Robust Sparse Hierarchical Clustering

• Activity Number: 614
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Hongyang Zhang* and Andrew Leung and Ruben Zamar
• Companies: The University of British Columbia and The University of British Columbia and The University of British Columbia
• Keywords: Hierarchical clustering ; High-dimensional data ; Variable selection ; Robust estimation ; Tau-estimator ; Lasso

Abstract

We consider the problem of hierarchical clustering when the data set has a large number of variables and a relatively small number of observations. Non-informative noise variables and outlying observations are likely to occur in this context. The inclusion of non-informative noise variables may impede the finding of the underlying clusters. Sparse hierarchical clustering (SHC), which uses a subset of adaptively chosen informative variables, outperforms classical hierarchical methods based on all the variables. However, in the presence of outliers, SHC yields poor results. We propose two approaches for robust sparse hierarchical clustering (RSHC) to deal with both noise variables and outliers. The proposed RSHC methods are based on ?-estimator and Lasso-type penalty. The first approach is a direct robustification of SHC. The second approach introduces a new framework that scales better with the number of observations. Experiments with both simulated and real data sets show that RSHC approaches work well on clean data and outperform the non-robust alternatives when the data set contains outliers.