Gram matrices of reproducing kernel Hilbert spaces over graphs

Seto, Michio; Suda, Sho; Taniguchi, Tetsuji

doi:10.1016/j.laa.2013.12.001

Cited by 16 publications

(5 citation statements)

References 10 publications

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“…Since the Sobolev inequalities are useful analytical tools, they have been extended to the discrete setting [14,58]. For finite graphs, Sobolev inequalities and sharp constants have been obtained by [55,56,67,69,80,81]. In this article, we generalize our previous results on the existence of extremal functions for the first-order Sobolev inequality [33] to higher order inequalities on Cayley graphs of groups of polynomial growth.…”

Section: Introductionmentioning

confidence: 70%

Extremal functions for the second-order Sobolev inequality on groups of polynomial growth

Hua¹,

Li²,

Münch³

2022

Preprint

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Section: Introductionmentioning

confidence: 70%

Extremal functions for the second-order Sobolev inequality on groups of polynomial growth

Hua¹,

Li²,

Münch³

2022

Preprint

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“…In particular, in [7], we have already obtained the sharp constants for the discrete Sobolev inequalities that correspond to a regular polyhedron. It is also interesting to note that Seto et al [8] found essentially the sharp constants of discrete Sobolev inequalities.…”

Section: Introductionmentioning

confidence: 95%

“…Our purpose herein is the same as that of [7,8]. In particular we generalize the conventional framework of the regular polyhedron.…”

Section: Introductionmentioning

confidence: 99%

Two types of discrete Sobolev inequalities on a weighted Toeplitz graph

Takemura

Nagai

Kametaka

2016

Linear Algebra and its Applications

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In this paper, two types of discrete Sobolev inequalities that correspond to the generalized graph Laplacian A on a weighted Toeplitz graph are obtained. The sharp constants C 0 (a) and C 0 are calculated using the Green matrix G(a) = (A + aI) −1 (0 < a < ∞) and pseudo-Green matrix G * = A † (Penrose-Moore generalized inverse matrix of A). The sharp constants are expressed as reciprocals of the harmonic mean corresponding to eigenvalues of each matrix A + aI and A except an eigenvalue 0.

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“…Specifically, G =( k ( x , y )) x , y may be determined with a self-adjoint matrix in the case where X is a finite set, known as the Gram matrix of H [ 26 ]. Also, it follows from the reproducing property that:

…”

Section: Theoretical Fundamentalsmentioning

confidence: 99%

Deep Hybrid Multimodal Biometric Recognition System Based on Features‐Level Deep Fusion of Five Biometric Traits

Safavipour

Doostari

2023

Computational Intelligence and Neuroscience

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The need for information security and the adoption of the relevant regulations is becoming an overwhelming demand worldwide. As an efficient solution, hybrid multimodal biometric systems utilize fusion to combine multiple biometric traits and sources with improving recognition accuracy, higher security assurance, and to cope with the limitations of the uni-biometric system. In this paper, three strategies for dealing with a feature-level deep fusion of five biometric traits (face, both irises, and two fingerprints) derived from three sources of evidence are proposed and compared. In the first two proposed methodologies, each feature vector is mapped from the feature space into the reproducing kernel Hilbert space (RKHS) separately by selecting the appropriate reproducing kernel. In this higher space, where the result is the conversion of nonlinear relations to linear ones, dimensionality reduction algorithms (KPCA, KLDA) and quaternion-based algorithms (KQPCA, KQPCA) are used for the fusion of the feature vectors. In the third methodology, the fusion of feature spaces based on deep learning is administered by combining feature vectors in in-depth and fully connected layers. The experimental results on 6 databases in the proposed hybrid multibiometric system clearly show the multimodal template obtained from the deep fusion of feature spaces; while being secure against spoof attacks and making the system robust, they can use the low dimensionality of the fused vector to increase the accuracy of a hybrid multimodal biometric system to 100%, showing a significant improvement compared with uni-biometric and other multimodal systems.

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Gram matrices of reproducing kernel Hilbert spaces over graphs

Cited by 16 publications

References 10 publications

Extremal functions for the second-order Sobolev inequality on groups of polynomial growth

Extremal functions for the second-order Sobolev inequality on groups of polynomial growth

Two types of discrete Sobolev inequalities on a weighted Toeplitz graph

Deep Hybrid Multimodal Biometric Recognition System Based on Features‐Level Deep Fusion of Five Biometric Traits

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