Canonical Correlation Analysis of Datasets With a Common Source Graph
Canonical Correlation Analysis of Datasets With a Common Source Graph
复制标题
DOI：
10.1109/tsp.2018.2853130
复制
发表时间：
2018-08-15
影响因子：
5.4
通讯作者：
Giannakis, Georgios B.
中科院分区：
文献类型：
--
作者：
Chen, Jia;Wang, Gang;Giannakis, Georgios B.
典型相关分析（CCA）是一种强大的技术，用于发现隐藏源是否通常存在于两个（或多个）数据集中。它的优点包括降维、聚类、分类、特征选择和数据融合。然而，标准CCA不利用公共源的几何形状，公共源的几何形状可以从给定的数据中获得或者可以从（交叉）相关性中推导出。在本文中，由生成数据的公共源提供的这些额外信息被编码在图中，并被调用作为图正则化器。这导致了一种新的图正则化CCA方法，即所谓的图（g）CCA。新的gCCA占图诱导的知识的共同来源，同时最大限度地减少所需的典型变量之间的距离。针对数据数量小于数据向量维度的各种实际环境，也开发了gCCA的双重公式。一种这样的设置包括被并入以考虑非线性数据依赖性的内核。得到的图核CCA也得到了封闭的形式。最后，确证图像分类测试在几个真实的数据集展示的优点，新的线性，双，和内核的方法相对于竞争的替代品。
Canonical correlation analysis (CCA) is a powerful technique for discovering whether or not hidden sources are commonly present in two (or more) datasets. Its well-appreciated merits include dimensionality reduction, clustering, classification, feature selection, and data fusion. The standard CCA, however, does not exploit the geometry of the common sources, which may be available from the given data or can be deduced from (cross-) correlations. In this paper, this extra information provided by the common sources generating the data is encoded in a graph, and is invoked as a graph regularizer. This leads to a novel graph-regularized CCA approach, that is termed graph (g) CCA. The novel gCCA accounts for the graph-induced knowledge of common sources, while minimizing the distance between the wanted canonical variables. Tailored for diverse practical settings where the number of data is smaller than the data vector dimensions, the dual formulation of gCCA is developed too. One such setting includes kernels that are incorporated to account for nonlinear data dependencies. The resultant graph-kernel CCA is also obtained in closed form. Finally, corroborating image classification tests over several real datasets are presented to showcase the merits of the novel linear, dual, and kernel approaches relative to competing alternatives.