Manifold Alpha-Integration

Manifold learning has been successfully used for finding dominant factors (low-dimensional manifold) in a high-dimensional data set. However, most existing manifold learning algorithms only consider one Manifold based on one dissimilarity matrix. For utilizing multiple manifolds, a key question is how different pieces of information can be integrated when multiple measurements are available. Amari proposed alpha-integration for stochastic model integration, which is a generalized averaging method that includes as a special case arithmetic, geometric, and harmonic averages. In this paper, we propose a new generalized manifold integration algorithm equipped with alpha-integration, manifold alpha-integration (MAI). Interestingly, MAI can be shown to be a generalization of other integration methods (that may or may not use manifolds) like kernel fusion or mixture of random walk. Our experimental results also confirm that integration of multiple sources of information on individual manifolds is superior to the use of individual manifolds separately, in tasks including classification and sensorimotor integration.