Half Quadratic Analysis for Mean Shift: with Extension to A Sequential Data Mode-Seeking Method

Yuan, Xin; Li, S.Z.

doi:10.1109/iccv.2007.4408979

Cited by 10 publications

(7 citation statements)

References 19 publications

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“…As in [5], we apply mean shift to segment the image into super-pixels (mean shift variants can be used to obtain directly full segmentations [2,16,24]). We compare the speed and segmentation quality obtained by using mean shift, medoid shift, and quick shift (see Fig.…”

Section: Image Segmentationmentioning

confidence: 99%

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Quick Shift and Kernel Methods for Mode Seeking

Vedaldi

Soatto

2008

Lecture Notes in Computer Science

669

461

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Abstract. We show that the complexity of the recently introduced medoid-shift algorithm in clustering N points is O(N 2 ), with a small constant, if the underlying distance is Euclidean. This makes medoid shift considerably faster than mean shift, contrarily to what previously believed. We then exploit kernel methods to extend both mean shift and the improved medoid shift to a large family of distances, with complexity bounded by the effective rank of the resulting kernel matrix, and with explicit regularization constraints. Finally, we show that, under certain conditions, medoid shift fails to cluster data points belonging to the same mode, resulting in over-fragmentation. We propose remedies for this problem, by introducing a novel, simple and extremely efficient clustering algorithm, called quick shift, that explicitly trades off under-and overfragmentation. Like medoid shift, quick shift operates in non-Euclidean spaces in a straightforward manner. We also show that the accelerated medoid shift can be used to initialize mean shift for increased efficiency. We illustrate our algorithms to clustering data on manifolds, image segmentation, and the automatic discovery of visual categories.

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Section: Image Segmentationmentioning

confidence: 99%

“…spaces endowed with a distance). In fact, mean shift is essentially a gradient ascent algorithm [3,5,24] and the gradient may not be defined unless the data space has additional structure (e.g. Hilbert space or smooth manifold structure).…”

Section: Introductionmentioning

confidence: 99%

Quick Shift and Kernel Methods for Mode Seeking

Vedaldi

Soatto

2008

Lecture Notes in Computer Science

669

461

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“…Also, different kernels give rise to different versions of the MS algorithm [8]. More numerical analysis and extensions of MS can be found in [6][7] [8][10] [15].…”

Section: Introductionmentioning

confidence: 99%

Stochastic gradient kernel density mode-seeking

Yuan

2009

2009 IEEE Conference on Computer Vision and Pattern Recognition

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As a well known fixed-point iteration algorithm for kernel density mode-seeking, Mean-Shift has attracted wide attention in pattern recognition field. To date, Mean-Shift algorithm is typically implemented in a batch way with the entire data set known at once. In this paper, based on stochastic gradient optimization technique, we present the stochastic gradient Mean-Shift (SG-MS) along with its approximation performance analysis. We apply SG-MS to the speedup of Gaussian blurring Mean-Shift (GBMS) clustering. Experiments in toy problems and image segmentation show that, while the clustering accuracy is comparable between SG-GBMS and Naive-GBMS, the former significantly outperforms the latter in running time. 978-1-4244-3991-1/09/$25.00 ©2009 IEEE

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“…Recently, Yuan and Li [22] point out that convex kernel based MS is equivalent to half-quadratic (HQ) optimization for the KDE function (1.1). The HQ analysis framework of MS implies the fact that MS is a quadratic bounding (QB) optimization for KDE, which is also discovered by Fashing and Tomasi [11].…”

Section: Introductionmentioning

confidence: 99%

“…2 Quadratic Bounding Nature of MS The fact that MS is a QB optimization is originally discovered by Fashing and Tomasi in [11], motivated by the relationship between MS and Newton-Raphson method. Actually, the QB nature of MS can be more straightforwardly derived from the HQ optimization viewpoint of MS [22]: When kernel is convex and monotonically decreasing, the MS algorithm can be explained as HQ optimization forf k (x). This feature can be shown by using the theory of convex conjugated functions [17] to introduce the following augmented energy function with d + N variables:…”

Section: Introductionmentioning

confidence: 99%

Agglomerative Mean-Shift Clustering via Query Set Compression

Yuan¹,

Hu²,

He³

2009

Proceedings of the 2009 SIAM International Conference on Data Mining

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Mean-Shift (MS) is a powerful non-parametric clustering method. Although good accuracy can be achieved, its computational cost is particularly expensive even on moderate data sets. In this paper, for the purpose of algorithm speedup, we develop an agglomerative MS clustering method called Agglo-MS, along with its mode-seeking ability and convergence property analysis. Our method is built upon an iterative query set compression mechanism which is motivated by the quadratic bounding optimization nature of MS. The whole framework can be efficiently implemented in linear running time complexity. Furthermore, we show that the pairwise constraint information can be naturally integrated into our framework to derive a semi-supervised non-parametric clustering method. Extensive experiments on toy and real-world data sets validate the speedup advantage and numerical accuracy of our method, as well as the superiority of its semi-supervised version.

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Half Quadratic Analysis for Mean Shift: with Extension to A Sequential Data Mode-Seeking Method

Abstract: Theoretical understanding and extension of mean shift procedure has received much attention recently [8,18,3]

Cited by 10 publications

References 19 publications

Quick Shift and Kernel Methods for Mode Seeking

Quick Shift and Kernel Methods for Mode Seeking

Stochastic gradient kernel density mode-seeking

Agglomerative Mean-Shift Clustering via Query Set Compression

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