Theoretical Analysis of a Rigid Coreset Minimum Enclosing Ball Algorithm for Kernel Regression Estimation

Wei, Xunkai; Li, Yinghong

doi:10.1007/978-3-540-87732-5_83

Cited by 3 publications

(4 citation statements)

References 10 publications

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“…In real-world applications [13,28,31], it is required to compute the coreset for MEB in a reproducing kernel Hilbert space (RKHS) instead of Euclidean space. Given a symmetric positive definite kernel k(·, ·) : R m × R m → R and its associated feature mapping ϕ(·) where k(p, q) = ϕ(p), ϕ(q) for any p, q ∈ R m , the kernelized MEB of a set of points P is the smallest ball B * (c * , r * ) in the RKHS such that the maximum distance from c * to ϕ(p) is no greater than r * , which can be formulated as follows:…”

Section: Generalization To Kernelized Mebmentioning

confidence: 99%

“…Coresets for minimum enclosing balls (MEB) [1,4,5,22,23,32,33] have received significant attention due to its wide applications in clustering [4,5,22], support vector machines [28], kernel regression [31], fuzzy inference [13], shape fitting [23], and approximate furthest neighbor search [25]. Given a set of points P , the minimum enclosing ball of P , denoted by MEB(P ), is the smallest ball that contains all points in P .…”

Section: Introductionmentioning

confidence: 99%

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Coresets for Minimum Enclosing Balls over Sliding Windows

Wang

Tan

2019

Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery &Amp; Data Mining

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Coresets are important tools to generate concise summaries of massive datasets for approximate analysis. A coreset is a small subset of points extracted from the original point set such that certain geometric properties are preserved with provable guarantees. This paper investigates the problem of maintaining a coreset to preserve the minimum enclosing ball (MEB) for a sliding window of points that are continuously updated in a data stream. Although the problem has been extensively studied in batch and append-only streaming settings, no efficient sliding-window solution is available yet. In this work, we first introduce an algorithm, called AOMEB, to build a coreset for MEB in an append-only stream. AOMEB improves the practical performance of the state-of-the-art algorithm while having the same approximation ratio. Furthermore, using AOMEB as a building block, we propose two novel algorithms, namely SWMEB and SWMEB+, to maintain coresets for MEB over the sliding window with constant approximation ratios. The proposed algorithms also support coresets for MEB in a reproducing kernel Hilbert space (RKHS). Finally, extensive experiments on real-world and synthetic datasets demonstrate that SWMEB and SWMEB+ achieve speedups of up to four orders of magnitude over the state-of-the-art batch algorithm while providing coresets for MEB with rather small errors compared to the optimal ones.

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Section: Generalization To Kernelized Mebmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Coresets for Minimum Enclosing Balls over Sliding Windows

Wang

Tan

2019

Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery &Amp; Data Mining

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“…ere is an enormous body of work on other types of coresets, see the recent survey on coresets [17], including many for parametric regression variants like least-square regression [4] and l p regression [7]. e only non-parametric regression coreset we are aware of is a form of kernel regression [26] related to the smallest enclosing ball. It predicts the value at a point q ∈ R d as f (q) = β+ p ∈P α p K(p x , q) with loss function p ∈P max{0, | f (p x ) −p | −ε}, for a parameterε.…”

Section: Related Workmentioning

confidence: 99%

“…e only non-parametric regression coreset we are aware of is a form of kernel regression [26] related to the smallest enclosing ball. It predicts the value at a point q ∈ R d as f (q) = β+ p ∈P α p K(p x , q) with loss function p ∈P max{0, | f (p x ) −p | − ε}, for a parameter ε.…”

Section: Related Workmentioning

confidence: 99%

Coresets for Kernel Regression

Zheng

Phillips

2017

Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

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Kernel regression is an essential and ubiquitous tool for non-parametric data analysis, particularly popular among time series and spatial data. However, the central operation which is performed many times, evaluating a kernel on the data set, takes linear time. is is impractical for modern large data sets.In this paper we describe coresets for kernel regression: compressed data sets which can be used as proxy for the original data and have provably bounded worst case error. e size of the coresets are independent of the raw number of data points; rather they only depend on the error guarantee, and in some cases the size of domain and amount of smoothing. We evaluate our methods on very large time series and spatial data, and demonstrate that they incur negligible error, can be constructed extremely e ciently, and allow for great computational gains.

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Coresets for Kernel Regression

Zheng

Phillips

2017

Preprint

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Theoretical Analysis of a Rigid Coreset Minimum Enclosing Ball Algorithm for Kernel Regression Estimation

Cited by 3 publications

References 10 publications

Coresets for Minimum Enclosing Balls over Sliding Windows

Coresets for Minimum Enclosing Balls over Sliding Windows

Coresets for Kernel Regression

Coresets for Kernel Regression

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