Parameter Learning for Alpha Integration

Abstract

In pattern recognition, data integration is an important issue, and when properly done, it can lead to improved performance. Also, data integration can be used to help model and understand multimodal processing in the brain. Amari proposed [Formula: see text]-integration as a principled way of blending multiple positive measures (e.g., stochastic models in the form of probability distributions), enabling an optimal integration in the sense of minimizing the [Formula: see text]-divergence. It also encompasses existing integration methods as its special case, for example, a weighted average and an exponential mixture. The parameter [Formula: see text] determines integration characteristics, and the weight vector [Formula: see text] assigns the degree of importance to each measure. In most work, however, [Formula: see text] and [Formula: see text] are given in advance rather than learned. In this letter, we present a parameter learning algorithm for learning [Formula: see text] and [Formula: see text] from data when multiple integrated target values are available. Numerical experiments on synthetic as well as real-world data demonstrate the effectiveness of the proposed method.