Analysis of Temporal Tensor Datasets on Product Grassmann Manifold
Analysis of Temporal Tensor Datasets on Product Grassmann Manifold
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DOI：
10.1109/cvprw56347.2022.00534
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发表时间：
2022-06
期刊：
影响因子：
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通讯作者：
Bojan Batalo;L. S. Souza;B. Gatto;Naoya Sogi;K. Fukui
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作者：
Bojan Batalo;L. S. Souza;B. Gatto;Naoya Sogi;K. Fukui
越来越多的多维数据增加了有效的数据探索和分析的需求。在本文中，我们通过解决张量数据集可视化和聚类的任务来满足这一需求，因为张量是多维数据的自然形式。先前的工作表明，通过各自的线性子空间代表单个张量模式并在产品Grassmann歧管（PGM）上统一它们是一种有效且记忆效率高的表示方式。但是，这种表示可能导致损失有价值的时间信息。为了解决此问题，我们用类似Hankel的矩阵对时间张量模式进行建模，保留序列信息并使用与PGM完全兼容的线性子空间编码它。统一常规张量张量模式的常规张量模式和类似Hankel的表示，然后在PGM上富集表示，计算复杂性的增加最小。通过依赖于歧管上的大地距离，我们通过两种方式促进对多维数据集的分析：1）通过使用诸如T-SNE等算法的直接可视化启用直接可视化； 2）通过使用基于距离或相似性的方法（例如光谱聚类）来促进数据聚类。我们将手势和动作识别数据集评估为时间张量数据集的示例。
Growing abundance of multi-dimensional data creates a need for efficient data exploration and analysis. In this paper, we address this need by tackling the task of tensor dataset visualization and clustering, as tensors are a natural form of multi-dimensional data. Previous work has shown that representing individual tensor modes via respective linear subspaces and unifying them on the product Grassmann manifold (PGM) is an effective and memory-efficient way of representation. However, such representation may lead to loss of valuable temporal information. To address this issue, we model temporal tensor modes with a Hankel-like matrix, preserving sequence information and encoding it with a linear subspace, fully compatible with PGM. Unifying regular tensor modes and Hankel-like representation of regular tensor modes then enriches representation on the PGM, with minimal increase in computational complexity. By relying on geodesic distance on the manifold, we facilitate analysis of multi-dimensional datasets in two ways: 1) by enabling straightforward visualizations using algorithms such as t-SNE; and 2) by fostering clustering of data using distance- or similarity-based methods such as spectral clustering. We evaluate our approach on hand gesture and action recognition datasets as exemplars of temporal tensor datasets.