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.

翻译：受限制的波尔茨曼机器(RBM)是一个两层神经网络,作为概率模型,其培训目的是通过对比差异(CD)机制最大限度地实现概率的产物。本文建议进行数据映射,以描述可见层和隐藏层之间的关系,而培训则是通过有限的差异学习尽量减少可见层和隐蔽层的方位错误。本文介绍了使用成果管理制的三种新特性:1)可见层和隐蔽层的节点可以在不作概率解释的情况下获取真实价值的矩阵数据;2)著名的CD1是梯度下沉的有限差异近似值;3)启动可采取非类体函数,如身份、累记和软信号。数据映射提供了一个关于维度减少、特征提取和Hinton及其同事开创和开发的数据代表的统一框架。作为梯度系的近似值,有限的差异学习适用于定向和非定向图形。进行了数值实验,以核实在非常低的维度减少、弹性时间序列数据激活和使用弹性数据方面的新特性。