The problem of maximizing (or minimizing) the agreement between clusterings, subject to given marginals, can be formally posed under a common framework for several agreement measures. Until now, it was possible to find its solution only through numerical algorithms. Here, an explicit solution is shown for the case where the two clusterings have two clusters each.

The k-means algorithm is widely used in various research fields because of its fast convergence to the cost function minima; however, it frequently gets stuck in local optima as it is sensitive to initial conditions. This paper explores a simple, computationally feasible method, which provides k-means with a set of initial seeds to cluster datasets of arbitrary dimensions. Our technique consists of

A generic method is introduced to visualize in a “Gaussian-like way,” and onto \(\mathbb {R}^{2}\), results of Gaussian or non-Gaussian–based clustering. The key point is to explicitly force a visualization based on a spherical Gaussian mixture to inherit from the within cluster overlap that is present in the initial clustering mixture. The result is a particularly user-friendly drawing of the clusters

In many application areas, prediction rules trained based on high-dimensional data are subsequently applied to make predictions for observations from other sources, but they do not always perform well in this setting. This is because data sets from different sources can feature (slightly) differing distributions, even if they come from similar populations. In the context of high-dimensional data and

A model-based clustering method based on Gaussian Cox process is proposed to address the problem of clustering of count process data. The model allows for nonparametric estimation of intensity functions of Poisson processes, while simultaneous clustering count process observations. A logistic Gaussian process transformation is imposed on the intensity functions to enforce smoothness. Maximum likelihood

In comparing clustering partitions, the Rand index (RI) and the adjusted Rand index (ARI) are commonly used for measuring the agreement between partitions. Such external validation indexes can be used to quantify how close the clusters are to a reference partition (or to prior knowledge about the data) by counting classified pairs of elements. To evaluate the solution of a fuzzy clustering algorithm

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).

One of the challenges in cluster analysis is the evaluation of the obtained clustering results without using auxiliary information. To this end, a common approach is to use internal validity criteria. For mixtures of linear regressions whose parameters are estimated by maximum likelihood, we propose a three-term decomposition of the total sum of squares as a starting point to define some internal validity

k-means clustering is a well-known procedure for classifying multivariate observations. The resulting centroid matrix of clusters by variables is noted for interpreting which variables characterize clusters. However, between-clusters differences are not always clearly captured in the centroid matrix. We address this problem by proposing a new procedure for obtaining a centroid matrix, so that it has

Feature ranking is a widely used feature selection method. It uses importance scores to evaluate features and selects those with high scores. Conventional unsupervised feature ranking methods do not consider the information on cluster structures; therefore, these methods may be unable to select the relevant features for clustering analysis. To address this limitation, we propose a feature ranking algorithm

The distinction between classification and clustering is often based on a priori knowledge of classification labels. However, in the purely theoretical situation where a data-generating model is known, the optimal solutions for clustering do not necessarily correspond to optimal solutions for classification. Exploring this divergence leads us to conclude that no standard measures of either internal

Choosing a journal to publish a work is a task that involves many variables. Usually, the authors’ experience allows them to classify journals into categories, according to their suitability and the characteristics of the article. However, there are certain aspects in the choice that are probabilistic in nature, whose modelling may provide some help. Suppose an author has to choose a journal from a

In this work, we analytically study the peaking phenomenon in the context of linear discriminant analysis in the multivariate Gaussian model under the assumption of a common known covariance matrix. The focus is finite-sample setting where the sample size and observation dimension are comparable. Therefore, in order to study the phenomenon in such a setting, we use an asymptotic technique whereby the

Because the validity of diagnostic information generated by cognitive diagnosis models (CDMs) depends on the appropriateness of the estimated attribute profiles, it is imperative to ensure the accurate measurement of students’ test performance by conducting person fit (PF) evaluation to avoid flawed remediation measures. The standardized log-likelihood statistic lZ has been extended to the CDM framework

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

In this work we use a novel methodology for the classification of time series data, through a natural, unsupervised data learning process. This strategy is based on the sequential use of Multiple Factor Analysis and an ascending Hierarchical Classification Analysis. These two exploratory techniques complement each other and allow for a clustering of the series based on their time paths and on the reduction

The mixture of factor analyzers model was first introduced over 20 years ago and, in the meantime, has been extended to several non-Gaussian analogs. In general, these analogs account for situations with heavy tailed and/or skewed clusters. An approach is introduced that unifies many of these approaches into one very general model: the mixture of hidden truncation hyperbolic factor analyzers (MHTHFA)

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

Fast centroid-based clustering algorithms such as k-means usually converge to a local optimum. In this work, we propose a method for constructing a better clustering from two such suboptimal clustering solutions based on the fact that each suboptimal clustering has benefits regarding to including some of the correct clusters. We develop the new method COTCLUS to find two centroids from one clustering

The latent attribute space in cognitive diagnosis models (CDMs) is often assumed to be unstructured or saturated. In recent years, the number of latent attributes in real tests has often been found to be large, and polytomous latent attributes have been advocated. Therefore, it is preferable to adopt substantive theories to connect seemingly unrelated latent attributes, to replace the unstructured

We develop a Bayesian local influence procedure for generalized failure time models with latent variables and multivariate censored data. We propose to use the penalized splines (P-splines) approach to formulate the unknown functions of the proposed models. We assess the effects of minor perturbations to individual observations, the prior distributions of parameters, and the sampling distribution on

We show the geometrical structure of the moduli space of positive-weighted trees with n labels 1,…,n which realize the same family of positive (n − 1)-weights and we characterize them as a family of positive multi-weights.

In this article, we develop a clique-based method for social network clustering. We introduce a new index to evaluate the quality of clustering results, and propose an efficient algorithm based on recursive bipartition to maximize an objective function of the proposed index. The optimization problem is NP-hard, so we approximate the semi-optimal solution via an implicitly restarted Lanczos method.

Recently, Shafaei and Kayid (Statistical Papers, 2017) introduced and studied the bivariate quantile residual life model. It has been shown that two suitable bivariate quantile residual life functions characterize the underlying distribution uniquely. In the current investigation, we first propose a nonparametric estimator of this new model. The estimator is strongly consistent and, on proper normalization

We extend the standard Bayesian multivariate Gaussian generative data classifier by considering a generalization of the conjugate, normal-Wishart prior distribution, and by deriving the hyperparameters analytically via evidence maximization. The behaviour of the optimal hyperparameters is explored in the high-dimensional data regime. The classification accuracy of the resulting generalized model is

We show in this paper a bijection between totally balanced hypergraphs and so-called totally balanced dissimilarities. We give an efficient way (O(n3) where n is the number of elements) to (i) recognize if a given dissimilarity is totally balanced and (ii) approximate it if it is not the case. We also introduce a new kind of dissimilarity which generalizes chordal graphs and allows a polynomial number

Model-based clustering of human population genomic data, composed of 1,318 individuals arisen from western Central Africa and 160,470 markers, is considered. This challenging analysis leads us to develop a new methodology for variable selection in clustering. To explain the differences between subpopulations and to increase the accuracy of the estimates, variable selection is done simultaneously to

It is customary to split clustering analysis into an optimization level, then a (preferably) graphical representation level to take benefit of human vision for an effective understanding of (big) data structure. This article aspires to clarify relationships between clustering, both its process and its representation, and the underlying structural graph properties, both algebraic and geometric, starting

The random forest is a popular and effective classification method. It uses a combination of bootstrap resampling and subspace sampling to construct an ensemble of decision trees that are then averaged for a final prediction. In this paper, we propose a potential improvement on the random forest that can be thought of as applying a weight to each tree before averaging. The new method is motivated by

Ordinal classification problems are applied in many fields. In the field of multivariate statistical analysis, these tasks are referred to as ordinal regression problems. In the field of management decision-making, they are known as multi-criteria decision analyses or sorting problems. This paper introduces the PairCode algorithm for ordinal classification with small sample sizes, which is based on

Real-world data sets often contain mislabelled entities. This can be particularly problematic if the data set is being used by a supervised classification algorithm at its learning phase. In this case, the accuracy of this classification algorithm, when applied to unlabelled data, is likely to suffer considerably. In this paper, we introduce a clustering-based method capable of reducing the number

Existing clustering methods range from simple but very restrictive to complex but more flexible. The K-means algorithm is one of the most popular clustering procedures due to its computational speed and intuitive construction. Unfortunately, the application of K-means in its traditional form based on Euclidean distances is limited to cases with spherical clusters of approximately the same volume and

Models based on machine learning algorithms have been developed to detect the breast cancer disease early. Feature selection is commonly applied to improve the performance of these models through selecting only relevant features. However, selecting relevant features in unsupervised learning is much difficult. This is due to the absence of class labels that guide the search for relevant information

We analyze the problem of classifying individuals in a group N taking into account their opinions about which of them should belong to a specific subgroup N′⊆ N, in the case that |N| > ∞. We show that this problem is relevant in cases in which the group changes in time and/or is subject to uncertainty. The approach followed here to find the ensuing classification is by means of a Collective Identity

Incomplete data are often represented as vectors with filled missing attributes joined with flag vectors indicating missing components. In this paper, we generalize this approach and represent incomplete data as pointed affine subspaces. This allows to perform various affine transformations of data, such as whitening or dimensionality reduction. Moreover, this representation preserves the information

The dendritic cell algorithm (DCA) is a classification algorithm based on the behavior of natural dendritic cells (DCs). In literature, DCA has given good classification results. However, DCA was known to be sensitive to the order of the instance classes. To solve this limitation, a fuzzy DCA version was developed stating that the cause of such sensitivity is related to the DCA crisp classification

The ordinal forest method is a random forest–based prediction method for ordinal response variables. Ordinal forests allow prediction using both low-dimensional and high-dimensional covariate data and can additionally be used to rank covariates with respect to their importance for prediction. An extensive comparison study reveals that ordinal forests tend to outperform competitors in terms of prediction

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