关键词: 非负矩阵分解, 不完备数据集, 随机修复, 加权, 区域权重

Abstract: Nonnegative Matrix Factorization （NMF） is a new method for feature extraction and data dimension reduction. It has an advantage over traditional algorithms in the simple implementation and the interpretability of factorization form and factorization result. But NMF could not decompose the samples matrix when it is incomplete. However, when dealing with incomplete dataset, NMFI (Weighted Non-negative Matrix Factorization for Incomplete Dataset) made use of random repair to decrease the error and weighted method to control weights of the samples, which could weaken the disturbance of missing data as much as possible. In addition, NMFI used regional weight for further reducing the impact of missing data in critical region. The experimental results demonstrate that NMFI can effectively extract information from retained data and reduce the influence of missing data.

Key words: Nonnegative Matrix Factorization （NMF), incomplete dataset, random repair, weighting, regional weight