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

Gatto, Bernardo B.; Santos, Eulanda M. dos; Molinetti, Marco A. F.; Fukui, Kiichi

doi:10.1016/j.asoc.2021.107899

Cited by 5 publications

(3 citation statements)

References 58 publications

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“…Finally, clustering is performed on the product of manifolds. The proposed method [38] is evaluated on datasets containing gestures and actions in videos. We also compare it with commonly used tensor clustering approaches for tensor data and subspace-based methods adjusted to handle tensor data.…”

Section: Tensor Learning By Unsupervised Subspacesmentioning

confidence: 99%

Pattern-set Representations using Linear, Shallow and Tensor Subspaces

Gatto

Santos²,

Júnior³

2022

CLEIej

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Pattern-set matching refers to a class of problems where learning takes place through sets rather than elements. Much used in computer vision, this approach presents robustness to variations such as illumination, intrinsic parameters of the signal capture devices, and pose of the analyzed object. Inspired by applications of subspace analysis, three new collections of methods are presented in this paper: (1) New representations for two-dimensional sets; (2) Shallow networks for image classification; and (3) Subspaces for tensor representation and classification. New representations are proposed with the aim of preserving the spatial structure and maintaining a fast processing time. We also introduce a technique to keep temporal structure, even using the principal component analysis, which classically does not model sequences. In shallow networks, we present two convolutional neural networks that do not require backpropagation, employing only subspaces for its convolution filters. These networks present advantages when the training time and hardware resources are scarce. Finally, to handle tensor data, such as video data, we propose methods that employ subspaces for representation in a compact and discriminative way. Our proposed work has been applied to several problems, such as 2D data representation, shallow networks for image classification, and tensor representation and learning.

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Section: Tensor Learning By Unsupervised Subspacesmentioning

confidence: 99%

Pattern-set Representations using Linear, Shallow and Tensor Subspaces

Gatto

Santos²,

Júnior³

2022

CLEIej

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“…Some work also received international awards. A1 ICIP [14] A1 CVPRW [15], [16] A1 ICDAR [17] A2 IJCNN [18] A2 ICTAI [19] A3 SIBGRAPI [20] A3 MLSP [21], [22] A4 BRACIS [23], [24] A4 MVA [25], [26], [27] B1 A1 ASOC [28] A1 PR [29] A1 NEPL [30] A3 EURASIP JIVP [31] A4…”

Section: Awards Publications and Distinctionsmentioning

confidence: 99%

Advances in subspace learning and its applications

Gatto¹,

Fukui²,

Júnior³

et al. 2021

Anais Estendidos Da XXXIV Conference on Graphics, Patterns and Images (SIBRAPI Estendido 2021)

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Pattern-set matching refers to a class of problems where learning takes place through sets rather than elements. Much used in computer vision, this approach presents robustness to variations such as illumination, intrinsic parameters of the signal capture devices, and pose of the analyzed object. Inspired by applications of subspace analysis, three new collections of methods are presented in this thesis summary: (1) New representations for two-dimensional sets; (2) Shallow networks for image classification; and (3) Tensor data representation by subspaces. New representations are proposed to preserve the spatial structure and maintain a fast processing time. We also introduce a technique to keep temporal structure, even using the principal component analysis, which classically does not model sequences. In shallow networks, we present two convolutional neural networks that do not require backpropagation, employing only subspaces for their convolution filters. These networks present advantages when the training time and hardware resources are scarce. Finally, to handle tensor data, such as videos, we propose methods that employ subspaces for representation in a compact and discriminative way. Our proposed work has been applied in problems other than computer vision, such as representation and classification of bioacoustics and text patterns.

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“…Generally, clustering can be divided into five categories: partitioning [ 10 , 11 ], hierarchical [ 12 , 13 ], model-based [ 14 , 15 ], density-based [ 16 , 17 , 18 ], and grid-based algorithms. Partitioned clustering is designed to discover clusters in the data by optimizing a given objective function.…”

Section: Introductionmentioning

confidence: 99%

Grid-Based Clustering Using Boundary Detection

2022

Entropy

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Clustering can be divided into five categories: partitioning, hierarchical, model-based, density-based, and grid-based algorithms. Among them, grid-based clustering is highly efficient in handling spatial data. However, the traditional grid-based clustering algorithms still face many problems: (1) Parameter tuning: density thresholds are difficult to adjust; (2) Data challenge: clusters with overlapping regions and varying densities are not well handled. We propose a new grid-based clustering algorithm named GCBD that can solve the above problems. Firstly, the density estimation of nodes is defined using the standard grid structure. Secondly, GCBD uses an iterative boundary detection strategy to distinguish core nodes from boundary nodes. Finally, two clustering strategies are combined to group core nodes and assign boundary nodes. Experiments on 18 datasets demonstrate that the proposed algorithm outperforms 6 grid-based competitors.

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

Cited by 5 publications

References 58 publications

Pattern-set Representations using Linear, Shallow and Tensor Subspaces

Pattern-set Representations using Linear, Shallow and Tensor Subspaces

Advances in subspace learning and its applications

Grid-Based Clustering Using Boundary Detection

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