Anne M. Dougherty

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.

Rate-hardness: a new performance metric for haptic interfaces

Rate-hardness is introduced as a quality metric for hard virtual surfaces, and linked to human perception of hardness via a psychophysical study. A 3 degree-of-freedom haptic interface is used to present pairs of virtual walls to users for side-by-side comparison, 19 subjects are tested in a series of three blocks of trials, where different virtual walls are presented in randomly ordered pairs. Results strongly support the use of rate-hardness, as opposed to mechanical stiffness, as the more relevant metric for haptic interface performance in rendering hard virtual surfaces. It is also shown that common techniques of enhancing stability of the rendered surfaces tend to actually enhance performance as measured by rate-hardness.

Non-negative matrix factorization: Ill-posedness and a geometric algorithm

Non-negative matrix factorization (NMF) has been proposed as a mathematical tool for identifying the components of a dataset. However, popular NMF algorithms tend to operate slowly and do not always identify the components which are most representative of the data. In this paper, an alternative algorithm for performing NMF is developed using the geometry of the problem. The computational costs of the algorithm are explored, and it is shown to successfully identify the components of a simulated dataset. The development of the geometric algorithm framework illustrates the ill-posedness of the NMF problem and suggests that NMF is not sufficiently constrained to be applied successfully outside of a particular class of problems.