Mia Hubert, Peter Rousseeuw,
& Karlien Vanden Branden talk with
ScienceWatch.com and answer a few questions about
this month's Fast Moving Front in the field of
Article: ROBPCA: A new approach to robust principal
Authors: Hubert, M;Rousseeuw, PJ;Vanden Branden, K
Journal: TECHNOMETRICS, 47 (1): 64-79, FEB 2005
Addresses: Katholieke Univ Leuven, Dept Math, B-3001
Katholieke Univ Leuven, Dept Math, B-3001 Louvain,
Univ Antwerp, Dept Math & Comp Sci, B-2020 Antwerp,
Katholieke Univ Leuven, Dept Math, B-3001 Heverlee,
Why do you think your paper is highly
Our paper offers a solution to an important problem in statistics and data
analysis: how to perform data reduction when the observations may be
contaminated with outlying values. This problem is especially important for
the analysis of high-dimensional data sets, such as spectral data in
chemometrics and genetic data in bio-informatics. We propose an algorithm
which is highly robust and computationally feasible, and we also provide a
graphical tool for outlier detection.
Karlien Vanden Branden
Moreover, our method serves as the cornerstone of new highly robust
calibration methods (principal component regression and partial least
squares regression), a robust classifier, and robust multi-way techniques.
The availability of user-friendly software in our Matlab toolbox LIBRA has
facilitated the practical use of our algorithm. So far applications of our
method have been developed in chemometrics,
bio-informatics, image analysis, face recognition methods, computer
vision, sensory analysis, statistical quality control, and fault
Does it describe a new discovery, methodology, or
synthesis of knowledge?
The new method combines elements of two existing approaches. The first is
the minimum covariance determinant method, which dates back to 1984 and for
which a fast algorithm was constructed in 1999 (Rousseeuw P and Van
Driessen K, "A fast algorithm for the minimum covariance determinant
estimator," Technometrics 42: 212-23, 1991). This approach is
quite accurate, but is not applicable when there are more dimensions than
observations (as in the case of spectra).
The second approach is principal component analysis by projection pursuit,
as advocated by several authors. That approach can deal with
high-dimensional data but is typically less accurate. Our proposed method,
ROBPCA (Robust Principal Component Analysis), combines the advantages of
both approaches by being robust, more accurate, and able to handle
Would you summarize the significance of your paper
in layman's terms?
Principal component analysis is the most popular technique for data
reduction. It transforms data with many variables (columns) to a coordinate
system with fewer variables, which often have a meaningful interpretation.
Data reduction is extremely useful nowadays, as new data collection methods
are widely applied and data storage has become much cheaper.
Consider, for example, microarray data containing gene expressions of
thousands of genes, or online process measurements. Unfortunately, the more
data are gathered, the more likely it becomes that outliers will be
present. Hence, there is a need for statistical methods that perform data
reduction while at the same time being robust against outliers, i.e., able
to resist the ill effects of outlying cases and able to detect these cases.
The proposed method is robust in this sense, and the outlying cases can be
detected by the outlier map that is a part of the output.
Where do you see your research leading in the
We continue to do work on constructing robust versions of other statistical
techniques, with an eye toward computational feasibility.
Do you foresee any social or political implications for your
We don't expect a direct effect, but statistical methods are used in all
fields of science (including sociology) as well as in business and for
political decision-making. Therefore, developing better statistical tools
holds the promise of improving the insights and conclusions of research
work done in all these areas.
Professor Mia Hubert
Department of Mathematics
Katholieke Universiteit Leuven
Professor Peter Rousseeuw
Department of Mathematics and Computer Science
University of Antwerp
Karlien Vanden Branden, Ph.D.
Keywords: high-dimensional data sets, spectral data
in chemometrics, matlab toolbox libra, robust principal component