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

摘要： 针对超高维数据进行非负矩阵分解的计算代价大，特征提取速度慢问题，提出一种非负矩阵分解的快速算法。该算法通过代数变换，把对原高维矩阵的非负分解转换成非负的低维矩阵的非负分解，其求解过程只需要对一个阶数等于样本数的对角矩阵进行非负矩阵分解，同时提取某样本特征时只需要计算该样本与所有训练样本的内积。对高维小样本的基因表达数据降维后进行k均值聚类分析，实验结果表明，该算法在不影响非负矩阵分解性能的前提下，大大提高了计算速度。

关键词: 非负矩阵分解, 基因表达数据, 快速算法