Selective smoothing of the generative topographic mapping.

Generative topographic mapping is a nonlinear latent variable model introduced by Bishop et al. as a probabilistic reformulation of self-organizing maps. The complexity of this model is mostly determined by the number and form of basis functions generating the nonlinear mapping from latent space to data space, but it can be further controlled by adding a regularization term to increase the stiffness of the mapping and avoid data over-fitting. In this paper, we improve the map smoothing by introducing multiple regularization terms, one associated with each of the basis functions. A similar technique to that of automatic relevance determination, our selective map smoothing locally controls the stiffness of the mapping depending on length scales of the underlying manifold, while optimizing the effective number of active basis functions.

Translation, rotation, and scale invariant pattern recognition by high-order neural networks and moment classifiers.

The classification and recognition of two-dimensional patterns independently of their position, orientation, and size by using high-order networks are discussed. A method is introduced for reducing and controlling the number of weights of a third-order network used for invariant pattern recognition. The method leads to economical networks that exhibit high recognition rates for translated, rotated, and scaled, as well as locally distorted, patterns. The performance of these networks at recognizing types and handwritten numerals independently of their position, size, and orientation is compared with and found superior to the performance of a layered feedforward network to which image features extracted by the method of moments are presented as input.