Multilinear discriminant analysis (MLDA), a novel approach based upon recent developments in tensor-tensor decomposition, has been proposed recently and showed better performance than traditional matrix linear discriminant analysis (LDA). The current paper presents a nonlinear generalization of MLDA (referred to as KMLDA) by extending the well known ``kernel trick" to multilinear data. The approach proceeds by defining a new dot product based on new tensor operators for third-order tensors. Experimental results on the ORL, extended Yale B, and COIL-100 data sets demonstrate that performing MLDA in feature space provides more class separability. It is also shown that the proposed KMLDA approach performs better than the Tucker-based discriminant analysis methods in terms of image classification.
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This content will become publicly available on August 1, 2025
Tensor discriminant analysis on grassmann manifold with application to video based human action recognition
Representing videos as linear subspaces on Grassmann manifolds has made great strides in action recognition problems. Recent studies have explored the convenience of discriminant analysis by making use of Grassmann kernels. However, traditional methods rely on the matrix representation of videos based on the temporal dimension and suffer from not considering the two spatial dimensions. To overcome this problem, we keep the natural form of videos by representing video inputs as multidimensional arrays known as tensors and
propose a tensor discriminant analysis approach on Grassmannian manifolds. Because matrix algebra does not handle tensor data, we introduce a new Grassmann projection kernel based on the tensor-tensor decomposition and product. Experiments with human action databases show that the proposed method performs well compared with the state-of-the-art algorithms.
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- Award ID(s):
- 2007367
- NSF-PAR ID:
- 10529074
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- International Journal of Machine Learning and Cybernetics
- Volume:
- 15
- Issue:
- 8
- ISSN:
- 1868-8071
- Page Range / eLocation ID:
- 3353 to 3365
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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