Canonical correlation analysis using within-class coupling

Fisher’s linear discriminant analysis (LDA) is one of the most popular supervised linear dimensionality reduction methods. Unfortunately, LDA is not suitable for problems where the class labels are not available and only the spatial or temporal association of data samples is implicitly indicative of class membership. In this study, a new strategy for reducing LDA to Hotelling’s canonical correlation analysis (CCA) is proposed. CCA seeks prominently correlated projections between two views of data and it has been long known to be equivalent to LDA when the data features are used in one view and the class labels are used in the other view. The basic idea of the new equivalence between LDA and CCA, which we call within-class coupling CCA (WCCCA), is to apply CCA to pairs of data samples that are most likely to belong to the same class. We prove the equivalence between LDA and such an application of CCA. With such an implicit representation of the class labels, WCCCA is applicable both to regular LDA problems and to problems in which only spatial and/or temporal continuity provides clues to the class labels.

Research highlights
► Samples versus class-labels equivalence between LDA and CCA is extended to samples versus samples basis, which can be viewed as accomplishing LDA through a rather indirect and distributed style of an implicit presentation of the categorical class labels.
► Applicable both to regular LDA problems and to problems in which only spatial and/or temporal continuity provides clues to the class labels rather than being explicitly available, where they can be tracked down in the patterns of the data, such as for the tasks of splitting a video into scenes (sequences of relevant frames), segmentation of an image into image regions sharing certain visual characteristics, speech analysis, or biological sequence analysis.
► For demonstration, the ORL face dataset is made into a movie in a way that the consecutive frames are more likely to be of the pictures of the same individuals rather than different.
► When a scene change occurs, the movie continues with the pictures of another individual and so on.
► The method is applied on this movie and it can work just like when the LDA is given the actual class labels.