On Clustering Histograms with k-Means by Using Mixed α-Divergences

Nielsen, Frank; Nock, Richard; Амари, Шун-ичи

doi:10.3390/e16063273

Cited by 29 publications

(20 citation statements)

References 31 publications

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“…Another interesting case of study is the

-divergence that can be obtained from the

-divergences for the parametrization

. As mentioned before, there are closed formulas for the computation of sided centroids for the k -means with

-divergences [ 7 , 9 ]. However, to compare the formulas, it is necessary to take into account that there are two equivalent ways to define the

-divergence family.…”

Section: Relations With Known Centroid-based Algorithmsmentioning

confidence: 99%

“…For the specific case of

-divergences, closed formulas for the computation of the sided centroids were derived in [ 6 ] for the right-type, and in [ 7 , 8 ] for the left-type. Symmetrized centroids have also been derived for clustering histograms in the Bag-of-Words modeling paradigm in [ 9 ]. Total Bregman divergences (TDB), which are invariant to particular transformations on the natural space, have also been used for estimating the center of a set of vectors in [ 10 ] in the context of the shape retrieval problem.…”

Section: Introductionmentioning

confidence: 99%

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Centroid-Based Clustering with αβ-Divergences

Sarmiento

Fondón

Durán-Díaz

et al. 2019

Entropy

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Centroid-based clustering is a widely used technique within unsupervised learning algorithms in many research fields. The success of any centroid-based clustering relies on the choice of the similarity measure under use. In recent years, most studies focused on including several divergence measures in the traditional hard k-means algorithm. In this article, we consider the problem of centroid-based clustering using the family of α β -divergences, which is governed by two parameters, α and β . We propose a new iterative algorithm, α β -k-means, giving closed-form solutions for the computation of the sided centroids. The algorithm can be fine-tuned by means of this pair of values, yielding a wide range of the most frequently used divergences. Moreover, it is guaranteed to converge to local minima for a wide range of values of the pair ( α , β ). Our theoretical contribution has been validated by several experiments performed with synthetic and real data and exploring the ( α , β ) plane. The numerical results obtained confirm the quality of the algorithm and its suitability to be used in several practical applications.

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“…Another interesting case of study is the

-divergence that can be obtained from the

-divergences for the parametrization

. As mentioned before, there are closed formulas for the computation of sided centroids for the k -means with

-divergences [ 7 , 9 ]. However, to compare the formulas, it is necessary to take into account that there are two equivalent ways to define the

-divergence family.…”

Section: Relations With Known Centroid-based Algorithmsmentioning

confidence: 99%

“…For the specific case of

Section: Introductionmentioning

confidence: 99%

Centroid-Based Clustering with αβ-Divergences

Sarmiento

Fondón

Durán-Díaz

et al. 2019

Entropy

View full text Add to dashboard Cite

show abstract

“…We use JS-divergence as the objective function dq in our experiments (see Section 5). JS-divergence is a standard measure for quantifying distances between probability distributions, which is often used in histogram/vector classification [45] and clustering [51]. Given two histograms H 1 , H 2 , the JS-divergence between them is defined as…”

Section: Quality Lossmentioning

confidence: 99%

Location histogram privacy by Sensitive Location Hiding and Target Histogram Avoidance/Resemblance

Loukides

Theodorakopoulos

2019

Knowl Inf Syst

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A location histogram is comprised of the number of times a user has visited locations as they move in an area of interest, and it is often obtained from the user in the context of applications such as recommendation and advertising. However, a location histogram that leaves a user's computer or device may threaten privacy when it contains visits to locations that the user does not want to disclose (sensitive locations), or when it can be used to profile the user in a way that leads to price discrimination and unsolicited advertising (e.g. as "wealthy" or "minority member"). Our work introduces two privacy notions to protect a location histogram from these threats: sensitive location hiding, which aims at concealing all visits to sensitive locations, and target avoidance/resemblance, which aims at concealing the similarity/dissimilarity of the user's histogram to a target histogram that corresponds to an undesired/desired profile. We formulate an optimization problem around each notion: Sensitive Location Hiding (SLH), which seeks to construct a histogram that is as similar as possible to the user's histogram but associates all visits with nonsensitive locations, and Target Avoidance/Resemblance (T A/T R), which seeks to construct a histogram that is as dissimilar/similar as possible to a given target histogram but remains useful for getting a good response from the application that analyzes the histogram. We develop an optimal algorithm for each notion, which operates on a notion-specific search space graph and finds a shortest or longest path in the graph that corresponds to a solution histogram. In addition, we develop a greedy heuristic for the T A/T R problem, which operates directly on a user's histogram. Our experiments demonstrate that all algorithms are effective at preserving the distribution of locations in a histogram and the quality of location recommendation. They also demonstrate that the heuristic produces near-optimal solutions while being orders of magnitude faster than the optimal algorithm for T A/T R.

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“…The k-means clustering algorithm [ 9 , 10 , 11 ] is a hard clustering algorithm, which is representative of a typical prototype-based clustering method for objective functions. It utilizes the distance from data points to the prototype as an optimized objective function and an adjustment rule of iterative operation is obtained by using the method of function extreme value evaluation [ 12 , 13 , 14 , 15 ]. Entropy is a method of measuring and quantitatively describing the randomness or irregularity of a time series or nonlinear signals [ 16 ].…”

Section: Introductionmentioning

confidence: 99%

Magnetotelluric Signal-Noise Identification and Separation Based on ApEn-MSE and StOMP

Cai

Peng

et al. 2019

Entropy

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Natural magnetotelluric signals are extremely weak and susceptible to various types of noise pollution. To obtain more useful magnetotelluric data for further analysis and research, effective signal-noise identification and separation is critical. To this end, we propose a novel method of magnetotelluric signal-noise identification and separation based on ApEn-MSE and Stagewise orthogonal matching pursuit (StOMP). Parameters with good irregularity metrics are introduced: Approximate entropy (ApEn) and multiscale entropy (MSE), in combination with k-means clustering, can be used to accurately identify the data segments that are disturbed by noise. Stagewise orthogonal matching pursuit (StOMP) is used for noise suppression only in data segments identified as containing strong interference. Finally, we reconstructed the signal. The results show that the proposed method can better preserve the low-frequency slow-change information of the magnetotelluric signal compared with just using StOMP, thus avoiding the loss of useful information due to over-processing, while producing a smoother and more continuous apparent resistivity curve. Moreover, the results more accurately reflect the inherent electrical structure information of the measured site itself.

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On Clustering Histograms with k-Means by Using Mixed α-Divergences

Cited by 29 publications

References 31 publications

Centroid-Based Clustering with αβ-Divergences

Centroid-Based Clustering with αβ-Divergences

Location histogram privacy by Sensitive Location Hiding and Target Histogram Avoidance/Resemblance

Magnetotelluric Signal-Noise Identification and Separation Based on ApEn-MSE and StOMP

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