Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Fast Nonnegative Matrix Factorization and Its Application for Protein Fold Recognition | Hindawi Publishing Corporation EURASIP Journal on Applied Signal Processing Volume 2006 Article ID 71817 Pages 1-8 DOI ASP 2006 71817 Fast Nonnegative Matrix Factorization and Its Application for Protein Fold Recognition Oleg Okun and Helen Priisalu Machine Vision Group Infotech Oulu and Department of Electrical and Information Engineering University of Oulu . Box 4500 90014 Finland Received 27 April 2005 Revised 29 September 2005 Accepted 8 December 2005 Linear and unsupervised dimensionality reduction via matrix factorization with nonnegativity constraints is studied. Because of these constraints it stands apart from other linear dimensionality reduction methods. Here we explore nonnegative matrix factorization in combination with three nearest-neighbor classifiers for protein fold recognition. Since typically matrix factorization is iteratively done convergence can be slow. To speed up convergence we perform feature scaling normalization prior to the beginning of iterations. This results in a significantly more than 11 times faster algorithm. Justification of why it happens is provided. Another modification of the standard nonnegative matrix factorization algorithm is concerned with combining two known techniques for mapping unseen data. This operation is typically necessary before classifying the data in low-dimensional space. Combining two mapping techniques can yield better accuracy than using either technique alone. The gains however depend on the state of the random number generator used for initialization of iterations a classifier and its parameters. In particular when employing the best out of three classifiers and reducing the original dimensionality by around 30 these gains can reach more than 4 compared to the classification in the original high-dimensional space. Copyright 2006 Hindawi Publishing Corporation. All rights reserved. 1. INTRODUCTION It is not uncommon that for certain data sets their dimensionality n is higher than the number
