Robust Analysis of Clustered Principal Component Analysis Method for Large Multivariate Data

• Activity Number: 137
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Nasser Fard and Yuanchen Fang*+ and Huyang Xu
• Companies: Northeastern University and Northeastern University and Northeastern University
• Keywords: Correlation Matrix ; Clustering ; PCA ; Robust Analysis ; Weighted Variance ; Eigen Value

Abstract

Weighted-variances clustering is used for constructing interpretable components from clusters of variables. This will lead to determination of the important variables constituting a certain component are more correlated to each other than to the other variables. Variables are optimally clustered using the objective criterion to obtain the nonzero-loadings of an interpretable component from the correlation matrix of the variables in their corresponding cluster while the loading of the remaining variables become zero. A significant advantage of weighted-variance clustering component analysis is that the optimal number of PCs are determined, which avoids the subjective bias caused by fixing a priori number. A robust correlation matrix, instead of empirical correlation matrix throughout the weighted-variance algorithm is utilized. A robust correlation measure, which is derived from minimum covariance determinant (MCD) estimator, into the weighted-variance clustering model is introduced.