Clustering-based initialization for non-negative matrix factorization

Abstract

Non-negative matrix factorization (NMF) is an unsupervised learning algorithm that can extract parts from visual data. The goal of this technique is to find intuitive basis such that training examples can be faithfully reconstructed using linear combination of basis images which are restricted to non-negative values. Thus, NMF basis images can be understood as localized features that correspond better with intuitive notions of parts of images. However, there has been few systematic study to explore various methods for initialization of NMF algorithm, which is crucial for the performance of NMF algorithm in data analysis. In this paper, we discuss a structured NMF initialization scheme based on the clustering method. Comparing with the random initialization in common use, our method achieved faster convergence while maintaining the data structure and also obtained good result for the face recognition task. Furthermore, we also proposed to use a normalized AIC incorporated with our NMF initialization for rank selection of traditional NMF at the cost of much less computational load while obtaining a good performance in face recognition.