Improving non-negative matrix factorizations through structured initialization

In this paper we explore a recent iterative compression technique called non-negative matrix factorization (NMF). Several special properties are obtained as a result of the constrained optimization problem of NMF. For facial images, the additive nature of NMF results in a basis of features, such as eyes, noses, and lips. We explore various methods for efficiently computing NMF, placing particular emphasis on the initialization of current algorithms. We propose using Spherical K-Means clustering to produce a structured initialization for NMF. We demonstrate some of the properties that result from this initialization and develop an efficient way of choosing the rank of the low-dimensional NMF representation.