Abstract
Multi-set canonical correlation analysis (MCCA) is a famous multi-modal coherent subspace learning method. However, sample-based between-modal and within-modal covariance matrices of MCCA usually deviate from real covariance matrices due to noise information and limited sample size. The deviation will weaken the performance of MCCA, especially in image recognition. Aiming at this challenging issue, we correct singular values of sample covariance matrices with the employment of Cauchy estimate theory and further obtain Cauchy covariance matrices that are closer to real covariance matrices. On the basis of Cauchy covariance matrices, we develop a novel multi-modal subspace fusion method, i.e. Cauchy multi-set canonical correlations. By maximizing Cauchy correlations between different modalities and constraining Cauchy scatters of within-modal data, the method can learn a Cauchy coherent fusion subspace with well discriminative power from a few images. Experiment results have shown the effectiveness of the proposed method, promising to the aims of this research.
Highlights
One object usually possesses multiple data representations in real-world applications
Canonical correlation analysis (CCA) aims at simultaneously learning correlation projection directions of two-modal data on the basis of maximal between-modal correlations, and raw multi-modal data can be projected into the coherent fusion subspace
Covariance matrices based on image samples will have a great deviation degree, which is an important reason why Multi-set canonical correlation analysis (MCCA) and many feature learning methods based on covariance matrices show the bad performance of image recognition
Summary
One object usually possesses multiple data representations in real-world applications. According to the advantages of Hessian, Liu et al [25] developed a novel Hessian multi-set canonical correlations method, which exploits graph-based geometry manifolds of raw multi-modal data and effectively integrates the manifold structure into the coherent fusion subspace. We embed Cauchy covariance matrices into the correlation analysis framework and propose a novel Cauchy subspace fusion method for multi-modal highdimensional data, i.e. Cauchy multi-set canonical correlations (CauMCCs). By maximizing Cauchy correlations between different modalities and simultaneously constraining Cauchy scatters of within-modal data, the proposed method can learn a Cauchy coherent fusion subspace with well discriminative power from a few training high-dimensional samples. In the Cauchy coherent fusion subspace, multi-modal data can be effectively fused, and the fused low-dimensional data possess well class separability, which is beneficial to final recognition tasks.
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