Supervised dimensionality reduction for sequence data projects the observations in sequences onto a low-dimensional subspace to better separate different sequence classes. It is typically more challenging than conventional dimensionality reduction for static data, because measuring the separability of sequences involves non-linear procedures to manipulate the temporal structures. This paper presents a linear method, namely Order-preserving Wasserstein Discriminant Analysis (OWDA), which learns the projection by maximizing the inter-class distance and minimizing the intra-class scatter. For each class, OWDA extracts the order-preserving Wasserstein barycenter and constructs the intra-class scatter as the dispersion of the training sequences around the barycenter. The inter-class distance is measured as the order-preserving Wasserstein distance between the corresponding barycenters. OWDA is able to concentrate on the distinctive differences among classes by lifting the geometric relations with temporal constraints. Experiments show that OWDA achieves competitive results on three 3D action recognition datasets.
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Linear and Deep Order-Preserving Wasserstein Discriminant Analysis
Supervised dimensionality reduction for sequence data learns a transformation that maps the observations in sequences onto a low-dimensional subspace by maximizing the separability of sequences in different classes. It is typically more challenging than
conventional dimensionality reduction for static data, because measuring the separability of sequences involves non-linear procedures to manipulate the temporal structures. In this paper, we propose a linear method, called Order-preserving Wasserstein Discriminant
Analysis (OWDA), and its deep extension, namely DeepOWDA, to learn linear and non-linear discriminative subspace for sequence data, respectively. We construct novel separability measures between sequence classes based on the order-preserving Wasserstein (OPW) distance to capture the essential differences among their temporal structures. Specifically, for each class, we extract the OPW barycenter and construct the intra-class scatter as the dispersion of the training sequences around the barycenter. The inter-class distance is measured as the OPW distance between the corresponding barycenters. We learn the linear and non-linear transformations by maximizing the inter-class distance and minimizing the intra-class scatter. In this way, the proposed OWDA and
DeepOWDA are able to concentrate on the distinctive differences among classes by lifting the geometric relations with temporal constraints. Experiments on four 3D action recognition datasets show the effectiveness of OWDA and DeepOWDA.
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- Award ID(s):
- 1815561
- NSF-PAR ID:
- 10279302
- Date Published:
- Journal Name:
- IEEE Transactions on Pattern Analysis and Machine Intelligence
- ISSN:
- 0162-8828
- Page Range / eLocation ID:
- 1 to 1
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1109/TPAMI.2021.3050750
