Wavelet transform based on inner product in fault diagnosis of rotating machinery: A review
J Chen, Z Li, J Pan, G Chen, Y Zi, J Yuan… - Mechanical systems and …, 2016 - Elsevier
As a significant role in industrial equipment, rotating machinery fault diagnosis (RMFD)
always draws lots of attention for guaranteeing product quality and improving economic …
always draws lots of attention for guaranteeing product quality and improving economic …
Sparse machine learning in Banach spaces
Y Xu - Applied Numerical Mathematics, 2023 - Elsevier
The aim of this expository paper is to explain to graduate students and beginning
researchers in the field of mathematics, statistics and engineering the fundamental concept …
researchers in the field of mathematics, statistics and engineering the fundamental concept …
On reproducing kernel Banach spaces: Generic definitions and unified framework of constructions
Recently, there has been emerging interest in constructing reproducing kernel Banach
spaces (RKBS) for applied and theoretical purposes such as machine learning, sampling …
spaces (RKBS) for applied and theoretical purposes such as machine learning, sampling …
Reproducing kernel Banach spaces with the ℓ1 norm
G Song, H Zhang, FJ Hickernell - Applied and Computational Harmonic …, 2013 - Elsevier
Targeting at sparse learning, we construct Banach spaces B of functions on an input space
X with the following properties:(1) B possesses an ℓ1 norm in the sense that B is …
X with the following properties:(1) B possesses an ℓ1 norm in the sense that B is …
Reproducing Kernel Banach Spaces with the ℓ1 Norm II: Error Analysis for Regularized Least Square Regression
G Song, H Zhang - Neural computation, 2011 - ieeexplore.ieee.org
A typical approach in estimating the learning rate of a regularized learning scheme is to
bound the approximation error by the sum of the sampling error, the hypothesis error, and …
bound the approximation error by the sum of the sampling error, the hypothesis error, and …
[HTML][HTML] Vector-valued reproducing kernel Banach spaces with applications to multi-task learning
H Zhang, J Zhang - Journal of Complexity, 2013 - Elsevier
Motivated by multi-task machine learning with Banach spaces, we propose the notion of
vector-valued reproducing kernel Banach spaces (RKBSs). Basic properties of the spaces …
vector-valued reproducing kernel Banach spaces (RKBSs). Basic properties of the spaces …
Separability of reproducing kernel spaces
H Owhadi, C Scovel - Proceedings of the American Mathematical Society, 2017 - ams.org
Separability of reproducing kernel spaces Page 1 PROCEEDINGS OF THE AMERICAN
MATHEMATICAL SOCIETY Volume 145, Number 5, May 2017, Pages 2131–2138 http://dx.doi.org/10.1090/proc/13354 …
MATHEMATICAL SOCIETY Volume 145, Number 5, May 2017, Pages 2131–2138 http://dx.doi.org/10.1090/proc/13354 …
Frames, semi-frames, and Hilbert scales
JP Antoine, P Balazs - Numerical functional analysis and …, 2012 - Taylor & Francis
Given a total sequence in a Hilbert space, we speak of an upper (resp. lower) semi-frame if
only the upper (resp. lower) frame bound is valid. Equivalently, for an upper semi-frame, the …
only the upper (resp. lower) frame bound is valid. Equivalently, for an upper semi-frame, the …
Multi-task learning in vector-valued reproducing kernel Banach spaces with the ℓ1 norm
Targeting at sparse multi-task learning, we consider regularization models with an ℓ 1
penalty on the coefficients of kernel functions. In order to provide a kernel method for this …
penalty on the coefficients of kernel functions. In order to provide a kernel method for this …
On the inclusion relation of reproducing kernel Hilbert spaces
H Zhang, L Zhao - Analysis and Applications, 2013 - World Scientific
To help understand various reproducing kernels used in applied sciences, we investigate
the inclusion relation of two reproducing kernel Hilbert spaces. Characterizations in terms of …
the inclusion relation of two reproducing kernel Hilbert spaces. Characterizations in terms of …