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.

中文翻译：

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基于柯西多集典型相关的多模态子空间融合

多集典型相关分析（MCCA）是一种著名的多模态相干子空间学习方法。然而，由于噪声信息和有限的样本量，基于样本的 MCCA 模态间和模态内协方差矩阵通常会偏离实际协方差矩阵。这种偏差会削弱 MCCA 的性能，尤其是在图像识别方面。针对这一具有挑战性的问题，我们利用柯西估计理论校正样本协方差矩阵的奇异值，进一步得到更接近真实协方差矩阵的柯西协方差矩阵。在柯西协方差矩阵的基础上，我们开发了一种新的多模态子空间融合方法，即柯西多集典型相关。通过最大化不同模态之间的柯西相关性并约束模态内数据的柯西散布，该方法可以从几幅图像中学习到具有良好判别能力的柯西相干融合子空间。实验结果表明了所提出方法的有效性，有望实现本研究的目标。