Subspace Classifier For Tissue Classification With Gene Microarray Data-A Non-negative Matrix Factorization Approach

Unsupervised algorithms such as principal component analysis(PCA) , vector quantization(VQ), independent component analysis(ICA) and factor analysis (FA) can be understood as factorizing a data matrix subject to different constraints. Non-negative matrix factorization (NMF) discussed in this paper has the similar model with these unsupervised algorithms. Non-negative matrix factorization is distinguished from the other methods by its use of non-negativity constraints. These constraints lead to a parts-based representation because they allow only additive, not subtractive, combinations. The non-negative basis vectors can represent the local features of the data.This paper presents a new subspace classifier method based on non-negative matrix factorization (NMF). For classification of non-negative data, the basis obtained from the data of a pattern, with the proposed NMF based subspace method, is more compact in expressing the data of the pattern, compared with PCA based subspace classifier approach, thus the classifier designed by such compact expression of patterns results in a better classification performance. Our experiments on benchmark Iris data and real DNA micro-array data (Yeast data and MIT data) show that the proposed NMF based subspace classifier has a great improvement on separability of the data and the recognition rate of the classifier compared with the PCA based subspace classifier.