18,900 research outputs found
Clustering South African households based on their asset status using latent variable models
The Agincourt Health and Demographic Surveillance System has since 2001
conducted a biannual household asset survey in order to quantify household
socio-economic status (SES) in a rural population living in northeast South
Africa. The survey contains binary, ordinal and nominal items. In the absence
of income or expenditure data, the SES landscape in the study population is
explored and described by clustering the households into homogeneous groups
based on their asset status. A model-based approach to clustering the Agincourt
households, based on latent variable models, is proposed. In the case of
modeling binary or ordinal items, item response theory models are employed. For
nominal survey items, a factor analysis model, similar in nature to a
multinomial probit model, is used. Both model types have an underlying latent
variable structure - this similarity is exploited and the models are combined
to produce a hybrid model capable of handling mixed data types. Further, a
mixture of the hybrid models is considered to provide clustering capabilities
within the context of mixed binary, ordinal and nominal response data. The
proposed model is termed a mixture of factor analyzers for mixed data (MFA-MD).
The MFA-MD model is applied to the survey data to cluster the Agincourt
households into homogeneous groups. The model is estimated within the Bayesian
paradigm, using a Markov chain Monte Carlo algorithm. Intuitive groupings
result, providing insight to the different socio-economic strata within the
Agincourt region.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS726 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
EM Algorithms for Weighted-Data Clustering with Application to Audio-Visual Scene Analysis
Data clustering has received a lot of attention and numerous methods,
algorithms and software packages are available. Among these techniques,
parametric finite-mixture models play a central role due to their interesting
mathematical properties and to the existence of maximum-likelihood estimators
based on expectation-maximization (EM). In this paper we propose a new mixture
model that associates a weight with each observed point. We introduce the
weighted-data Gaussian mixture and we derive two EM algorithms. The first one
considers a fixed weight for each observation. The second one treats each
weight as a random variable following a gamma distribution. We propose a model
selection method based on a minimum message length criterion, provide a weight
initialization strategy, and validate the proposed algorithms by comparing them
with several state of the art parametric and non-parametric clustering
techniques. We also demonstrate the effectiveness and robustness of the
proposed clustering technique in the presence of heterogeneous data, namely
audio-visual scene analysis.Comment: 14 pages, 4 figures, 4 table
Model-based approach for household clustering with mixed scale variables
The Ministry of Social Development in Mexico is in charge of creating and assigning social programmes targeting specific needs in the population for the improvement of the quality of life. To better target the social programmes, the Ministry is aimed to find clusters of households with the same needs based on demographic characteristics as well as poverty conditions of the household. Available data consists of continuous, ordinal, and nominal variables, all of which come from a non-i.i.d complex design survey sample. We propose a Bayesian nonparametric mixture model that jointly models a set of latent variables, as in an underlying variable response approach, associated to the observed mixed scale data and accommodates for the different sampling probabilities. The performance of the model is assessed via simulated data. A full analysis of socio-economic conditions in households in the Mexican State of Mexico is presented
Model Based Clustering for Mixed Data: clustMD
A model based clustering procedure for data of mixed type, clustMD, is
developed using a latent variable model. It is proposed that a latent variable,
following a mixture of Gaussian distributions, generates the observed data of
mixed type. The observed data may be any combination of continuous, binary,
ordinal or nominal variables. clustMD employs a parsimonious covariance
structure for the latent variables, leading to a suite of six clustering models
that vary in complexity and provide an elegant and unified approach to
clustering mixed data. An expectation maximisation (EM) algorithm is used to
estimate clustMD; in the presence of nominal data a Monte Carlo EM algorithm is
required. The clustMD model is illustrated by clustering simulated mixed type
data and prostate cancer patients, on whom mixed data have been recorded
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