Component analysis (CA) is a powerful technique for learning discriminative representations in various computer vision tasks. Typical CA methods are essentially based on the covariance matrix of training data. But, the covariance matrix has obvious disadvantages such as failing to model complex relationship among features and singularity in small sample size cases. In this letter, we propose a general covariance measure to achieve better data representations. The proposed covariance is characterized by a nonlinear mapping determined by domain-specific applications, thus leading to more advantages, flexibility, and applicability in practice. With general covariance, we further present two novel CA methods for learning compact representations and discuss their differences from conventional methods. A series of experimental results on nine benchmark data sets demonstrate the effectiveness of the proposed methods in terms of accuracy.

中文翻译：

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通过一般协方差学习无监督和有监督的表示

分量分析 (CA) 是一种强大的技术，可用于在各种计算机视觉任务中学习判别式表示。典型的 CA 方法本质上是基于训练数据的协方差矩阵。但是，协方差矩阵有明显的缺点，例如无法在小样本量的情况下对特征和奇异性之间的复杂关系进行建模。在这封信中，我们提出了一种通用的协方差度量，以实现更好的数据表示。所提出的协方差的特点是由特定领域的应用程序确定的非线性映射，从而在实践中带来更多的优势、灵活性和适用性。通过一般协方差，我们进一步提出了两种新的 CA 方法来学习紧凑表示，并讨论它们与传统方法的区别。