Invariant Feature Set Generation with the Linear Manifold Self-organizing Map

One of the most important challenges faced by computer vision is the almost unlimited possibilities of variation associated with the objects. It has been hypothesized that the brain represents image manifolds as manifolds of stable neural-activity patterns. In this paper, we explore the possibility of manifold representation with a set of to-pographically organized neurons with each representing a local linear manifold and capturing some local linear feature invariance. In particular, we propose to consider the local subspace learning at each neuron of the network from a Gaussian likelihood point of view. Robustness of the algorithm with respect to the learning rate issue is obtained by considering statistical efficiency. Compared to its predecessors, the proposed network is more adaptive and robust in learning globally nonlinear data manifolds, which is verified by experiments on handwritten digit image modeling.