Robust Canonical Correlation Analysis Based On Kernel-induced Measure And Its Relative Applications

Data dimensionality reduction is a important part of pattern recognition, its basic task is toextract stable and effective features from high-dimensional data to meet the subsequent learningtask. Canonical correlation analysis (CCA) is a classic multi-view data dimensionality reductionmethod, which aims to searching for the linear correlation between the two sets of variables of thesame object. In recent years, CCA is commonly used and has attracted much attention in the filedof pattern recognition. However, for the data in real world, such as face recognition, CCA has thefollowing shortcomings:(1) as a linear algorithm, which can not be directly applied to nonlinearproblems;(2) Dataset is inevitable with the outliers in the real world, and the Euclidean distancemeasure used in CCA results in robustness problem. Recent years, many improved CCAalgorithms have been proposed by researchers, however, most of them just solve the nonlineardefect of CCA, robustness is still a problem. In the paper, we focus on the robustness of canonicalcorrelation analysis, the main contents and achievements are as follows:(1) A novel robust CCA is developed based on kernel-induced measure which is called KI-CCA.The RBF kernel-induced measure used in KI-CCA not only overcomes the shortcomings of CCAand some related algorithms which are not robust but also makes the robust principal componentanalysis based on Maximum Entropy to be a special case. And because of the diversity of kernelfunctions, KI-CCA is a general algorithm. The solution can be obtained by solving a generalizedeigenvalue problem as CCA. Experiments on toy problem, Multiple Feature Database (MFD) andface datasets (Yale, AR, ORL) demonstrate the effectiveness of KI-CCA.(2) According to the different ways of Robustness, robust CCA can be specifically divided intotwo classes: directly-robustified canonical correlation analysis and indirectly-robustifiedcanonical correlation analysis. KI-CCA we have already proposed can be categorized asdirectly-robustified CCA.In this paper, we process a novel indirectly-robustified CCA frame,which use a novel robust PCA named KI-PCA as the data preprocessing method. The essence ofrobustness of the framework is to find outliers by using the data preprocessing method, and ensurethe robustness for the subsequent tasks of CCA.(3)we do further research on robust CCAs of the two different ways, conclusions summarized bythe results of the experiments is to provide meaningful guidance for the subsequent learning.