Facing with rapidly increasing demands for analyzing high-order data or multiway data, feature-extracting methods become imperative for analysis and processing. The traditional feature-extracting methods, however, either need to overly vectorize the data and smash the original structure hidden in data, such as PCA and PCA-like methods, which is unfavorable to the data recovery, or cannot eliminate the redundant information very well, such as tucker decomposition (TD) and TD-like methods. To overcome these limitations, we propose a more flexible and more powerful tool, called the multiview principal components analysis (Multiview-PCA) in this article. By segmenting a random tensor into equal-sized subarrays called sections and maximizing variations caused by orthogonal projections of these sections, the Multiview-PCA finds principal components in a parsimonious and flexible way. In so doing, two new operations on tensors, the SS -direction inner/outer product, are introduced to formulate tensor projection and recovery. With different segmentation ways characterized by section depth and direction, the Multiview-PCA can be implemented many times in different ways, which defines the sequential and global Multiview-PCA, respectively. These multiple Multiview-PCA take the PCA and PCA-like, and TD and TD-like as the special cases, which correspond to the deepest section depth and the shallowest section depth, respectively. We propose an adaptive depth and direction selection algorithm for the implementation of Multiview-PCA. The Multiview-PCA is then tested in terms of subspace recovery ability, compression ability, and feature extraction performance when applied to a set of artificial data, surveillance videos, and hyperspectral imaging data. All numerical results support the flexibility, effectiveness, and usefulness of Multiview-PCA.

中文翻译：

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多视图PCA：一种高阶数据特征提取和降维方法


面对快速增长的高阶数据或多路数据分析需求，特征提取方法成为分析处理的必然要求。然而，传统的特征提取方法要么需要对数据进行过度矢量化，打碎隐藏在数据中的原始结构，例如PCA和类PCA方法，不利于数据恢复，要么不能很好地消除冗余信息，例如塔克分解（TD）和类TD方法。为了克服这些限制，我们提出了一种更灵活、更强大的工具，在本文中称为多视图主成分分析（Multiview-PCA）。通过将随机张量分割成大小相等的子数组（称为截面）并最大化这些截面的正交投影引起的变化，多视图 PCA 以简约且灵活的方式找到主成分。在此过程中，引入了两种新的张量运算（SS 方向内/外积）来制定张量投影和恢复。通过以截面深度和方向为特征的不同分割方式，Multiview-PCA可以以不同的方式实现多次，这分别定义了顺序Multiview-PCA和全局Multiview-PCA。这些多重Multiview-PCA以PCA和PCA-like、TD和TD-like为特例，分别对应于最深截面深度和最浅截面深度。我们提出了一种自适应深度和方向选择算法来实现多视图-PCA。然后，在应用于一组人工数据、监控视频和高光谱成像数据时，测试 Multiview-PCA 的子空间恢复能力、压缩能力和特征提取性能。 所有数值结果都支持 Multiview-PCA 的灵活性、有效性和实用性。