Analysis of Temporal Tensor Datasets on Product Grassmann Manifold

Bojan Batalo, Lincon S. Souza, Bernardo B. Gatto, Naoya Sogi, Kazuhiro Fukui; Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2022, pp. 4869-4877


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.

Related Material

@InProceedings{Batalo_2022_CVPR, author = {Batalo, Bojan and Souza, Lincon S. and Gatto, Bernardo B. and Sogi, Naoya and Fukui, Kazuhiro}, title = {Analysis of Temporal Tensor Datasets on Product Grassmann Manifold}, booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops}, month = {June}, year = {2022}, pages = {4869-4877} }