10,170 research outputs found
Rao\u27s Quadratic Entropy and Some New Applications
Many problems in statistical inference are formulated as testing the diversity of populations. The entropy functions measure the similarity of a distribution function to the uniform distribution and hence can be used as a measure of diversity. Rao (1982a) proposed the concept of quadratic entropy. Its concavity property makes the decomposition similar to ANOVA for categorical data feasible. In this thesis, after reviewing the properties and providing a modification to quadratic entropy, various applications of quadratic entropy are explored. First, analysis of quadratic entropy with the suggested modification to analyze the contingency table data is explored. Then its application to ecological biodiversity is established by constructing practically equivalent confidence intervals. The methods are applied on a real dinosaur diversity data set and simulation experiments are performed to study the validity of the intervals. Quadratic entropy is also used for clustering multinomial data. Another application of quadratic entropy that is provided here is to test the association of two categorical variables with multiple responses. Finally, the gene expression data inspires another application of quadratic entropy in analyzing large scale data, where a hill-climbing type iterative algorithm is developed based on a new minimum quadratic entropy criterion. The algorithm is illustrated on both simulated and real data
Mutual information based clustering of market basket data for profiling users
Attraction and commercial success of web sites depend heavily on the additional values visitors may find. Here, individual, automatically obtained and maintained user profiles are the key for user satisfaction. This contribution shows for the example of a cooking information site how user profiles might be obtained using category information provided by cooking recipes. It is shown that metrical distance functions and standard clustering procedures lead to erroneous results. Instead, we propose a new mutual information based clustering approach and outline its implications for the example of user profiling
Clustering and variable selection for categorical multivariate data
This article investigates unsupervised classification techniques for
categorical multivariate data. The study employs multivariate multinomial
mixture modeling, which is a type of model particularly applicable to
multilocus genotypic data. A model selection procedure is used to
simultaneously select the number of components and the relevant variables. A
non-asymptotic oracle inequality is obtained, leading to the proposal of a new
penalized maximum likelihood criterion. The selected model proves to be
asymptotically consistent under weak assumptions on the true probability
underlying the observations. The main theoretical result obtained in this study
suggests a penalty function defined to within a multiplicative parameter. In
practice, the data-driven calibration of the penalty function is made possible
by slope heuristics. Based on simulated data, this procedure is found to
improve the performance of the selection procedure with respect to classical
criteria such as BIC and AIC. The new criterion provides an answer to the
question "Which criterion for which sample size?" Examples of real dataset
applications are also provided
Evidence Transfer for Improving Clustering Tasks Using External Categorical Evidence
In this paper we introduce evidence transfer for clustering, a deep learning
method that can incrementally manipulate the latent representations of an
autoencoder, according to external categorical evidence, in order to improve a
clustering outcome. By evidence transfer we define the process by which the
categorical outcome of an external, auxiliary task is exploited to improve a
primary task, in this case representation learning for clustering. Our proposed
method makes no assumptions regarding the categorical evidence presented, nor
the structure of the latent space. We compare our method, against the baseline
solution by performing k-means clustering before and after its deployment.
Experiments with three different kinds of evidence show that our method
effectively manipulates the latent representations when introduced with real
corresponding evidence, while remaining robust when presented with low quality
evidence
Enhancing the selection of a model-based clustering with external qualitative variables
In cluster analysis, it can be useful to interpret the partition built from
the data in the light of external categorical variables which were not directly
involved to cluster the data. An approach is proposed in the model-based
clustering context to select a model and a number of clusters which both fit
the data well and take advantage of the potential illustrative ability of the
external variables. This approach makes use of the integrated joint likelihood
of the data and the partitions at hand, namely the model-based partition and
the partitions associated to the external variables. It is noteworthy that each
mixture model is fitted by the maximum likelihood methodology to the data,
excluding the external variables which are used to select a relevant mixture
model only. Numerical experiments illustrate the promising behaviour of the
derived criterion
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