Multilinear clustering via tensor Fukunaga-Koontz transform with Fisher eigenspectrum regularization
Multilinear clustering via tensor Fukunaga-Koontz transform with Fisher eigenspectrum regularization
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DOI：
10.1016/j.asoc.2021.107899
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发表时间：
2021-09-29
影响因子：
8.7
通讯作者：
Fukui, Kazuhiro
中科院分区：
文献类型：
--
作者：
Gatto, Bernardo B.;Santos, Eulanda M. dos;Fukui, Kazuhiro
聚类是一项基本的学习任务，在许多领域有着广泛的应用。最近提出的技术表明，在区分空间中执行聚类可提供可靠的结果。基于这些结果以及子空间表示的发展，本文提出了一种新的对张量数据进行判别聚类的学习模型。该方法利用多线性数据提供的固有张量模式表示，提取每个模式中的区分空间，并将其组合在乘积空间中。在以前的工作中，Fukunaga-Koontz变换被扩展到通过使用张量表示来处理多线性数据。这项工作在对视频中的手势和动作进行聚类方面取得了显着的成果。然而，由于没有应用正则化过程，该模型可能会过度拟合。为此，本文提出了一种高效的基于Fisher评分的正则化方法来优化聚类模型。除了新的正则化方案和判别性外，我们的方法的优点包括(1)足够的灵活性来适应从子空间学习继承的低计算代价的分层和k-均值聚类算法，(2)关于空间乘积的两个张量之间的平均值的新公式，以及(3)多线性数据的Fisher分数定义。在不同的真实数据集上的综合实验结果证实，该方法提供的结果与现有张量聚类算法的结果具有竞争力。
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.