Kernel k-Groups via Hartigan's Method.

Energy statistics was proposed by Székely in the 80's inspired by Newton's gravitational potential in classical mechanics and it provides a model-free hypothesis test for equality of distributions. In its original form, energy statistics was formulated in euclidean spaces. More recently, it was generalized to metric spaces of negative type. In this paper, we consider a formulation for the clustering problem using a weighted version of energy statistics in spaces of negative type. We show that this approach leads to a quadratically constrained quadratic program in the associated kernel space, establishing connections with graph partitioning problems and kernel methods in machine learning. To find local solutions of such an optimization problem, we propose kernel k-groups, which is an extension of Hartigan's method to kernel spaces. Kernel k-groups is cheaper than spectral clustering and has the same computational cost as kernel k-means (which is based on Lloyd's heuristic) but our numerical results show an improved performance, especially in higher dimensions. Moreover, we verify the efficiency of kernel k-groups in community detection in sparse stochastic block models which has fascinating applications in several areas of science.

A new nonlinear classifier with a penalized signed fuzzy measure using effective genetic algorithm.

This paper proposes a new nonlinear classifier based on a generalized Choquet integral with signed fuzzy measures to enhance the classification accuracy and power by capturing all possible interactions among two or more attributes. This generalized approach was developed to address unsolved Choquet-integral classification issues such as allowing for flexible location of projection lines in n-dimensional space, automatic search for the least misclassification rate based on Choquet distance, and penalty on misclassified points. A special genetic algorithm is designed to implement this classification optimization with fast convergence. Both the numerical experiment and empirical case studies show that this generalized approach improves and extends the functionality of this Choquet nonlinear classification in more real-world multi-class multi-dimensional situations.

Power of Models in Longitudinal Study: Findings From a Full-Crossed Simulation Design.

Because the power properties of traditional repeated measures and hierarchical multivariate linear models have not been clearly determined in the balanced design for longitudinal studies in the literature, the authors present a power comparison study of traditional repeated measures and hierarchical multivariate linear models under 3 variance-covariance structures. The results from a full-crossed simulation design suggest that traditional repeated measures have significantly higher power than do hierarchical multivariate linear models for main effects, but they have significantly lower power for interaction effects in most situations. Significant power differences are also exhibited when power is compared across different covariance structures.

Pattern Recognition of Longitudinal Trial Data with Nonignorable Missingness: An Empirical Case Study.

Methods for identifying meaningful growth patterns of longitudinal trial data with both nonignorable intermittent and drop-out missingness are rare. In this study, a combined approach with statistical and data mining techniques is utilized to address the nonignorable missing data issue in growth pattern recognition. First, a parallel mixture model is proposed to model the nonignorable missing information from a real-world patient-oriented study and concurrently to estimate the growth trajectories of participants. Then, based on individual growth parameter estimates and their auxiliary feature attributes, a fuzzy clustering method is incorporated to identify the growth patterns. This case study demonstrates that the combined multi-step approach can achieve both statistical gener ality and computational efficiency for growth pattern recognition in longitudinal studies with nonignorable missing data.

A Monte Carlo Power Analysis of Traditional Repeated Measures and Hierarchical Multivariate Linear Models in Longitudinal Data Analysis.

The power properties of traditional repeated measures and hierarchical linear models have not been clearly determined in the balanced design for longitudinal studies in the current literature. A Monte Carlo power analysis of traditional repeated measures and hierarchical multivariate linear models are presented under three variance-covariance structures. Results suggest that traditional repeated measures have higher power than hierarchical linear models for main effects, but lower power for interaction effects. Significant power differences are also exhibited when power is compared across different covariance structures. Results also supplement more comprehensive empirical indexes for estimating model precision via bootstrap estimates and the approximate power for both main effects and interaction tests under standard model assumptions.