On weighted kernels

1952 ◽  
Vol 2 (1) ◽  
pp. 126-149 ◽  
Author(s):  
Zeev Nehari
Keyword(s):  
Weighted Kernels

scholarly journals Weighted p-regular kernels for reproducing kernel Hilbert spaces and Mercer Theorem

2019 ◽  
Vol 18 (03) ◽  
pp. 359-383
Author(s):  
L. Agud ◽  
J. M. Calabuig ◽  
E. A. Sánchez Pérez
Keyword(s):  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Banach Function Space ◽  
Finite Measure ◽  
Reproducing Kernel Hilbert Spaces ◽  
Kernel Operator ◽  
Finite Measure Space ◽  
Kernel Hilbert Spaces ◽  
Vector Valued Function ◽  
Weighted Kernels

Let [Formula: see text] be a finite measure space and consider a Banach function space [Formula: see text]. Motivated by some previous papers and current applications, we provide a general framework for representing reproducing kernel Hilbert spaces as subsets of Köthe–Bochner (vector-valued) function spaces. We analyze operator-valued kernels [Formula: see text] that define integration maps [Formula: see text] between Köthe–Bochner spaces of Hilbert-valued functions [Formula: see text] We show a reduction procedure which allows to find a factorization of the corresponding kernel operator through weighted Bochner spaces [Formula: see text] and [Formula: see text] — where [Formula: see text] — under the assumption of [Formula: see text]-concavity of [Formula: see text] Equivalently, a new kernel obtained by multiplying [Formula: see text] by scalar functions can be given in such a way that the kernel operator is defined from [Formula: see text] to [Formula: see text] in a natural way. As an application, we prove a new version of Mercer Theorem for matrix-valued weighted kernels.

On Weighted Kernels of Two Posets

Order ◽  
2015 ◽  
Vol 33 (1) ◽  
pp. 51-65 ◽  
Author(s):  
Tamás Fleiner ◽  
Zsuzsanna Jankó
Keyword(s):  
Weighted Kernels

Rough Set-Based Feature Weighted Kernels for Support Vector Machine

2012 ◽  
Vol 9 (12) ◽  
pp. 2250-2254
Author(s):  
Xiangjun Li ◽  
Fen Rao ◽  
Tinghua Wang ◽  
Taorong Qiu
Keyword(s):  
Support Vector Machine ◽  
Rough Set ◽  
Support Vector ◽  
Weighted Kernels

scholarly journals Learning to Diversify for Ensembling of An Amount of Classifiers

2021 ◽  
Author(s):  
Chun Yang ◽  
Xu-Cheng Yin
Keyword(s):  
Loss Function ◽  
State Of The Art ◽  
Grand Challenge ◽  
Training Algorithm ◽  
Simple Criterion ◽  
Kernel Weights ◽  
Novel Approach ◽  
Adaptive Diversity ◽  
Benchmark Datasets ◽  
Weighted Kernels

Abstract Not only common man but also intelligent machine always merge all available decisions to solve problems. However, given an amount of learned classifiers, how to select and combine diverse classifiers for machine is still a grand challenge in the literature for decades of history. In this paper, we introduce a novel approach for classifier ensemble, learning to diversify, which learns to adaptively combine classifiers by considering both accuracy and diversity. Specifically, our approach, learning to diversify via weighted kernels, performs classifier combination by optimizing a direct but simple criterion: maximizing ensemble accuracy and adaptive diversity simultaneously by minimizing a loss function. Given a measure formulation, the diversity is calculated with weighted kernels, i.e., the diversity is measured on the component classifiers’ outputs which are kernelized and weighted. Moreover, we propose an iterative training algorithm for weights optimization, where this loss function is iteratively minimized by estimating the kernel weights in conjunction with the classifier weights. Extensive experiments on a variety of classification benchmark datasets show that the proposed approach consistently outperforms state-of-the-art ensembles.

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