molecule. The ordinary adjacency matrix is suitable to compare the local structures of molecules such as functio...

An orthogonal similarity reduction of a matrix to semiseparable form. Abstract It is well known how any symmetric matrix can be reduced by an orthogonal similarity transformation into tridiagonal form. Once the tridiagonal matrix has been computed, several algorithms can be used to compute either the whole spectrum or part of it. In this paper, we propose an algorithm to reduce any symmetric ma...

Shaded similarity matrix has long been used in visual cluster analysis. This paper investigates how it can be used in classification visualization. We focus on two popular classification methods: nearest neighbor and decision tree. Ensemble classifier visualization is also presented for handling large data sets.

Repetition is a fundamental element in generating and perceiving structure in music. Recent work has applied this principle to separate the musical background from the vocal foreground in a mixture, by simply extracting the underlying repeating structure. While existing methods are effective, they depend on an assumption of periodically repeating patterns. In this work, we generalize the repeti...