This 122-page book is intended to be a practical guide to CoDa analysis and its easyto-read format and didactic layout are designed for students and researchers alike from different fields. For more insight, the interested reader can find other books that present the subject in a more up-to-date manner and cover more multivariate techniques with applications and examples from geochemistry.

Mixture model-based clustering has become an increasingly popular data analysis technique since its introduction over fifty years ago, and is now commonly utilized within a family setting. Families of mixture models arise when the component parameters, usually the component covariance (or scale) matrices, are decomposed and a number of constraints are imposed. Within the family setting, model selection

Recent technological advances have enabled the easy collection of consumer behavior data in real time. Typically, these data contain the time at which a consumer engages in a particular activity such as entering a store, buying a product, or making a call. The occurrence time of certain events must be analyzed as circular random variables, with 24:00 corresponding to 0:00. To effectively implement

This paper presents a new rule-based classification method that partitions data under analysis into spherical patterns. The forte of the method is twofold. One, it exploits the efficiency of distance metric-based clustering to fast collect similar data into spherical patterns. The other, spherical patterns are each a trait shared among one type of data only, hence are built for classification of new

A subspace constrained mean shift (SCMS) algorithm is a non-parametric iterative technique to estimate principal curves. Principal curves, as a nonlinear generalization of principal components analysis (PCA), are smooth curves (or surfaces) that pass through the middle of a data set and provide a compact low-dimensional representation of data. The SCMS algorithm combines the mean shift (MS) algorithm

Classifier performance assessment (CPA) is a challenging task for pattern recognition. In recent years, various CPA metrics have been developed to help assess the performance of classifiers. Although the classification accuracy (CA), which is the most popular metric in pattern recognition area, works well if the classes have equal number of samples, it fails to evaluate the recognition performance

Classifiers for a highly imbalanced dataset tend to bias in majority classes and, as a result, the minority class samples are usually misclassified as majority class. To overcome this, a proper undersampling technique that removes some majority samples can be an alternative. We propose an efficient and simple undersampling method for imbalanced datasets and show that the proposed method outperforms

The paper discusses a new approach for incorporating hard constraints into the K-means algorithm for semi-supervised clustering. An analytic modification of the objective function of K-means is proposed that has not been previously considered in the literature.

A robust version of reduced and factorial k-means is proposed that is based on the idea of trimming. Reduced and factorial k-means are data reduction techniques well suited for simultaneous dimension and sample reduction through PCA and clustering. The occurrence of data inadequacies can invalidate standard analyses. Actually, contamination in the data at hand can hide the underlying clustered structure

In the paper, we introduce novel model selection measures based on Lorenz zonoids which, differently from measures based on correlations, are based on a mutual notion of variability and are more robust to the presence of outlying observations. By means of Lorenz zonoids, which in the univariate case correspond to the Gini coefficient, the contribution of each explanatory variable to the predictive

Often tree-based accounts of statistical learning problems yield multiple decision trees which together constitute a forest. Reasons for this include examining tree instability, improving prediction accuracy, accounting for missingness in the data, and taking into account multiple outcome variables. A key disadvantage of forests, unlike individual decision trees, is their lack of transparency. Hence

Cognitive diagnostic computerized adaptive testing (CD-CAT) purports to combine the strengths of both CAT and cognitive diagnosis. Currently, large number of CD-CAT researches focus on the dichotomous data. In our knowledge, there are no researches on CD-CAT for polytomously scored items or data. However, polytomously scored items have been broadly used in a variety of tests for their advantages of

In analysis of binary outcomes, the receiver operator characteristic (ROC) curve is heavily used to show the performance of a model or algorithm. The ROC curve is informative about the performance over a series of thresholds and can be summarized by the area under the curve (AUC), a single number. When a predictor is categorical, the ROC curve has one less than number of categories as potential thresholds;

The concept of proximity curve and a new algorithm are proposed for obtaining clusters in a finite set of data points in the finite dimensional Euclidean space. Each point is endowed with a potential constructed by means of a multi-dimensional Cauchy density, contributing to an overall anisotropic potential function. Guided by the steepest descent algorithm, the data points are successively visited

In this paper, an optimal weight semi-supervised learning machine for a single-hidden layer feedforward network (SLFN) with time delay is developed. Both input weights and output weights of the SLFN are globally optimized with manifold regularization. By feature mapping, input vectors can be placed at the prescribed positions in the feature space in the sense that the separability of all nonlinearly

This paper discusses the challenges presented by tall data problems associated with Bayesian classification (specifically binary classification) and the existing methods to handle them. Current methods include parallelizing the likelihood, subsampling, and consensus Monte Carlo. A new method based on the two-stage Metropolis-Hastings algorithm is also proposed. The purpose of this algorithm is to reduce

In model-based clustering based on normal-mixture models, a few outlying observations can influence the cluster structure and number. This paper develops a method to identify these, however it does not attempt to identify clusters amidst a large field of noisy observations. We identify outliers as those observations in a cluster with minimal membership proportion or for which the cluster-specific variance

This paper addresses measurement error in food security in the USA. In particular, it uses a Bayesian 4-parameter IRT model to look at the likelihood of over- or under-reporting of the conditions that comprise the food security module (FSM), the data collection administered in many US surveys to assess and monitor food insecurity. While this model’s parameters are only partially identified, we learn

The original version of this article unfortunately contained a mistake in Title and reference Thurstone, L. L. (1927).

The authors missed an important reference “Liu, Luo, & Liu, 2014” on the original version of this article.

The piecewise growth mixture model is used in longitudinal studies to tackle non-continuous trajectories and unobserved heterogeneity in a compound way. This study investigated how factors such as latent distance and shape influence the model. Two simulation studies were used exploring the 2- and 3-class situation with sample size, latent distance (Mahalanobis distance), and shape being considered

Support vector machine (SVM) parameters such as penalty parameter and kernel parameters have a great influence on the complexity and accuracy of SVM model. In this paper, quantum-behaved particle swarm optimization (QPSO) has been employed to optimize the parameters of SVM, so that the classification error can be reduced. To evaluate the proposed model (QPSO-SVM), the experiment adopted seven standard