基于深度学习的监督型典型相关分析

典型相关分析（CCA）是利用综合变量对之间的相关关系反映两组指标之间整体相关性的多元统计方法。传统的CCA方法无法有效利用样本的标签信息，导致准确率降低。将类信息融入到深度学习与CCA相结合的深度典型相关分析中，提出一种监督型降维方法DL-SCCA，用于处理带标签的非线性可分数据。在2个独立的深度神经网络（DNN）结构上，增加1个公共的输出维数与数据集类别数相同的全连接层，并且以softmax函数作为该层的激活函数，输出带有概率意义的编码向量。在此基础上，利用全连接输出与样本标签信息之间的交叉熵对DNN进行训练，获得分类性能较优的低维特征。实验结果表明，该方法采用最近邻分类器和网络本身结构得到的分类准确率分别为98.00%和97.82%，相比CCA、DisCCA、DCCA等方法，能够有效利用样本的标签信息，并且具有较优的分类性能。

Supervised Canonical Correlation Analysis Based on Deep Learning

Canonical Correlation Analysis (CCA) is a multivariate statistical method, which uses the correlation between comprehensive variable pairs to reflect the overall correlation between two groups of indicators.The traditional CCA method can not effectively use the label information of samples, resulting in low accuracy.The class information is integrated into the Deep Canonical Correlation Analysis (DCCA) combined with deep learning and CCA, and a supervised dimensionality reduction method, DL-SCCA, is proposed to deal with nonlinear separable data with labels.Different Deep Neural Networks (DNN) are established for the samples of two views, and their nonlinear transformation and correlation analysis are carried out.Based on the structure of Deep Neural Networks (DNN), a full connection layer with the same common output dimension and number of categories of the data set is added to the two independent DNN.The softmax function is used as the activation function of this layer, which outputs coding vector with probability significance.On this basis, the DNN is trained using the cross-entropy between the full connection output and the sample label information, and low-dimensional features with better classification performance are obtained.The experimental results show that the classification accuracy of this method is 98.00% and 97.82% by using nearest neighbor classifier and network structure respectively.Compared with CCA, DisCCA, and DCCA, the proposed method can effectively use the label imformation of samples and has better classification performace.