联合标签预测与判别投影学习的半监督典型相关分析

目的 典型相关分析是一种经典的多视图学习方法。为了提高投影方向的判别性能，现有典型相关分析方法通常采用引入样本标签信息的策略。然而，获取样本的标签信息需要付出大量的人力与物力，为此，提出了一种联合标签预测与判别投影学习的半监督典型相关分析算法。方法 将标签预测与模型构建相融合，具体地说，将标签预测融入典型相关分析框架中，利用联合学习框架学得的标签矩阵更新投影方向，进而学得的投影方向又重新更新标签矩阵。标签预测与投影方向的学习过程相互依赖、交替更新，预测标签不断地接近其真实标签，有利于学得最优的投影方向。结果 本文方法在AR、Extended Yale B、Multi-PIE和ORL这4个人脸数据集上分别进行实验。特征维度为20时，在AR、Extended Yale B、Multi-PIE和ORL人脸数据集上分别取得87%、55%、83%和85%识别率。取训练样本中每人2（3，4，5）幅人脸图像为监督样本，提出的方法识别率在4个人脸数据集上均高于其他方法。训练样本中每人5幅人脸图像为监督样本，在AR、Extended Yale B、Multi-PIE和ORL人脸数据集上分别取得94.67%、68%、83%和85%识别率。实验结果表明在训练样本标签信息较少情况下以及特征降维后的维数较低的情况下，联合学习模型使得降维后的数据最大限度地保存更加有效的信息，得到较好的识别结果。结论 本文提出的联合学习方法提高了学习的投影方向的判别性能，能够有效地处理少量的有标签样本和大量的无标签样本的情况以及解决两步学习策略的缺陷。

Joint label prediction and discriminant projection learning for semi-supervised canonical correlation analysis

Objective Canonical correlation analysis (CCA) is a classic method of multi-view learning. Existing CCA-based methods often adopt the strategy of embedding the label information of samples into the models to improve the discriminative capability of the learning projection direction. However, obtaining the label information of data in real life is highly difficult and requires substantial manpower and material resources. In this respect, scholars have proposed the model of semi-supervised canonical correlation analysis, which can utilize limited number of labeled data and a quantity of unlabeled ones for training to learn the projection direction. However, the existing models of semi-supervised canonical correlation analysis adopt a two-step learning strategy. The model is developed after label prediction. Thus, the processes of label prediction and model development are independent. Using the prediction label of the unlabeled sample to construct the model leads to local optimization of the projection direction, thereby affecting the next classification results. This work proposes joint label prediction and discriminant projection learning for semi-supervised canonical correlation analysis to solve the semi-supervised learning problem and shortcomings of the two-step learning strategy. Method The algorithm combines label prediction with model development. Specifically, the label prediction is integrated into the framework of canonical correlation analysis. The label matrix of the training samples learned by the joint learning framework is used to update the projection direction. Then, the learned projection direction renews the labels of unlabeled data. The learning process of the label prediction and the projection direction depend on each other and are alternately updated. The predicted tag value should be as close as possible to its true value, which is beneficial to learning the optimal projection direction. The optimization of the joint learning framework adopts an alternate iterative strategy to achieve optimal values for the predicted label and projection direction. The discriminant features of the testing images are extracted from the discriminant projection direction acquired by the joint learning framework. Finally, the discriminant features of the testing images are categorized by the classifier. Result Experiments regarding the proposed algorithm are performed on four face datasets, including AR, Extended Yale B, Multi-PIE, and ORL. The experiment results show that the proposed method can obtain enhanced recognition outcomes only by few features and labeled data. Specifically, three face images of each person in the training samples are selected as supervised samples to analyze the effects of experimental results from the different sample dimensions. Face recognition is high as face image dimension is high in any method. The face recognition rate of the proposed algorithm exhibits significant advantages in low dimension compared with other methods. When the feature dimension is 20, the recognition rates on the AR, Extend-ed Yale B, Multi-PIE, and ORL face datasets are 87%, 55%, 83%, and 85%, respectively. The 2 (3, 4, 5) face images of each person in the training samples are selected as supervised samples to analyze the effects of experimental results from the different numbers of labeled data. Face recognition is high as the number of labeled face image is large in any method. Five face images per person in the training sample were supervised samples. The recognition rates on the AR, Extended Yale B, Multi-PIE, and ORL face datasets are 94.67%, 68%, 83%, and 85%, respectively. Conclusion The work proposes a joint learning method that render the learning projection direction highly discriminative, which can effectively handle a limited number of labeled data and a quantity of the unlabeled data and solve the shortcomings of the two-step learning strategy. The experiment results on the AR, Extended Yale B, Multi-PIE, and ORL face datasets demonstrate that the recognition rate of the proposed method is significantly higher than those of other methods. This condition occurs when the supervised samples in the training samples are scarce, and the dimensionality of the data features after dimension reduction is low. The convergence of the proposed iterative algorithm is confirmed by experiments. This finding shows that the feature extracted using discriminant projection direction learned by the joint learning model leads data after dimension reduction to keep the information inherent in the data as much as possible. Finally, enhanced classification results can be obtained using the classifier to categorize the extracted features.