A Collective Neurodynamic Optimization Approach to Nonnegative Matrix Factorization
The unsupervised learning of spectro-temporal patterns within speech signals is of interest in a broad range of applications. Where patterns are non-negative and convolutive in nature, relevant learning algorithms include convolutive non-negative matrix factorization (CNMF) and its sparse alternative, convolutive non-negative sparse coding (CNSC). Both algorithms, however, place unrealistic demands on computing power and memory which prohibit their application in large scale tasks. This paper proposes a new online implementation of CNMF and CNSC which processes input data piece-by-piece and updates learned patterns gradually with accumulated statistics. The proposed approach facilitates pattern learning with huge volumes of training data that are beyond the capability of existing alternatives. We show that, with unlimited data and computing resources, the new online learning algorithm almost surely converges to a local minimum of the objective cost function. In more realistic situations, where the amount of data is large and computing power is limited, online learning tends to obtain lower empirical cost than conventional batch learning.