关键词: 非负矩阵分解, 基因表达数据, 快速算法

Abstract: The algorithm of Nonnegative Matrix Factorization suffers from the large computation complexity and the slow speed of feature extraction for high-dimension-small-sample data.Therefore，a fast algorithm of NMF is presented.By some algebra formulation，the matrix to be factorized is changed into a low-dimension matrix which is a diagonal matrix whose dimension is related to the number of samples.Moreover the feature extraction for one sample only needs to calculate the inner product.A method is used for dimension reduction of gene expression data and the reduced data is used for clustering analysis via k-means.The results show that this method can improve the speed greatly while achieve nearly the same performance as NMF.

Key words: Nonnegative Matrix Factorization（NMF）, gene expression data, fast algorithm