Abstract: As an important matrix factorization model,non-negative matrix factorization(NMF) is widely used in the fields of data mining and machine learning.It is often used to extract low-dimensional,sparse,and meaningful features from a collection of non-negative data vectors.Although effective in some scenarios,standard NMF utilizes squared Frobenius norm to quantify the reconstruction residual,which make it very sensitive to non-gaussian noises and outliers.As many real data inevitably contain various kind of noises,it is desirable to use robust version of NMF which is insensitive to non-gaussian noise and outliers.This paper proposes to use the Cauchy function to measure the quality of approximation instead of squared Euclidean distance for each sample and take the dependencies between different feature dimensions into account.Based on the theory of half-quadratic programming,this paper derives multiplicative updating rules to solve the proposed model effectively.To verify the effectiveness of the proposed approach,extensive unsupervised clustering experiments are conducted on several benchmark face image datasets.The experimental results show that the proposed model is robust to head poses variations,lighting,and emotion changes.Further,our model achieves consistently good performance when the parameter c varies in a large range on all three benchmark datasets.

Key words: Cauchy loss, Clustering, Data representation, Nonnegative matrix factorization