In this paper, we group South American countries based on the number of infected cases and deaths due to COVID-19. The countries considered are: Argentina, Bolivia, Brazil, Chile, Colombia, Ecuador, Peru, Paraguay, Uruguay, and Venezuela. The data used are collected from a database of Johns Hopkins University, an institution that is dedicated to sensing and monitoring the evolution of the COVID-19 pandemic. A statistical analysis, based on principal components with modern and recent techniques, is conducted. Initially, utilizing the correlation matrix, standard components and varimax rotations are calculated. Then, by using disjoint components and functional components, the countries are grouped. An algorithm that allows us to keep the principal component analysis updated with a sensor in the data warehouse is designed. As reported in the conclusions, this grouping changes depending on the number of components considered, the type of principal component (standard, disjoint or functional) and the variable to be considered (infected cases or deaths). The results obtained are compared to the k-means technique. The COVID-19 cases and their deaths vary in the different countries due to diverse reasons, as reported in the conclusions.

One of the main drawbacks of the traditional methods for computing components in the three-way Tucker model is the complex structure of the final loading matrices preventing an easy interpretation of the obtained results. In this paper, we propose a heuristic algorithm for computing disjoint orthogonal components facilitating the analysis of three-way data and the interpretation of results. We observe in the computational experiments carried out that our novel algorithm ameliorates this drawback, generating final loading matrices with a simple structure and then easier to interpret. Illustrations with real data are provided to show potential applications of the algorithm.

In this paper, we extend the use of disjoint orthogonal components to three-way table analysis with the parallel factor analysis model. Traditional methods, such as scaling, orthogonality constraints, non-negativity constraints, and sparse techniques, do not guarantee that interpretable loading matrices are obtained in this model. We propose a novel heuristic algorithm that allows simple structure loading matrices to be obtained by calculating disjoint orthogonal components. This algorithm is also an alternative approach for solving the well-known degeneracy problem. We carry out computational experiments by utilizing simulated and real-world data to illustrate the benefits of the proposed algorithm.

The Hotelling T² chart relies on Phase 1 parameters estimated from in-control data. When the calibration sample contains outlying observations or anomalous batches, the classical covariance is inflated, and this masking effect hides later mean shifts. We propose MFA-MCD, a robust T² chart for batch processes. It estimates the covariance of each batch with the minimum covariance determinant (MCD), weights each batch by the inverse of its first eigenvalue, as in multiple factor analysis (MFA), and obtains the reference center with a second MCD on the batch centers. The control limit is a heuristic F-type approximation, not an exact distributional result, based on the size of the MCD subset. With six of thirty Phase 1 batches contaminated and a one-standard-deviation shift in all variables, it detects 88.5% of the shifted batches, against 27.0% for the classical chart and 73.0% for the MCD alone; its advantage stays above 0.49 across nine configurations. With a clean Phase 1 and shifts that do not move all variables together, it detects between 5.3 and 5.8 points less than the classical chart. On the Tennessee Eastman process it detects all twenty faulty batches without false alarms; the classical chart detects two. The method targets mean shifts and is implemented in the R package robustT2AFM.

In this paper, we propose an alternative method to the disjoint principal component analysis. The method consists of a principal component analysis with constraints, which allows us to determine disjoint components that are linear combinations of disjoint subsets of the original variables. The proposed method is named constrained binary optimization by particle swarm disjoint principal component analysis, since it is based on the particle swarm optimization. The method uses stochastic optimization to find solutions in cases of high computational complexity. The algorithm associated with the method starts generating randomly a particle population which iteratively evolves until attaining a global optimum which is function of the disjoint components. Numerical results are provided to confirm the quality of the solutions attained by the proposed method. Illustrative examples with real data are conducted to show the potential applications of the method.