A validation study of a variable weighting algorithm for cluster analysis

Milligan, Glenn W.

doi:10.1007/bf01908588

Cited by 72 publications

(57 citation statements)

References 22 publications

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“…As pointed out by several authors (e.g., Fowlkes, Gnanadesikan, and Kettering 1988;Milligan 1989;Gnanadesikan, Kettering, and Tao 1995;Brusco and Cradit 2001), the inclusion of unnecessary covariates could complicate or even mask the recovery of the clusters. Common approaches to mitigating the effect of noisy variables or identifying those that define true cluster structure involve differentially weighting the covariates or selecting the discriminating ones.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Variable Selection in Clustering High-Dimensional Data

Tadesse

Sha

Vannucci

2005

Journal of the American Statistical Association

215

219

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Over the last decade, technological advances have generated an explosion of data with substantially smaller sample size relative to the number of covariates ( p n). A common goal in the analysis of such data involves uncovering the group structure of the observations and identifying the discriminating variables. In this article we propose a methodology for addressing these problems simultaneously. Given a set of variables, we formulate the clustering problem in terms of a multivariate normal mixture model with an unknown number of components and use the reversible-jump Markov chain Monte Carlo technique to define a sampler that moves between different dimensional spaces. We handle the problem of selecting a few predictors among the prohibitively vast number of variable subsets by introducing a binary exclusion/inclusion latent vector, which gets updated via stochastic search techniques. We specify conjugate priors and exploit the conjugacy by integrating out some of the parameters. We describe strategies for posterior inference and explore the performance of the methodology with simulated and real datasets.

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Section: Introductionmentioning

confidence: 99%

Bayesian Variable Selection in Clustering High-Dimensional Data

Tadesse

Sha

Vannucci

2005

Journal of the American Statistical Association

215

219

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“…The method is computationally intensive, with the amount of computation increasing with the square of the number of variables. Milligan (1989) examined the use of a variable weighting procedure (De Soete, 1986, 1988 to deal with irrelevant variables. The method selects weights such that the distances computed from the weighted variables maximally satisfy the ultrametric inequality:…”

Section: Methods To Deal With Irrelevant Variablesmentioning

confidence: 99%

Variable Screening for Cluster Analysis

Donoghue

1994

ETS Research Report Series

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Inclusion of irrelevant variables in a cluster analysis adversely affects subgroup recovery. This paper examines using moment-based statistics to screen variables; only variables which pass the screening are then used in clustering. Normal mixtures are analytically shown often to possess negative kurtosis. Two related measures, m and coefficient of bimodality b, are also 'examined.A Monte Carlo study compared the screening measures to no selection, De Soete's (1988) ultrametric weights, and Fowlkes, Gnanadesikan, and Kettenring's (1988) forward selection procedure. Screening based on kurtosis degraded recovery and is not recommended.In contrast, screening on m or on b improved recovery over both no selection and forward selection, and screening performed as well as ultrametric weights. Combining screening with ultrametric weights performed extremely well. All methods were found to be somewhat sensitive to other types of error.Screening variables appears a viable alternative to both ultrametric weights and forward selection. The potential advantages and disadvantages of screening are considered.

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“…An overview of the clustering analysis critical steps is presented in [5]. In cluster analysis, a fundamental problem is to determine the best number of clusters.…”

Section: Related Workmentioning

confidence: 99%

Increasing the Adaptivity of an Intelligent Tutoring System with Educational Data Mining: A System Overview

Jugo

Kovačić

Slavuj

2016

Int. J. Emerg. Technol. Learn.

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Abstract-Intelligent Tutoring Systems (ITSs) are inherently adaptive e-learning systems usually created for teaching well-defined domains (e.g., mathematics). Their objective is to guide the student towards a predefined goal such as completing a lesson, task, or mastering a skill. Defining goals and guiding students is more complex in ill-defined domains where the expert defines the model of the knowledge domain or the students have freedom to follow their own path through it. In this paper we present an overview of our system's architecture that integrates the ITS with data mining tools and performs a number of educational data mining processes to increase the adaptivity and, consequently, the efficiency of the ITS.Index Terms-e-learning, intelligent tutoring systems, educational data mining, adaptive e-learning.

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A validation study of a variable weighting algorithm for cluster analysis

Abstract: Ultrametric trees, Hierarchical clustering, Euclidean distances,

Cited by 72 publications

References 22 publications

Bayesian Variable Selection in Clustering High-Dimensional Data

Bayesian Variable Selection in Clustering High-Dimensional Data

Variable Screening for Cluster Analysis

Increasing the Adaptivity of an Intelligent Tutoring System with Educational Data Mining: A System Overview

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