A note on the convergence of the mean shift

Li, Xiangru; Hu, Zhanyi; Wu, Fuchao

doi:10.1016/j.patcog.2006.10.016

Cited by 54 publications

(50 citation statements)

References 5 publications

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“…This assignment can be performed using the mean shift algorithm which is an iterative procedure which starts at the vector x n and converges to the nearest mode of the pdf estimatef (x). This idea was introduced in [50] and further studied in [51] [52] [53] [54]. Here, we will use one variant of the mean shift algorithm.…”

Section: Mean Shift Clustering Algorithmmentioning

confidence: 99%

“…This type of mean shift algorithm appears in [53] and [54]. However, the algorithm is not fully understood.…”

Section: Mean Shift Clustering Algorithmmentioning

confidence: 99%

“…However, the algorithm is not fully understood. It is not clearly explained in [53] or [54] how one can arrive at iterations (2.21). Convergence of the fixed scale algorithm was proved in [52].…”

Section: Mean Shift Clustering Algorithmmentioning

confidence: 99%

“…Convergence of the fixed scale algorithm was proved in [52]. Convergence of the variable scale algorithm is proved under some assumptions in [54]. However, these proofs assume α = 1 and study convergence of the discrete sequence of points y j for …”

Section: Mean Shift Clustering Algorithmmentioning

confidence: 99%

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Localization of packet based radio transmitters in space, time, and frequency

Ivkovic

Spasojević

Seskar

2008

2008 42nd Asilomar Conference on Signals, Systems and Computers

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We consider the scenario where one or more sensors observe a frequency band potentially used by multiple radio transmitters forming packet based networks. Our goal is to develop algorithms for estimation of spectrum usage in space, time, and frequency. This estimation is obtained by performing some form of analysis of the received signals at the sensors. The proposed algorithms can be used for achieving efficient spectrum utilization by identifying unused portions of spectrum in space, time and frequency as well as for other applications requiring spectrum monitoring.The received signals consist of packets from multiple transmitters with possible timefrequency collisions. Each received signal consists of multiple statistically homogeneous segments where each combination of active transmitted signals creates one or more of such segments. In order to perform any form of statistical analysis using conventional methods for stationary or cyclostationary signals these segments must be first localized in time. In the first part of the thesis we propose a nonparametric algorithm for solving this problem. Initial segmentation is computed using a variant of mean shift algorithm, which is a clustering tool based on nonparametric estimate of the underlying probability distribution. We show that this type of mean shift algorithm is based on the modified Newton's method and provide a convergence analysis which explains how and why ii the algorithm works. Final segmentation results are obtained after applying a cluster validation procedure and impulse noise filtering on the initial segmentation results.In the second part of the thesis we propose a method for analysis of the segments localized in the first step. This method is useful if transmitted signals are linearly modulated or can be approximated as sums of linearly modulated signals. For each set of segments generated by the same combination of the transmitted signals we compute a certain two dimensional slice of the fourth order spectrum. These slices are arranged in a three way array. We show that under certain conditions it is possible to recover contributions of individual signals to the observed three way array by decomposing the array into low rank terms. Thus, for each received signal we can estimate its spectrum and the associated activity sequence in time. We discuss the uniqueness conditions, treat the nontrivial problem of fourth order spectrum estimation and propose a numerical algorithm for estimation of the spectra and the associated activity sequences of individual signals from the observed three way array.The algorithms for segmentation and fourth order spectrum based analysis require only one sensor. In the third part of the thesis we assume that multiple sensors are available. Using the algorithms mentioned above for each transmitter we can estimate its received spectrum at different sensors. From the received spectra of the same transmitted signal at different sensors it is possible to estimate the source signal spectrum and transfer functions of the ch...

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Section: Mean Shift Clustering Algorithmmentioning

confidence: 99%

“…This type of mean shift algorithm appears in [53] and [54]. However, the algorithm is not fully understood.…”

Section: Mean Shift Clustering Algorithmmentioning

confidence: 99%

Section: Mean Shift Clustering Algorithmmentioning

confidence: 99%

Section: Mean Shift Clustering Algorithmmentioning

confidence: 99%

See 2 more Smart Citations

Localization of packet based radio transmitters in space, time, and frequency

Ivkovic

Spasojević

Seskar

2008

2008 42nd Asilomar Conference on Signals, Systems and Computers

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“…The convergence of the nonblurring version of mean-shift was studied in Cheng (1995), Meer (2000, 2001), and Li et al (2007).…”

Section: Introductionmentioning

confidence: 99%

On the convergence and consistency of the blurring mean-shift process

Chen

2014

Ann Inst Stat Math

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The mean-shift algorithm is a popular algorithm in computer vision and image processing. It can also be cast as a minimum gamma-divergence estimation. In this paper we focus on the "blurring" mean shift algorithm, which is one version of the mean-shift process that successively blurs the dataset. The analysis of the blurring mean-shift is relatively more complicated compared to the nonblurring version, yet the algorithm convergence and the estimation consistency have not been well studied in the literature. In this paper we prove both the convergence and the consistency of the blurring mean-shift. We also perform simulation studies to compare the efficiency of the blurring and the nonblurring versions of the meanshift algorithms. Our results show that the blurring mean-shift has more efficiency.

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Design of Blurring Mean-Shift Algorithms for Data Classification

Grillenzoni

2016

J Classif

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The mean-shift algorithm is an iterative method of mode seeking and data clustering based on the kernel density estimator. The blurring mean-shift is an accelerated version which uses the original data only in the first step, then re-smoothes previous estimates. It converges to local centroids, but may suffer from problems of asymptotic bias, which fundamentally depend on the design of its smoothing components. This paper develops nearest-neighbor implementations and data-driven techniques of bandwidth selection, which enhance the clustering performance of the blurring method. These solutions can be applied to the whole class of mean-shift algorithms, including the iterative local mean method. Extended simulation experiments and applications to well known data-sets show the goodness of the blurring estimator with respect to other algorithms

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A note on the convergence of the mean shift

Cited by 54 publications

References 5 publications

Localization of packet based radio transmitters in space, time, and frequency

Localization of packet based radio transmitters in space, time, and frequency

On the convergence and consistency of the blurring mean-shift process

Design of Blurring Mean-Shift Algorithms for Data Classification

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