Statisticians typically estimate the parameters of latent class and latent profile models using the Expectation-Maximization algorithm. This paper proposes an alternative two-stage approach to model fitting. The first stage uses the modified k-means and hierarchical clustering algorithms to identify the latent classes that best satisfy the conditional independence assumption underlying the latent variable model. The second stage then uses mixture modeling treating the class membership as known. The proposed approach is theoretically justifiable, directly checks the conditional independence assumption, and converges much faster than the full likelihood approach when analyzing high-dimensional data. This paper also develops a new classification rule based on latent variable models. The proposed classification procedure reduces the dimensionality of measured data and explicitly recognizes the heterogeneous nature of the complex disease, which makes it perfect for analyzing high-throughput genomic data. Simulation studies and real data analysis demonstrate the advantages of the proposed method.

One of the main problems in cluster analysis is that of determining the number of groups in the data. In general, the approach taken depends on the cluster method used. For K-means, some of the most widely employed criteria are formulated in terms of the decomposition of the total point scatter, regarding a two-mode data set of N points in p dimensions, which are optimally arranged into K classes. This paper addresses the formulation of criteria to determine the number of clusters, in the general situation in which the available information for clustering is a one-mode $N\times N$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$N\times N$$\end{document} dissimilarity matrix describing the objects. In this framework, p and the coordinates of points are usually unknown, and the application of criteria originally formulated for two-mode data sets is dependent on their possible reformulation in the one-mode situation. The decomposition of the variability of the clustered objects is proposed in terms of the corresponding block-shaped partition of the dissimilarity matrix. Within-block and between-block dispersion values for the partitioned dissimilarity matrix are derived, and variance-based criteria are subsequently formulated in order to determine the number of groups in the data. A Monte Carlo experiment was carried out to study the performance of the proposed criteria. For simulated clustered points in p dimensions, greater efficiency in recovering the number of clusters is obtained when the criteria are calculated from the related Euclidean distances instead of the known two-mode data set, in general, for unequal-sized clusters and for low dimensionality situations. For simulated dissimilarity data sets, the proposed criteria always outperform the results obtained when these criteria are calculated from their original formulation, using dissimilarities instead of distances.

Given that a minor condition holds (e.g., the number of variables is greater than the number of clusters), a nontrivial lower bound for the sum-of-squares error criterion in K-means clustering is derived. By calculating the lower bound for several different situations, a method is developed to determine the adequacy of cluster solution based on the observed sum-of-squares error as compared to the minimum sum-of-squares error.

Several neural networks have been proposed in the general literature for pattern recognition and clustering, but little empirical comparison with traditional methods has been done. The results reported here compare neural networks using Kohonen learning with a traditional clustering method (K-means) in an experimental design using simulated data with known cluster solutions. Two types of neural networks were examined, both of which used unsupervised learning to perform the clustering. One used Kohonen learning with a conscience and the other used Kohonen learning without a conscience mechanism. The performance of these nets was examined with respect to changes in the number of attributes, the number of clusters, and the amount of error in the data. Generally, the K-means procedure had fewer points misclassified while the classification accuracy of neural networks worsened as the number of clusters in the data increased from two to five.

Dual scaling (DS) is a multivariate exploratory method equivalent to correspondence analysis when analysing contingency tables. However, for the analysis of rating data, different proposals appear in the DS and correspondence analysis literature. It is shown here that a peculiarity of the DS method can be exploited to detect differences in response styles. Response styles occur when respondents use rating scales differently for reasons not related to the questions, often biasing results. A spline-based constrained version of DS is devised which can detect the presence of four prominent types of response styles, and is extended to allow for multiple response styles. An alternating nonnegative least squares algorithm is devised for estimating the parameters. The new method is appraised both by simulation studies and an empirical application.

An extension of multiple correspondence analysis is proposed that takes into account cluster-level heterogeneity in respondents’ preferences/choices. The method involves combining multiple correspondence analysis and k-means in a unified framework. The former is used for uncovering a low-dimensional space of multivariate categorical variables while the latter is used for identifying relatively homogeneous clusters of respondents. The proposed method offers an integrated graphical display that provides information on cluster-based structures inherent in multivariate categorical data as well as the interdependencies among the data. An empirical application is presented which demonstrates the usefulness of the proposed method and how it compares to several extant approaches.

Minimization of the within-cluster sums of squares (WCSS) is one of the most important optimization criteria in cluster analysis. Although cluster analysis modules in commercial software packages typically use heuristic methods for this criterion, optimal approaches can be computationally feasible for problems of modest size. This paper presents a new branch-and-bound algorithm for minimizing WCSS. Algorithmic enhancements include an effective reordering of objects and a repetitive solution approach that precludes the need for splitting the data set, while maintaining strong bounds throughout the solution process. The new algorithm provided optimal solutions for problems with up to 240 objects and eight well-separated clusters. Poorly separated problems with no inherent cluster structure were optimally solved for up to 60 objects and six clusters. The repetitive branch-and-bound algorithm was also successfully applied to three empirical data sets from the classification literature.

In this article, we analyse the usefulness of multidimensional scaling in relation to performing K-means clustering on a dissimilarity matrix, when the dimensionality of the objects is unknown. In this situation, traditional algorithms cannot be used, and so K-means clustering procedures are being performed directly on the basis of the observed dissimilarity matrix. Furthermore, the application of criteria originally formulated for two-mode data sets to determine the number of clusters depends on their possible reformulation in a one-mode situation. The linear invariance property in K-means clustering for squared dissimilarities, together with the use of multidimensional scaling, is investigated to determine the cluster membership of the observations and to address the problem of selecting the number of clusters in K-means for a dissimilarity matrix. In particular, we analyse the performance of K-means clustering on the full dimensional scaling configuration and on the equivalently partitioned configuration related to a suitable translation of the squared dissimilarities. A Monte Carlo experiment is conducted in which the methodology examined is compared with the results obtained by procedures directly applicable to a dissimilarity matrix.

Under the European Union’s Solvency II regulations, insurance firms are required to use a one-year VaR (Value at Risk) approach. This involves a one-year projection of the balance sheet and requires sufficient capital to be solvent in 99.5% of outcomes. The Solvency II Internal Model risk calibrations require annual changes in market indices/term structure/transitions for the estimation of the risk distribution for each of the Internal Model risk drivers.

Transition and default risk are typically modelled using transition matrices. To model this risk requires a model of transition matrices and how these can change from year to year. In this paper, four such models have been investigated and compared to the raw data they are calibrated to. The models investigated are:

• A bootstrapping approach – sampling from an historical data set with replacement.

• The Vašíček model was calibrated using the Belkin approach.

• The K-means model – a new non-parametric model produced using the K-means clustering algorithm.

• A two-factor model – a new parametric model, using two factors (instead of a single factor with the Vašíček) to represent each matrix.

The models are compared in several ways:

1. 1. A principal components analysis (PCA) approach that compares how closely the models move compared to the raw data.

2. 2. A backtesting approach that compares how each model’s extreme percentile compares to regulatory backtesting requirements.

3. 3. A commentary on the amount of expert judgement in each model.

4. 4. Model simplicity and breadth of uses are also commented on.

Findings of bilingual participants outperforming their monolingual counterparts in executive functioning tasks have been repeatedly reported in the literature (Bialystok, 2017). However, uncontrolled factors or imperfectly matched samples might affect the reliability of these findings. This study aims to take into account a range of relevant variables in combination with innovative analyses to investigate the performance of one unstudied language group, Greek–English bilingual children in the north of England, compared to monolingual control groups. Our battery of executive function tasks taps into inhibition, updating and shifting. We use k-means nearest neighbour methods to match the groups and factor analysis to determine language proficiency. We find that bilinguals’ accuracy is on a par with their monolingual peers – however, they are faster in inhibition and working memory tasks. Our study provides strong evidence for the presence of a bilingual advantage in these domains, while making important methodological contributions to the field.

Conceptual design is a key stage of product design and has received increasing attention in recent years. However, this stage is characterized by limited information, large uncertainty, and multidisciplinary aspects. Thus, increased workload and time cost are associated with conceptual design information acquisition; sometimes, it is difficult to develop novel solutions and the feasibility of the solutions obtained according to these limited and uncertain information is difficult to guarantee. Genetics-based design (GBD) is an effective approach to develop novel solutions and improve the reuse of knowledge, which is consistent with the goal of the conceptual design process. Product-gene acquisition is the premise and basis of GBD. At present, there are few reported studies in this area; most of the existing works are constrained by the structural aspects of the acquisition process, and there are limited studies on specific implementation techniques. To explore the specific implementation technologies of product-gene acquisition, an intelligent acquisition method based on K-means clustering and mutual information-based feature selection algorithm is proposed in this paper. The product genes defined in this paper are key product information that determines the nature of the product and influences the conceptual design process. Thus, solutions obtained according to them are more feasible than that based on limited and uncertain information. An illustrative example is presented. The results show that the proposed method can achieve intelligent acquisition of product genes to a certain extent. Further, the proposed method will allow designers to quickly search for the corresponding product genes when performing similar functional design tasks.

Several industrial systems are characterized by high nonlinearities with wide operating ranges and large set point changes. Identification and representation of these systems represent a challenge, especially for control engineers. Multimodel technique is one effective approach that can be used to describe nonlinear systems through the combination of several submodels, where each is contributing to the output with a certain degree of validity. One major concern in this technique, especially for systems with unknown operating conditions, is the partitioning of the system's operating space and thus the identification of different submodels. This paper proposes a three-stage approach to obtain a multimodel representation of a nonlinear system. A reinforced combinatorial particle swarm optimization and hybrid K-means are used to determine the number of submodels and their respective parameters. The proposed method automatically optimizes the number of submodels with respect to the submodel complexity. This allows operating space partition and generation of a parsimonious number of submodels without prior knowledge. The application of this approach on several examples, including a continuous stirred tank reactor, demonstrates its effectiveness.

Image segmentation is a fundamental problem in both image processing and computer vision with numerous applications. In this paper, we propose a two-stage image segmentation scheme based on inexact alternating direction method. Specifically, we first solve the convex variant of the Mumford-Shah model to get the smooth solution, the segmentation are then obtained by apply the K-means clustering method to the solution. Some numerical comparisons are arranged to show the effectiveness of our proposed schemes by segmenting many kinds of images such as artificial images, natural images, and brain MRI images.

This paper introduces a dynamic classification method inspired by DBSCAN clustering method for machine condition monitoring in general and for bearings in particular. This method has been developed for two purposes; first to monitor the health condition of a bearing in real time and second to study the behavior of defected rolling element bearing. To fulfill those purposes, the temporal indicator RMS (Root Mean Square) has been chosen as an indicator of the bearing health condition; this indicator has been computed from signals extracted from an experimental bench by two piezoelectric sensors placed radially and axially. The decision upon the right classification method was taken after a comparative study between two classical of the clustering methods (K-means and Density Based Spatial Clustering of Applications with Noise DBSCAN), which led to the conclusion that DBSCAN is more adapted to vibratory signals. DBSCAN was re-adapted to follow any changing in bearings behavior.