An Interface between Grassmann manifolds and vector spaces

Souza, Lincon S.; Sogi, Naoya; Gatto, Bernardo B.; Kobayashi, Takumi; Fukui, Kiichi

doi:10.1109/cvprw50498.2020.00431

Cited by 6 publications

(2 citation statements)

References 31 publications

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“…A popular procedure for measuring the similarity between subspaces is by computing the principal angles, also known as canonical angles [7,8]. Jordan introduced the theory of computing the canonical angles between subspaces.…”

Section: Computing the Similarity Between 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: Computing the Similarity Between Subspacesmentioning

confidence: 99%

Pattern-set Representations using Linear, Shallow and Tensor Subspaces

Gatto

Santos²,

Júnior³

2022

CLEIej

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show abstract

“…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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