Moment-Guided Discriminative Manifold Correlation Learning on Ordinal Data

Canonical correlation analysis (CCA) is a typical and useful learning paradigm in big data analysis for capturing correlation across multiple views of the same objects. When dealing with data with additional ordinal information, traditional CCA suffers from poor performance due to ignoring the ordinal relationships within the data. Such data is becoming increasingly common, as either temporal or sequential information is often associated with the data collection process. To incorporate the ordinal information into the objective function of CCA, the so-called ordinal discriminative CCA has been presented in the literature. Although ordinal discriminative CCA can yield better ordinal regression results, its performance deteriorates when data is corrupted with noise and outliers, as it tends to smear the order information contained in class centers. To address this issue, in this article we construct a robust manifold-preserved ordinal discriminative correlation regression (rmODCR). The robustness is achieved by replacing the traditional (l₂-norm) class centers with l_p-norm centers, where p is efficiently estimated according to the moments of the data distributions, as well as by incorporating the manifold distribution information of the data in the objective optimization. In addition, we further extend the robust manifold-preserved ordinal discriminative correlation regression to deep convolutional architectures. Extensive experimental evaluations have demonstrated the superiority of the proposed methods.