Canonical correlation analysis (CCA) is a typical and useful learning paradigm in big data analysis for capturing correlation across multiple views of the same objects. When dealing with data with additional ordinal information, traditional CCA suffers from poor performance due to ignoring the ordinal relationships within the data. Such data is becoming increasingly common, as either temporal or sequential information is often associated with the data collection process. To incorporate the ordinal information into the objective function of CCA, the so-called ordinal discriminative CCA has been presented in the literature. Although ordinal discriminative CCA can yield better ordinal regression results, its performance deteriorates when data is corrupted with noise and outliers, as it tends to smear the order information contained in class centers. To address this issue, in this article we construct a robust manifold-preserved ordinal discriminative correlation regression (rmODCR). The robustness is achieved by replacing the traditional ( l 2 -norm) class centers with l p -norm centers, where p is efficiently estimated according to the moments of the data distributions, as well as by incorporating the manifold distribution information of the data in the objective optimization. In addition, we further extend the robust manifold-preserved ordinal discriminative correlation regression to deep convolutional architectures. Extensive experimental evaluations have demonstrated the superiority of the proposed methods.

中文翻译：

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序数数据上的矩引导判别流形相关学习

典型相关分析 (CCA) 是大数据分析中一种典型且有用的学习范式，用于捕获同一对象的多个视图之间的相关性。在处理带有额外序数信息的数据时，传统的 CCA 由于忽略了数据中的序数关系而表现不佳。此类数据正变得越来越普遍，因为时间或顺序信息通常与数据收集过程相关联。为了将序数信息纳入 CCA 的目标函数，文献中提出了所谓的序数判别式 CCA。尽管序数判别式 CCA 可以产生更好的序数回归结果，但当数据被噪声和异常值破坏时，它的性能会下降，因为它倾向于涂抹类中心中包含的顺序信息。为了解决这个问题，在本文中，我们构建了一个稳健的流形保留序判别相关回归 (rmODCR)。通过替换传统的（l 2-norm) 班级中心lp -范数中心，其中p根据数据分布的矩，以及在目标优化中结合数据的流形分布信息，进行有效估计。此外，我们进一步将鲁棒的流形保留序判别相关回归扩展到深度卷积架构。广泛的实验评估证明了所提出方法的优越性。