Number Of Groups In Data Research Articles

Clustering Individuals on Limited Features of a Vector Autoregressive Model

Dynamical interplays in emotions have been investigated using vector autoregressive (VAR) models, whose estimates can be used to cluster participants into unknown groups. The present study evaluated a clustering algorithm, the alternating least square (ALS) algorithm, for accuracy in predicting individual group membership. We systematically manipulated (a) the number of variables in a model, (b) the size of group differences in regression coefficients, and (c) the number of regression coefficients that vary across the groups (i.e., effective features). The ALS algorithm works reliably when there are at least 5 effective features with very large group differences in a 5-variable model; and 9 effective features with very large group differences in a 10-variable model. These findings suggest that the ALS algorithm is sensitive to group differences that are present only in several coefficients of a VAR model, but that the group differences have to be large. We also found that the ALS algorithm outperforms another clustering method, Gaussian mixture modeling. The ALS algorithm was further evaluated with unbalanced sample sizes between groups and with a greater number of groups in data (Study 2). A real data application was provided to illustrate how to interpret the detected group differences (Study 3).

K-means clustering analysis and artificial neural network classification of fatigue strain signals

This paper focuses on the analysis based on the clustering and the classification method of fatigue strain signals. Very few detailed studies have been carried out on the classification of fatigue damage, especially in the automotive field. Fatigue strain signals were observed on the coil springs of vehicles during road tests. The strain signals were then extracted using the Wavelet Transform approach. The features extraction was grouped using the K-means clustering method to obtain the appropriate number of data groups. A classification process was executed to obtain the optimum pattern recognition through the use of artificial neural network (ANN). Based on the results of the ANN classification with an accuracy of 92 %, a total of five classes or levels of fatigue damage were obtained. Based on the results, the data distribution was mostly scattered in the lower class, namely in the first class with the fatigue damage ranging from 1.98 × 10−7 to 8.18 × 10−5. The highest fatigue damage was in the fifth class with values ranging from 1.14 × 10−3 to 1.65 × 10−3. Based on this clustering and classification, the level of fatigue damage could be classified into five stages.

A general framework for a reliable multivariate analysis and pattern recognition in high-dimensional epidemiological data, based on cluster robustness: A tutorial to enrich the epidemiologists’ toolkit

BackgroundIn an epidemiologist's toolbox, three main types of statistical tools can be found: means and proportions comparisons, linear or logistic regression models and Cox-type regression models. All these techniques have their own multivariate formulations, so that biases can be accounted for. Nonetheless, there is an entire set of natively massive multivariate techniques, which are based on weaker assumptions than classical statistical techniques are, and which seem to be underestimated or remain unknown to most epidemiologists. These techniques are used for pattern recognition or clustering – that is, for retrieving homogeneous groups in data without any a priori about these groups. They are widely used in connex domains such as genetics or biomolecular studies. MethodsMost clustering techniques require tuning specific parameters so that groups can be identified in data. A critical parameter to set is the number of groups the technique needs to discover. Different approaches to find the optimal number of groups are available, such as the silhouette approach and the robustness approach. This article presents the key aspects of clustering techniques (how proximity between observations is defined and how to find the number of groups), two archetypal techniques (namely the k-means and PAM algorithms) and how they relate to more classical statistical approaches. ResultsThrough a theoretical, simple example and a real data application, we provide a complete framework within which classical epidemiological concerns can be reconsidered. We show how to (i) identify whether distinct groups exist in data, (ii) identify the optimal number of groups in data, (iii) label each observation according to its own group and (iv) analyze the groups identified according to separate and explicative data. In addition, how to achieve consistent results while removing sensitivity to initial conditions is explained. ConclusionsClustering techniques, in conjunction with methods for parameter tuning, provide the epidemiologist with substantial additional tools. They differ from the usual approaches based on hypothesis-testing because no assumptions are made on the data and these clustering techniques are natively multivariate.

Mutual information and linkage disequilibrium based SNP association study by grouping case-control

Two main reasons for the difficulties to search for susceptibility single-nucleotide polymorphisms (SNPs) underlying genetic diseases are that the findings are not easy to be confirmed and the interactions between potential susceptibility SNPs are not clear. Many available association studies usually presented results with significance levels but did not illustrate the stability of the results. In some sense, their performances might be unclear in real practice. In this paper, we develop a novel method based on mutual information theory and linkage disequilibrium by grouping case-control. Mutual information (MI) is used to test multiple SNPs in combining with disease status. Those SNPs contributing the maximum MI are selected as potential susceptibility SNPs. Linkage disequilibrium (LD) analysis is used to extend MI detected result so that both direct and indirect factors can be included in the final result. The purpose of case-control grouping is to generate a number of data groups by randomly sampling from target samples. Each group is assumed to have almost the same number of individuals (cases and controls), and overlap is allowed among the groups. We apply the method to each data group, and then make comparisons and intersections between the results obtained from each of the groups so as to give the final result. We implement the method by continuously grouping until the final result reaches a stable state and a highly significance level. The experimental results indicate that our method to detect susceptibility SNPs in simulated and real data sets has shown remarkable success.

Development and Application of Suboptimal Test Signal Sequences for Identifying Non Linear Systems

The paper deals with the design of test signal sequences for estimating equidistant grid points of non-parametric models of Hammerstein and Wiener types respectively with second order nonlinearity for describing dynamic systems. The sequences are based on optimality criterions securing minimum variances and covariances for the estimated grid points and aiming at best possible agreement between estimated and measured system output at given number of data groups. The paper deals in particular with the formation of suboptimal test sequences on the base of Plackett-Burman designs since they are very effective due to their diagonal structure and to the possibility of simple extension to non-linear problems. The test sequences have been applied sucessfully for identifying processes of man’s heart-circulation behavior, as well as the stimulus transfer behaviour of cockroach Feriplaneta americana.