Multilinear clustering via tensor Fukunaga–Koontz transform with Fisher eigenspectrum regularization

• Published in: Applied soft computing 2021-12, Vol.113, p.107899, Article 107899
• Main Authors: Gatto, Bernardo B., dos Santos, Eulanda M., Molinetti, Marco A.F., Fukui, Kazuhiro
• Format: Article
• Language: English
• Subjects: [formula omitted]-mode SVD; Fukunaga–Koontz transform; Subspace method; Tensor analysis
• ISSN: 1568-4946; 1872-9681
• DOI: 10.1016/j.asoc.2021.107899

Clustering is a fundamental learning task with many applications in a wide range of fields. Recently proposed techniques have shown that performing clustering in a discriminative space provides reliable results. Motivated by these results, as well as by advances in subspace representation, we introduce in this paper a new learning model that performs discriminative clustering on tensor data. The proposed method exploits the inherent tensor mode representation provided by multilinear data, extracting discriminative spaces in each mode, which are further combined in a product space. In previous work, the Fukunaga–Koontz transform was extended to handle multilinear data through the use of a tensor representation. That work yielded notable results in the clustering of gestures and actions from videos. However, the model may overfit because no regularization process is applied. Therefore, an efficient regularization scheme based on the Fisher score is proposed in this paper to optimize the clustering model. In addition to a new regularization scheme and discriminative properties, the advantages of our method include (1) sufficient flexibility to adapt to hierarchical and k-means clustering algorithms with low computational cost inherited from subspace learning, (2) a new formulation of the mean between two tensors in terms of the product of spaces, and (3) a Fisher score definition for multilinear data. Comprehensive experimental results on diverse real-world datasets confirm that the proposed method provides results that are competitive with those from current tensor clustering algorithms. •Discriminative tensor data clustering by Fukunaga–Koontz Transform is proposed.•Eigenspectrum regularization based on the Fisher score for tensor data is proposed.•The Karcher mean is extended to handle tensor data.•Tensor data representation and manifold learning are integrated into a unified model.•Benchmark experiments support the effectiveness of RTFKT.