中文摘要：

为了解决深层感知器的结构设计问题,提出了一种逐层主成分分析方法.该方法根据训练数据集的分布特点,在适当控制信息损失的条件下,可以有效地确定每层神经元的个数.首先,依据样本维数和标签类数分别确定输入层和输出层神经元的个数;然后,对训练样本集进行主成分分析,利用降维后的维数确定第2层神经元的个数;最后,在确定其他层神经元的个数时,将上一次降维后的样本经过非线性激活函数作用,再进行主成分分析,得到降维后的样本维数即为该层神经元的个数.在MNIST手写字数据集上的实验结果表明：该方法有助于简化深层感知器的结构,在减少参数个数、缩短收敛时间和降低训练难度等方面均具有优越性.

英文摘要：

To design a deep perception structure,an effective method was presented in this paper. By appropriately controlling information loss of training data,the number of neurons in each layer of a deep perception was adaptively determined by layer-wise principal component analysis（ LPCA）. At first,the number of input neurons and output neurons were taken as the training data dimension and the number of class labels respectively. Then,the number of neurons in the second layer was computed as a principal component analysis（ PCA） dimension from the training data. Finally,the number of neurons in a layer between the second and the output layer were repeatedly computed from the activations of neurons in its previous layer followed by a PCA. Experimental results show that this LPCA method has superior performances in deep perception structure designing, such as simplifying the structure of deep perception, decreasing number of parameters, accelerating process of training, saving time for convergence. The idea of LPCA provides a new reference for designing deep perceptions and for applications.