In this paper, we propose a speed-up approach for subclass discriminant analysis and formulate a novel efficient multi-view solution to it. The speed-up approach is developed based on graph embedding and spectral regression approaches that involve eigendecomposition of the corresponding Laplacian matrix and regression to its eigenvectors. We show that by exploiting the structure of the between-class Laplacian matrix, the eigendecomposition step can be substituted with a much faster process. Furthermore, we formulate a novel criterion for multi-view subclass discriminant analysis and show that an efficient solution for it can be obtained in a similar to the single-view manner. We evaluate the proposed methods on nine single-view and nine multi-view datasets and compare them with related existing approaches. Experimental results show that the proposed solutions achieve competitive performance, often outperforming the existing methods. At the same time, they significantly decrease the training time.
In multi-view learning, the data @math is described from @math views and we seek to find @math matrices @math that project the data @math from all views @math to a common (latent) space, where the separability between the classes is the highest. A generalized framework for multi-view subspace learning, that includes many of the existing methods as special cases, was proposed in @cite_0 . Here, the optimization problem is defined as where @math and @math are the inter-view and intra-view covariance matrices. The solution is obtained by solving the generalized eigendecomposition problem ), where @math is the projection matrix of the view @math . The feature vectors in the latent space are obtained as @math , where @math is data representation in the view @math . =1pt Here, ), ), ), where @math is either @math or @math , as defined below, @math and @math are the view labels, and @math is the number of views.
@cite_0
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In this paper, the problem of multi-view embedding from different visual cues and modalities is considered. We propose a unified solution for subspace learning methods using the Rayleigh quotient, which is extensible for multiple views, supervised learning, and nonlinear embeddings. Numerous methods including canonical correlation analysis, partial least square regression, and linear discriminant analysis are studied using specific intrinsic and penalty graphs within the same framework. Nonlinear extensions based on kernels and (deep) neural networks are derived, achieving better performance than the linear ones. Moreover, a novel multi-view modular discriminant analysis is proposed by taking the view difference into consideration. We demonstrate the effectiveness of the proposed multi-view embedding methods on visual object recognition and cross-modal image retrieval, and obtain superior results in both applications compared to related methods.