  Restricted Boltzmann machine (RBM) is a two-layer neural network constructed
as a probabilistic model and its training is to maximize a product of
probabilities by the contrastive divergence (CD) scheme. In this paper a data
mapping is proposed to describe the relationship between the visible and hidden
layers and the training is to minimize a squared error on the visible layer by
a finite difference learning. This paper presents three new properties in using
the RBM: 1) nodes on the visible and hidden layers can take real-valued matrix
data without a probabilistic interpretation; 2) the famous CD1 is a finite
difference approximation of the gradient descent; 3) the activation can take
non-sigmoid functions such as identity, relu and softsign. The data mapping
provides a unified framework on the dimensionality reduction, the feature
extraction and the data representation pioneered and developed by Hinton and
his colleagues. As an approximation of the gradient descent, the finite
difference learning is applicable to both directed and undirected graphs.
Numerical experiments are performed to verify these new properties on the very
low dimensionality reduction, the collinearity of timer series data and the use
of flexible activations.
