Category: Journal of Classification

Abstract

Normal cluster-weighted models constitute a modern approach to linear regression which simultaneously perform model-based cluster analysis and multivariate linear regression analysis with random quantitative regressors. Robustified models have been recently developed, based on the use of the contaminated normal distribution, which can manage the presence of mildly atypical observations. A more flexible class of contaminated normal linear cluster-weighted models is specified here, in which the researcher is free to use a different vector of regressors for each response. The novel class also includes parsimonious models, where parsimony is attained by imposing suitable constraints on the component-covariance matrices of either the responses or the regressors. Identifiability conditions are illustrated and discussed. An expectation-conditional maximisation algorithm is provided for the maximum likelihood estimation of the model parameters. The effectiveness and usefulness of the proposed models are shown through the analysis of simulated and real datasets.

Abstract

A family of parsimonious contaminated shifted asymmetric Laplace mixtures is developed for unsupervised classification of asymmetric clusters in the presence of outliers and noise. A series of constraints are applied to a modified factor analyzer structure of the component scale matrices, yielding a family of twelve models. Application of the modified factor analyzer structure and these parsimonious constraints makes these models effective for the analysis of high-dimensional data by reducing the number of free parameters that need to be estimated. A variant of the expectation-maximization algorithm is developed for parameter estimation with convergence issues being discussed and addressed. Popular model selection criteria like the Bayesian information criterion and the integrated complete likelihood (ICL) are utilized, and a novel modification to the ICL is also considered. Through a series of simulation studies and real data analyses, that includes comparisons to well-established methods, we demonstrate the improvements in classification performance found using the proposed family of models.

Abstract

Nowadays, an increasing number of problems involve data with one infinite continuous dimension known as functional data. In this paper, we introduce the funLOCI algorithm, which enables the identification of functional local clusters or functional loci, i.e, subsets or groups of curves that exhibit similar behavior across the same continuous subset of the domain. The definition of functional local clusters incorporates ideas from multivariate and functional clustering and biclustering and is based on an additive model that takes into account the shape of the curves. funLOCI is a multi-step algorithm that relies on hierarchical clustering and a functional version of the mean squared residue score to identify and validate candidate loci. Subsequently, all the results are collected and ordered in a post-processing step. To evaluate our algorithm performance, we conduct extensive simulations and compare it with other recently proposed algorithms in the literature. Furthermore, we apply funLOCI to a real-data case regarding inner carotid arteries.

Abstract

Joint analysis with clustering and structural equation modeling is one of the most popular approaches to analyzing heterogeneous data. The methods involved in this approach estimate a path diagram of the same shape for each cluster and interpret the clusters according to the magnitude of the coefficients. However, these methods have problems with difficulty in interpreting the coefficients when the number of clusters and/or paths increases and are unable to deal with any situation where the path diagram for each cluster is different. To tackle these problems, we propose two methods for simplifying the path structure and facilitating interpretation by estimating a different form of path diagram for each cluster using sparse estimation. The proposed methods and related methods are compared using numerical simulation and real data examples. The proposed methods are superior to the existing methods in terms of both fitting and interpretation.

Abstract

In many applications there is ambiguity about which (if any) of a finite number N of hypotheses that best fits an observation. It is of interest then to possibly output a whole set of categories, that is, a scenario where the size of the classified set of categories ranges from 0 to N. Empty sets correspond to an outlier, sets of size 1 represent a firm decision that singles out one hypothesis, sets of size N correspond to a rejection to classify, whereas sets of sizes \(2,\ldots ,N-1\) represent a partial rejection to classify, where some hypotheses are excluded from further analysis. In this paper, we review and unify several proposed methods of Bayesian set-valued classification, where the objective is to find the optimal Bayesian classifier that maximizes the expected reward. We study a large class of reward functions with rewards for sets that include the true category, whereas additive or multiplicative penalties are incurred for sets depending on their size. For models with one homogeneous block of hypotheses, we provide general expressions for the accompanying Bayesian classifier, several of which extend previous results in the literature. Then, we derive novel results for the more general setting when hypotheses are partitioned into blocks, where ambiguity within and between blocks are of different severity. We also discuss how well-known methods of classification, such as conformal prediction, indifference zones, and hierarchical classification, fit into our framework. Finally, set-valued classification is illustrated using an ornithological data set, with taxa partitioned into blocks and parameters estimated using MCMC. The associated reward function’s tuning parameters are chosen through cross-validation.

Abstract

A dataset may exhibit multiple class labels for each observation; sometimes, these class labels manifest in a hierarchical structure. A textbook analogy would be that a book can be labelled as statistics as well as the encompassing label of non-fiction. To capture this behaviour in a model-based clustering context, we describe a model formulation and estimation procedure for performing clustering with nested Gaussian clusters in orthogonal intrinsic variable subspaces. We elucidate a two-stage clustering model, whereby the observed manifest variables are assumed to be a rotation of intrinsic primary and secondary clustering subspaces with additional noise subspaces. In a hierarchical sense, secondary clusters are presumed to be subclusters of primary clusters and so share Gaussian cluster parameters in the primary cluster subspace. An estimation procedure using the expectation-maximization algorithm is provided, with model selection via Bayesian information criterion. Real-world datasets are evaluated under the proposed model.

Abstract

The human microbiome plays an important role in human health and disease status. Next-generating sequencing technologies allow for quantifying the composition of the human microbiome. Clustering these microbiome data can provide valuable information by identifying underlying patterns across samples. Recently, Fang and Subedi (2023) proposed a logistic normal multinomial mixture model (LNM-MM) for clustering microbiome data. As microbiome data tends to be high dimensional, here, we develop a family of logistic normal multinomial factor analyzers (LNM-FA) by incorporating a factor analyzer structure in the LNM-MM. This family of models is more suitable for high-dimensional data as the number of free parameters in LNM-FA can be greatly reduced by assuming that the number of latent factors is small. Parameter estimation is done using a computationally efficient variant of the alternating expectation conditional maximization algorithm that utilizes variational Gaussian approximations. The proposed method is illustrated using simulated and real datasets.

Abstract

Model-based clustering tackles the task of uncovering heterogeneity in a data set to extract valuable insights. Given the common presence of outliers in practice, robust methods for model-based clustering have been proposed. However, the use of many methods in this area becomes severely limited in applications where partially observed records are common since their existing frameworks often assume complete data only. Here, a mixture of multiple scaled contaminated normal (MSCN) distributions is extended using the expectation-conditional maximization (ECM) algorithm to accommodate data sets with values missing at random. The newly proposed extension preserves the mixture’s capability in yielding robust parameter estimates and performing automatic outlier detection separately for each principal component. In this fitting framework, the MSCN marginal density is approximated using the inversion formula for the characteristic function. Extensive simulation studies involving incomplete data sets with outliers are conducted to evaluate parameter estimates and to compare clustering performance and outlier detection of our model to other mixtures.