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The Kernel Rough K-Means Algorithm
Recent Advances in Computer Science and Communications, 2020Background: Clustering is one of the most important data mining methods. The k-means (c-means ) and its derivative methods are the hotspot in the field of clustering research in recent years. The clustering method can be divided into two categories according to the uncertainty, which are hard clustering and soft clustering. The Hard C-Means clustering
Wang Meng +4 more
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Multilinear Singular Integrals with Rough Kernel
Acta Mathematica Sinica, English Series, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lu, Shan Zhen, Wu, Huo Xiong, Zhang, Pu
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A rough fuzzy kernel clustering algorithm
2015 IEEE International Conference on Communication Problem-Solving (ICCP), 2015Traditional clustering algorithm can't deal with non-linear fuzzy and boundary problem. This paper provides a rough fuzzy kernel clustering algorithm. The algorithm firstly using kernel function map input space to high-dimensional space, make the space can be partitioned linearly.
Ouyang Hao +3 more
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Vector‐valued singular integral operators with rough kernels
Mathematische Nachrichten, 2023AbstractIn this paper, we establish a weak‐type (1,1) boundedness criterion for vector‐valued singular integral operators with rough kernels. As applications, we obtain weak‐type (1,1) bounds for the convolution singular integral operator taking value in the Banach space Y with a rough kernel, the maximal operator taking vector value in Y with a rough ...
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2009
Kernel machines and rough sets are two classes of popular learning techniques. Kernel machines enhance traditional linear learning algorithms to deal with nonlinear domains by a nonlinear mapping, while rough sets introduce a human-like manner to deal with uncertainty in learning.
Qinghua Hu +3 more
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Kernel machines and rough sets are two classes of popular learning techniques. Kernel machines enhance traditional linear learning algorithms to deal with nonlinear domains by a nonlinear mapping, while rough sets introduce a human-like manner to deal with uncertainty in learning.
Qinghua Hu +3 more
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Marcinkiewicz integral with rough kernels
Frontiers of Mathematics in China, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Oscillatory Singular Integrals with Rough Kernel
1995This paper is devoted to the study on the L p -boundedness for the oscillatory singular integral defined by $$ Tf(x) = p.v.\int_{\mathbb{R}^n } {e^{iP(x,y)} } K(x - y)f(y)dy, $$ where P(x,y) is a real polynomial on ℝ n × ℝ n , and \( K(x) = \frac{{h(\mid x\mid \Omega (x)}} {{\mid x\mid ^n }} \) with Ω ∈ Llog + L(S n−1) and h ∈ BV(ℝ+) (i.e.
Yinsheng Jiang, Shanzhen Lu
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Rough bilinear fractional integrals with variable kernels
Frontiers of Mathematics in China, 2010The authors show in the paper that the bilinear operator \[ \tilde B_{\Omega,\alpha}(f,g)(x)= \int_{\mathbb R^n} f(x+y)g(x-y)\frac{\Omega(x,y')}{|y|^{n-\alpha}} dy \] where ...
Chen, Jiecheng, Fan, Dashan
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Rough Cluster Algorithm Based on Kernel Function
2008By means of analyzing kernel clustering algorithm and rough set theory, a novel clustering algorithm, rough kernel k-means clustering algorithm, was proposed for clustering analysis. Through using Mercer kernel functions, samples in the original space were mapped into a highdimensional feature space, which the difference among these samples in sample ...
Tao Zhou +4 more
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On Singular Integral Operators with Rough Kernel Along Surface
Integral Equations and Operator Theory, 2010Let \(\Omega\) be a homogeneous function of degree 0 on \(\mathbb{R}^n\), with \(\Omega \in L^1(S^{n-1})\) and \( \int \Omega (y') d\sigma (y')=0. \) Suppose that \(\Phi\) is a nonnegative (or nonpositive) and monotonic \(C^1\) function on \((0, \infty)\) such that \( \varphi (t) := \frac{\Phi(t)}{t \Phi'(t)} \) is bounded.
Ding, Yong +2 more
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