A model-based clustering approach assumes that each component or some combination of components corresponds to a cluster. When fitting the model in (1), the main task is to decide the number of components G. Titterington et al. (1985), McLachan and Basford (1988) and McLachan and Peel (2002) extensively reviewed mixture models, with a focus on Gaussian mixture models. Fraley and Raftery (2002) presented a review of work on Gaussian mixtures with a focus on clustering, discriminant analysis, and density estimation. They discuss a family of Gaussian mixture models, which arises from the imposition of constraints upon an eigen-decomposition of the component covariance structure. The family of mixture models they discuss, known as MCLUST, is actually a subset of the Gaussian parsimonious clustering models (GPCMs) of Celeux and Govaert (1995). When using the MCLUST models, one must choose the appropriate member of the family, i.e., the covariance structure, in addition to deciding the number of components G. Ghahramani and Hinton (1997) introduced a mixture of factor analyzers model, which was further developed by Tipping and Bishop (1999) and McLachlan and Peel (2000).

Given the limited performance of 2D cellular automata in terms of space when the number of documents increases and in terms of visualization clusters, our motivation was to experiment these cellular automata by increasing the size to view the impact of size on quality of results. The representation of textual data was carried out by a vector model whose components are derived from the overall balancing of the used corpus Term Frequency - Inverse Document Frequency (TF - IDF).The WorldNet thesaurus has been used to address the problem of the lemmatization of the words because the representation used in this study is that of the bags of words. Another independent method of the language was used to represent textual records is that of the n-grams. Several measures of similarity have been tested. To validate the classification we have used two measures of assessment based on the recall and precision (f-measure and entropy). The results are promising and confirm the idea to increase the dimension to the problem of the spatiality of the classes. The results obtained in terms of purity class (ie the minimum value of entropy) shows that the number of documents over longer believes the results are better for 3D cellular automata, which was not obvious to 2D the dimension. In terms of spatial navigation, cellular automata provide very good 3D performance visualization than 2D cellular automata.

A basic assumption of statistical learning theory is that train and test data are drawn from the same underlying distribution. Unfortunately, this assumption doesn't hold in many applications. Instead, ample labeled data might exist in a particular `source' domain while inference is needed in another, `target' domain. Domain adaptation methods leverage labeled data from both domains to improve classification on unseen data in the target domain. In this work we survey domain transfer learning methods for various application domains with focus on recent work in Computer Vision.

Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input variables of the model. When the statistics of the output event are known, these input variables have to be chosen in a specific way for the output to have the prescribed statistics. Because the probability distribution of the input random variables is not directly known but dictated implicitly by the statistics of the output random variables, this problem is usually intractable for classical sampling methods. Based on Markov Chain Monte Carlo we propose a novel method to sample random inputs to such models by introducing a modification to the standard Metropolis-Hastings algorithm. As an example we consider a system described by a stochastic differential equation (sde) and demonstrate how sample paths of a random process satisfying this sde can be generated with our technique.

Data clustering has various applications in a wide variety of fields ranging from social and biological sciences, to business, statistics, information retrieval, machine learning and data mining. Clustering refers to the process of grouping data based only on information found in the data which describes its characteristics and relationships. Although humans are generally very good at discovering patterns and classifying objects, clustering algorithms are able to discern similarities in data even when humans are not [6]. The main focus of our research has been document clustering, but we will demonstrate that our methods also work nicely on scientific data. In this paper, we propose an adaptation of the clustering algorithm known as Principal Direction Divisive Partitioning (PDDP) developed by Daniel Boley in [2] which is based Principal Components Analysis (PCA). PCA involves the eigenvector decomposition of a data covariance matrix, or equivalently a singular value decomposition (SVD) of a data matrix after mean centering. The name of our adaptation, Principal Direction Gap Partitioning (PDGP), borrows most of its name from PDDP as it follows many of the same steps that PDDP follows. The word "gap" replaces the word "divisive" in reference to how the algorithm splits data along natural gaps at each step. This concept will be further developed in the following sections, but it should be noted that PDGP is still a divisive algorithm in the same way that PDDP is.

Spectral clustering is a now well-known method for clustering which utilizes the spectrum of the data similarity matrix to perform this separation. Since the method relies on solving an eigenvector problem, it is computationally expensive for large datasets. T o overcome this constraint, approximation methods have been developed which aim to reduce running time while maintaining accurate classification. In this article, we summarize and experimentally evaluate several approximation methods for spectral clustering. From an applications standpoint, we employ spectral clustering to solve the so-called attrition problem, where one aims to identify from a set of employees those who are likely to voluntarily leave the company from those who are not. Our study sheds light on the empirical performance of existing approximate spectral clustering methods and shows the applicability of these methods in an important business optimization related problem. Clustering or cluster analysis addresses the problem of separating a set of objects into clusters so that objects within each cluster are more similar to each other than to objects in different clusters. The clustering problem has become ubiquitous in data mining and machine learning with applications ranging from image processing to bioinformatics. What one means by clustering, and the type of clustering desired is application dependent. For example, one may wish to segment an image such as that in Figure 1 (a)-(b). In medical imaging, segmentation may aid in the identification of tumors, assist physicians in surgery and separate anatomical structures. Computer vision applications utilize clustering methods to identify foreign objects in surveillance images or detect road signs for computer piloted vehicles. In statistical analysis, the objects to be clustered may represent individuals in a population viewed as a vector of personal attributes. For example, we will consider the attrition problem: from a dataset of employees one wishes to identify which cluster of employees are likely to voluntarily leave the company and which are not.

Network sampling is integral to the analysis of social, information, and biological networks. Since many real-world networks are massive in size, continuously evolving, and/or distributed in nature, the network structure is often sampled in order to facilitate study. For these reasons, a more thorough and complete understanding of network sampling is critical to support the field of network science. In this paper, we outline a framework for the general problem of network sampling, by highlighting the different objectives, population and units of interest, and classes of network sampling methods. In addition, we propose a spectrum of computational models for network sampling methods, ranging from the traditionally studied model based on the assumption of a static domain to a more challenging model that is appropriate for streaming domains. We design a family of sampling methods based on the concept of graph induction that generalize across the full spectrum of computational models (from static to streaming) while efficiently preserving many of the topological properties of the input graphs. Furthermore, we demonstrate how traditional static sampling algorithms can be modified for graph streams for each of the three main classes of sampling methods: node, edge, and topology-based sampling. Our experimental results indicate that our proposed family of sampling methods more accurately preserves the underlying properties of the graph for both static and streaming graphs. Finally, we study the impact of network sampling algorithms on the parameter estimation and performance evaluation of relational classification algorithms.

Ultrahigh-dimensional variable selection plays an increasingly important role in contemporary scientific discoveries and statistical research. Among others, Fan and Lv [J. R. Stat. Soc. Ser. B Stat. Methodol. 70 (2008) 849-911] propose an independent screening framework by ranking the marginal correlations. They showed that the correlation ranking procedure possesses a sure independence screening property within the context of the linear model with Gaussian covariates and responses. In this paper, we propose a more general version of the independent learning with ranking the maximum marginal likelihood estimates or the maximum marginal likelihood itself in generalized linear models. We show that the proposed methods, with Fan and Lv [J. R. Stat. Soc. Ser. B Stat. Methodol. 70 (2008) 849-911] as a very special case, also possess the sure screening property with vanishing false selection rate. The conditions under which the independence learning possesses a sure screening is surprisingly simple. This justifies the applicability of such a simple method in a wide spectrum. We quantify explicitly the extent to which the dimensionality can be reduced by independence screening, which depends on the interactions of the covariance matrix of covariates and true parameters. Simulation studies are used to illustrate the utility of the proposed approaches. In addition, we establish an exponential inequality for the quasi-maximum likelihood estimator which is useful for high-dimensional statistical learning.

A comparative study of the application of Gaussian Mixture Model (GMM) and Radial Basis Function (RBF) in biometric recognition of voice has been carried out and presented. The application of machine learning techniques to biometric authentication and recognition problems has gained a widespread acceptance. In this research, a GMM model was trained, using Expectation Maximization (EM) algorithm, on a dataset containing 10 classes of vowels and the model was used to predict the appropriate classes using a validation dataset. For experimental validity, the model was compared to the performance of two different versions of RBF model using the same learning and validation datasets. The results showed very close recognition accuracy between the GMM and the standard RBF model, but with GMM performing better than the standard RBF by less than 1% and the two models outperformed similar models reported in literature. The DTREG version of RBF outperformed the other two models by producing 94.8% recognition accuracy. In terms of recognition time, the standard RBF was found to be the fastest among the three models.

Unsupervised models can provide supplementary soft constraints to help classify new target data under the assumption that similar objects in the target set are more likely to share the same class label. Such models can also help detect possible differences between training and target distributions, which is useful in applications where concept drift may take place. This paper describes a Bayesian framework that takes as input class labels from existing classifiers (designed based on labeled data from the source domain), as well as cluster labels from a cluster ensemble operating solely on the target data to be classified, and yields a consensus labeling of the target data. This framework is particularly useful when the statistics of the target data drift or change from those of the training data. We also show that the proposed framework is privacy-aware and allows performing distributed learning when data/models have sharing restrictions. Experiments show that our framework can yield superior results to those provided by applying classifier ensembles only.