Mixture Model-based Approach Research Articles

Clustering Vibration Data Using a Temporally Coherent Expectation Maximization Approach

The estimation of the ground surface is essential for a mobile robot's safe traversal in an unknown environment. As a first step, terrain sections which exhibit similar features can be clustered together for establishing a broad structure of the underlying environment. In this work, we focus on an unsupervised learning approach to segment different terrain types according to the clustering of acquired vibration signals. We propose a Gaussian mixture model-based clustering approach taking the inherent temporal dependencies between consecutive measurements into account. Therefore, we combine the expectation maximization algorithm (EM) with the probabilistic framework of a Bayes filter. While the E-step of the EM algorithm determines the probability of each measurement to belong to a certain cluster, the Bayes technique then filters these probabilities over time for their later use in the M-step of the EM algorithm. In this context, time relates to the sequence in which the measurements occur during the robot traversal. The evaluation using data collected from our RWI ATRV-Jr robot shows that our approach generates stable models for a variety of robot driving speeds even in situations of high-frequency terrain changes.

Terrain Optimized Nonholonomic Following of Vehicle Tracks

The estimation of the ground surface is essential for a mobile robot's safe traversal in an unknown environment. As a first step, terrain sections which exhibit similar features can be clustered together for establishing a broad structure of the underlying environment. In this work, we focus on an unsupervised learning approach to segment different terrain types according to the clustering of acquired vibration signals. We propose a Gaussian mixture model-based clustering approach taking the inherent temporal dependencies between consecutive measurements into account. Therefore, we combine the expectation maximization algorithm (EM) with the probabilistic framework of a Bayes filter. While the E-step of the EM algorithm determines the probability of each measurement to belong to a certain cluster, the Bayes technique then filters these probabilities over time for their later use in the M-step of the EM algorithm. In this context, time relates to the sequence in which the measurements occur during the robot traversal. The evaluation using data collected from our RWI ATRV-Jr robot shows that our approach generates stable models for a variety of robot driving speeds even in situations of high-frequency terrain changes.

A mixture model-based approach to the clustering of exponential repeated data

The analysis of finite mixture models for exponential repeated data is considered. The mixture components correspond to different unknown groups of the statistical units. Dependency and variability of repeated data are taken into account through random effects. For each component, an exponential mixed model is thus defined. When considering parameter estimation in this mixture of exponential mixed models, the EM-algorithm cannot be directly used since the marginal distribution of each mixture component cannot be analytically derived. In this paper, we propose two parameter estimation methods. The first one uses a linearisation specific to the exponential distribution hypothesis within each component. The second approach uses a Metropolis–Hastings algorithm as a building block of a general MCEM-algorithm.

Robust Cluster Analysis via Mixture Models

Finite mixture models are being increasingly used to model the distributions of a wide variety of random phenomena and to cluster data sets. In this paper, we focus on the use of normal mixture models to cluster data sets of continuous multivariate data. As normality based methods of estimation are not robust, we review the use of t component distributions. With the t mixture model-based approach, the normal distribution for each component in the mixture model is embedded in a wider class of elliptically symmetric distributions with an additional parameter called the degrees of freedom. The advantage of the t mixture model is that, although the number of outliers needed for breakdown is almost the same as with the normal mixture model, the outliers have to be much larger. We also consider the use of the t distribution for the robust clustering of high-dimensional data via mixtures of factor analyzers. The latter enable a mixture model to be fitted to data which have high dimension relative to the number of data points to be clustered.

On a resampling approach for tests on the number of clusters with mixture model-based clustering of tissue samples

We consider the problem of assessing the number of clusters in a limited number of tissue samples containing gene expressions for possibly several thousands of genes. It is proposed to use a normal mixture model-based approach to the clustering of the tissue samples. One advantage of this approach is that the question on the number of clusters in the data can be formulated in terms of a test on the smallest number of components in the mixture model compatible with the data. This test can be carried out on the basis of the likelihood ratio test statistic, using resampling to assess its null distribution. The effectiveness of this approach is demonstrated on simulated data and on some microarray datasets, as considered previously in the bioinformatics literature.

A mixture model-based approach to the classification of ecological habitats using Forest Inventory and Analysis data

A Gaussian mixture model (GMM) is used to classify Forest Inventory and Analysis (FIA) plots into six ecological habitats in the northeastern USA. The GMM approach captures intra-class variation by modeling each habitat class as a mixture of subclasses of Gaussian distributions. The classification is achieved based on the appropriate posterior probability. The GMM classifier outperforms a traditional statistical method (i.e., linear discriminant analysis or LDA), and produces similar overall accuracy rates to a commonly used neural network model (i.e., multi-layer perceptrons or MLP). For the classifications of individual ecological habitats, however, MLP produces better (or same) producers' classification accuracies for five of the six ecological habitats than does GMM. But the GMM's accuracy rates are more consistent (92%–97%) across the six ecological habitats than those of the MLP model (82%–99%). This study shows that GMM offers an attractive alternative for modeling the complex stand structure and relationships between variables in mixed-species forest stands.

On a resampling approach for tests on the number of clusters with mixture model-based clustering of tissue samples

We consider the problem of assessing the number of clusters in a limited number of tissue samples containing gene expressions for possibly several thousands of genes. It is proposed to use a normal mixture model-based approach to the clustering of the tissue samples. One advantage of this approach is that the question on the number of clusters in the data can be formulated in terms of a test on the smallest number of components in the mixture model compatible with the data. This test can be carried out on the basis of the likelihood ratio test statistic, using resampling to assess its null distribution. The effectiveness of this approach is demonstrated on simulated data and on some microarray datasets, as considered previously in the bioinformatics literature.

Clustering gene-expression data with repeated measurements

Algorithms that take advantage of repeated measurements yield more accurate and more stable clusters.

A mixture model-based approach to the clustering of microarray expression data.

This paper introduces the software EMMIX-GENE that has been developed for the specific purpose of a model-based approach to the clustering of microarray expression data, in particular, of tissue samples on a very large number of genes. The latter is a nonstandard problem in parametric cluster analysis because the dimension of the feature space (the number of genes) is typically much greater than the number of tissues. A feasible approach is provided by first selecting a subset of the genes relevant for the clustering of the tissue samples by fitting mixtures of t distributions to rank the genes in order of increasing size of the likelihood ratio statistic for the test of one versus two components in the mixture model. The imposition of a threshold on the likelihood ratio statistic used in conjunction with a threshold on the size of a cluster allows the selection of a relevant set of genes. However, even this reduced set of genes will usually be too large for a normal mixture model to be fitted directly to the tissues, and so the use of mixtures of factor analyzers is exploited to reduce effectively the dimension of the feature space of genes. The usefulness of the EMMIX-GENE approach for the clustering of tissue samples is demonstrated on two well-known data sets on colon and leukaemia tissues. For both data sets, relevant subsets of the genes are able to be selected that reveal interesting clusterings of the tissues that are either consistent with the external classification of the tissues or with background and biological knowledge of these sets. EMMIX-GENE is available at http://www.maths.uq.edu.au/~gjm/emmix-gene/

Mixture modelling of gene expression data from microarray experiments.

Hierarchical clustering is one of the major analytical tools for gene expression data from microarray experiments. A major problem in the interpretation of the output from these procedures is assessing the reliability of the clustering results. We address this issue by developing a mixture model-based approach for the analysis of microarray data. Within this framework, we present novel algorithms for clustering genes and samples. One of the byproducts of our method is a probabilistic measure for the number of true clusters in the data. The proposed methods are illustrated by application to microarray datasets from two cancer studies; one in which malignant melanoma is profiled (Bittner et al., Nature, 406, 536-540, 2000), and the other in which prostate cancer is profiled (Dhanasekaran et al., 2001, submitted).