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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 0009 +4 more
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Space-carving Kernels for Accurate Rough Terrain Estimation
The International Journal of Robotics Research, 2010Accurate terrain estimation is critical for autonomous offroad navigation. Reconstruction of a three-dimensional (3D) surface allows rough and hilly ground to be represented, yielding faster driving and better planning and control. However, data from a 3D sensor samples the terrain unevenly, quickly becoming sparse at longer ranges and containing large
Raia Hadsell +3 more
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An extension of Marcinkiewicz integrals with rough kernels
Acta Mathematica ScientiazbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wu, Huoxiong, Wu, Lin
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Singular Integrals along Surfaces of Revolution with Rough Kernels
SUT Journal of Mathematics, 2003Let \(n\geq 2\) and \(S^{n-1}\) be the unit sphere in \(\mathbb{R}^n\) equipped with the normalized Lebesgue measure \(d\sigma\). Suppose that \(\Omega\) is a homogeneous function of degree zero on \(\mathbb{R}^n\) that satisfies \(\Omega\in B_q^{0,0}(S^{n-1})\) and \(\int_{S^{n-1}} \Omega (x)d\sigma=0\), where \(B_q^{0,0}\) is a certain block space ...
Al-Qassem, Hussain, Pan, Yibiao
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Rough Sets, Kernel Set, and Spatiotemporal Outlier Detection
IEEE Transactions on Knowledge and Data Engineering, 2014Nowadays, the high availability of data gathered from wireless sensor networks and telecommunication systems has drawn the attention of researchers on the problem of extracting knowledge from spatiotemporal data. Detecting outliers which are grossly different from or inconsistent with the remaining spatiotemporal data set is a major challenge in real ...
Alfredo Petrosino +2 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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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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A roughness-penalty view of kernel smoothing
Statistics & Probability Letters, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Commutators and rough kernels without zero homogeneous condition
International Journal of Wavelets, Multiresolution and Information Processing, 2018In this paper, we consider the commutator [Formula: see text] where [Formula: see text] and [Formula: see text] is defined by the convolution type Calderón–Zygmund operators satisfying the weak boundedness condition and Hörmander condition, we prove its continuity by using wavelets, decomposition of compensated quantity by wavelets and commutators on ...
Qixiang Yang, Zengjian Lou
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Parabolic singular integrals with rough kernels and extrapolation
SCIENTIA SINICA Mathematica, 2014This paper is devoted to studying the parabolic singular integrals with rough kernels both on the unit sphere and in the radial direction, as well as the corresponding maximal singular integrals. By the estimates of Fourier transforms, the Littlewood-Paley theory and the extrapolation arguments, under the rather weak size conditions, which are the best
Feng LIU, HuoXiong WU
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