Non-negative Matrix Factorization And Its Bioinformatic Applications

Nowadays, there are many types biological data, such as brain waves, gene microarray data, face data, iris, fingerprint etc.. With the rapid development of biological science and informatic science, people devote to seek solutions to the problems from the data, such as the gene microarray data analysis of difficult miscellaneous diseases, the electrocardiogram data analysis to human-compute integration, the DNA comparison into the criminal investigation, the face recognition of target tracking from video etc.. Non-negative matrix factorization is a data analysis method which is developed rapidly in recent years, and will have a wide application prospect in Bioinfomatics.Non-negative matrix factorization(NMF)aims to finding two lower dimensional non-negative matrices to approximate the high dimensional non-negative matrix, via minimizing their distance, which is better to the further analysis in the projected lower dimensional space.In this paper, we study the Non-negative matrix factorization algorithms, propose three special non-negative matrix factorization algorithms, and apply them to some biological data. The main works of this thesis includes:1) Gauss-seidel based Non-negative Matrix Factorization(GSNMF). GSNMF decomposes the non-negative matrix after the pre-projections. it aims to get two lower dimension non-negative matrices. This model not only decomposes the matrix faster than the traditional ones, but also is good at the gene microarray data which is badlyimbalanced.2) Correntropy Induced metric based Graph regularized Non-negative Matrix Factorization(CGNMF). CGNMF preserves the geometric properties via the adjacent graph learned from the original data, and minimizes its correntropy induce metric(CIM)to get the proper decomposition. This model could robustly learn the features used to cluster the data, and the experiments on face recognition and electrocardiogram recognition application suggest its better robustness.3) Correntropy Supervised Non-negative Matrix Factorization(CSNMF). CSNMF combines the CGNMF framework with label information to supervised learn the two lower dimensional matrices. This model could efficiently classify the data, and the classification experiments of the electrocardiogram data suggested that it can wellimprove the recognition rate.