Bisecting K-Means and 1D Projection Divisive Clustering: A Unified Framework and Experimental Comparison

Ковалева, Е. В.; Mirkin, Boris

doi:10.1007/s00357-015-9186-y

Cited by 21 publications

(11 citation statements)

References 26 publications

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“…Assigning observations to groups is a common goal in psychological research, whether it is via mixture modeling (McLachlan & Peel, 2000) or cluster analysis (Everitt et al, 2011). As such, much effort has been made in determining how to assess the performance of traditional clustering approaches (Bruzzese & Vistocco, 2015; Hofmans, Ceulemans, Steinley, & Van Mechelen, 2015; Steinley, 2003, 2006; Steinley & Brusco, 2007, 2008a, 2008b), mixture modeling (Steinley & Brusco, 2011; Vrbik & McNicholas, 2015), latent class analysis (Brusco, 2004), and latent profile analysis (Steinley & McDonald, 2007), among many other approaches such as divisive clustering (Kovaleva & Mirkin, 2015), facility location problems (Brusco & Steinley, 2015), and social network analysis (Brusco & Doreian, 2015). The measure of choice for determining the adequacy of a partition of observations into groups is the adjusted Rand index (ARI; Hubert & Arabie, 1985).…”

mentioning

confidence: 99%

The variance of the adjusted Rand index.

Steinley

Brusco

Hubert

2016

Psychological Methods

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For 30 years, the adjusted Rand index has been the preferred method for comparing 2 partitions (e.g., clusterings) of a set of observations. Although the index is widely used, little is known about its variability. Herein, the variance of the adjusted Rand index (Hubert & Arabie, 1985) is provided and its properties are explored. It is shown that a normal approximation is appropriate across a wide range of sample sizes and varying numbers of clusters. Further, it is shown that confidence intervals based on the normal distribution have desirable levels of coverage and accuracy. Finally, the first power analysis evaluating the ability to detect differences between 2, different adjusted Rand indices is provided. (PsycINFO Database Record

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mentioning

confidence: 99%

The variance of the adjusted Rand index.

Steinley

Brusco

Hubert

2016

Psychological Methods

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“…Then, the clustering method is used to eliminate the inclusion of support points that close to one another. Considering that the k-means method is easy to trap in local optimum [28], the bisecting k-means method [29] combined with the iterative self-organizing data technique algorithm (ISODATA) is used to implement the optimization. The steps for generating the support point set in each loop are listed as:…”

Section: An Adaptive Modeling Frameworkmentioning

confidence: 99%

Wind-Resistant Capacity Modeling for Electric Transmission Line Towers Using Kriging Surrogates and Its Application to Structural Fragility

Cai

Wan²

2021

Applied Sciences

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Wind loading on a transmission tower structure is jointly influenced by the wind field, structural parameters, and the geo-spatial configuration of the transmission line. Considering the multi-parametric effect, this paper aims at developing a limit capacity model for transmission towers under strong winds. To this end, the limit capacity of the tower is expressed via two equivalent means: one is the limit wind speed as a function of the wind angle of attack and the span of transmission line; the other is a limit capacity surface with three fundamental wind load components as the principal axes. An adaptive kriging surrogate modeling is constructed to approximate the function/surface with structural uncertainties considered. The performance of the surrogate model is improved by adding support points and then evaluated by the overall accuracy validation and local error check. A numerical example demonstrating the feasibility of the surrogate modeling for the limit capacity of the transmission tower under winds is presented. Finally, a fragility assessment concerning a practical transmission line and towers subjected to typhoons is accomplished using the established limit capacity model of the tower.

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“…To model quantitative features, we use conventional Gaussian distributions as within-cluster density functions. We apply design proposed in [45]. Each cluster is generated from a Gaussian distribution whose covariance matrix is diagonal with diagonal values uniformly random in the range [0.05, 0.1]-they specify the cluster's spread.…”

Section: Generating Quantitative Featuresmentioning

confidence: 99%

“…The closer the value of ARI to unity, the better the match between the two partitions; ARI = 1.0 shows that S = T. If one of the partitions consists of just one part, the set I itself, then ARI = 0. Cases at which ARI is negative may occur too; but these authors have observed them only at specially defined, 'dual', pairs of partitions (see in [45]).…”

Section: Evaluation Criterionmentioning

confidence: 99%

Least-squares community extraction in feature-rich networks using similarity data

Shalileh

Mirkin

2021

PLoS ONE

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We explore a doubly-greedy approach to the issue of community detection in feature-rich networks. According to this approach, both the network and feature data are straightforwardly recovered from the underlying unknown non-overlapping communities, supplied with a center in the feature space and intensity weight(s) over the network each. Our least-squares additive criterion allows us to search for communities one-by-one and to find each community by adding entities one by one. A focus of this paper is that the feature-space data part is converted into a similarity matrix format. The similarity/link values can be used in either of two modes: (a) as measured in the same scale so that one may can meaningfully compare and sum similarity values across the entire similarity matrix (summability mode), and (b) similarity values in one column should not be compared with the values in other columns (nonsummability mode). The two input matrices and two modes lead us to developing four different Iterative Community Extraction from Similarity data (ICESi) algorithms, which determine the number of communities automatically. Our experiments at real-world and synthetic datasets show that these algorithms are valid and competitive.

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Bisecting K-Means and 1D Projection Divisive Clustering: A Unified Framework and Experimental Comparison

Cited by 21 publications

References 26 publications

The variance of the adjusted Rand index.

The variance of the adjusted Rand index.

Wind-Resistant Capacity Modeling for Electric Transmission Line Towers Using Kriging Surrogates and Its Application to Structural Fragility

Least-squares community extraction in feature-rich networks using similarity data

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