Algorithms for Projection - Pursuit robust principal component analysis.

The results of a standard principal component analysis (PCA) can be affected by the presence of outliers. Hence robust alternatives to PCA are needed. One of the most appealing robust methods for principal component analysis uses the Projection-Pursuit principle. Here, one projects the data on a lower-dimensional space such that a robust measure of variance of the projected data will be maximized. The Projection-Pursuit-based method for principal component analysis has recently been introduced in the field of chemometrics, where the number of variables is typically large. In this paper, it is shown that the currently available algorithm for robust Projection-Pursuit PCA performs poor in the presence of many variables. A new algorithm is proposed that is more suitable for the analysis of chemical data. Its performance is studied by means of simulation experiments and illustrated on some real data sets. (c) 2007 Elsevier B.V. All rights reserved.multivariate statistics; optimization; numerical precision; outliers; robustness; scale estimators; estimators; regression;

Algorithms for projection-pursuit robust principal component analysis.

Principal Component Analysis (PCA) is very sensitive in presence of outliers. One of the most appealing robust methods for principal component analysis uses the Projection-Pursuit principle. Here, one projects the data on a lower-dimensional space such that a robust measure of variance of the projected data will be maximized. The Projection-Pursuit based method for principal component analysis has recently been introduced in the field of chemometrics, where the number of variables is typically large. In this paper, it is shown that the currently available algorithm for robust Projection-Pursuit PCA performs poor in presence of many variables. A new algorithm is proposed that is more suitable for the analysis of chemical data. Its performance is studied by means of simulation experiments and illustrated on some real datasets.Algorithms; Data; Field; IT; Methods; Outliers; Performance; Principal component analysis; Principal components analysis; Projection-pursuit; Robustness; Simulation; Space; Variables; Variance;

Distributed static linear Gaussian models using consensus

Algorithms for distributed agreement are a powerful means for formulating distributed versions of existing centralized algorithms. We present a toolkit for this task and show how it can be used systematically to design fully distributed algorithms for static linear Gaussian models, including principal component analysis, factor analysis, and probabilistic principal component analysis. These algorithms do not rely on a fusion center, require only low-volume local (1-hop neighborhood) communications, and are thus efficient, scalable, and robust. We show how they are also guaranteed to asymptotically converge to the same solution as the corresponding existing centralized algorithms. Finally, we illustrate the functioning of our algorithms on two examples, and examine the inherent cost-performance tradeoff

The usefulness of robust multivariate methods: A case study with the menu items of a fast food restaurant chain

Multivariate statistical methods have been playing an important role in statistics and data analysis for a very long time. Nowadays, with the increase in the amounts of data collected every day in many disciplines, and with the raise of data science, machine learning and applied statistics, that role is even more important. Two of the most widely used multivariate statistical methods are cluster analysis and principal component analysis. These, similarly to many other models and algorithms, are adequate when the data satisfies certain assumptions. However, when the distribution of the data is not normal and/or it shows heavy tails and outlying observations, the classic models and algorithms might produce erroneous conclusions. Robust statistical methods such as algorithms for robust cluster analysis and for robust principal component analysis are of great usefulness when analyzing contaminated data with outlying observations. In this paper we consider a data set containing the products available in a fast food restaurant chain together with their respective nutritional information, and discuss the usefulness of robust statistical methods for classification, clustering and data visualization