Award Abstract #0239053
CAREER: New Directions in Mixture Models and their Applications
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NSF Org: |
DMS
Division of Mathematical Sciences
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Initial Amendment Date: |
March 14, 2003 |
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Latest Amendment Date: |
May 15, 2006 |
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Award Number: |
0239053 |
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Award Instrument: |
Continuing grant |
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Program Manager: |
Grace L. Yang
DMS Division of Mathematical Sciences
MPS Directorate for Mathematical & Physical Sciences
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Start Date: |
June 1, 2003 |
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Expires: |
May 31, 2007 (Estimated) |
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Awarded Amount to Date: |
$313246 |
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Investigator(s): |
Ramani Pilla pilla@cwru.edu (Principal Investigator)
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Sponsor: |
Case Western Reserve University
Sears Library, 6th Floor
CLEVELAND, OH 44106 216/368-4510
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NSF Program(s): |
STATISTICS
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Field Application(s): |
0000099 Other Applications NEC
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Program Reference Code(s): |
OTHR,9229,1187,1045,0000
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Program Element Code(s): |
1269
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ABSTRACT
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Mixture models, which can be viewed also as clustering
techniques, have become widely used statistical tools in the
analysis of heterogeneous data, aiding researchers in
interpreting existing data or in classifying new data. This
project extends the current interests of the PI in mixture
models to new directions while integrating them into
education. It is well known that under the normal mixture
model with unequal variance, the likelihood is unbounded and
hence the global maximum likelihood estimator (MLE) does not
exist. High-dimensional data analysis is becoming increasingly
important in many applied fields, including bioinformatics,
astronomy and imaging. Moreover, finding the nonparametric MLE
is widely regarded as computationally intensive, with the
particular difficulty being locating the mass points. To
address these issues this project will (1) establish
spacings-based inferential tools and asymptotic theory for the
normal mixtures with unequal variances to overcome the
limitations of the likelihood approach; (2) generalize these
methods to multivariate normal mixture model; (3) develop
theory and algorithms for multivariate mixtures via the
penalized dual method; (4) develop methods for solving
nonparametric mixture problems; (5) extend the multivariate
mixture methods to identify features in spatial patterns and
in turn develop efficient pattern recognition algorithms for
use in hyperspectral image classification, mammography and
minefield detection; and (6) integrate research and education
to advance discovery and understanding of mixtures.
This project will: (1) promote discovery and understanding of
the mixture models for modeling univariate and multivariate
heterogeneous data; (2) broaden and initiate new applications
to advance mixture models to new frontiers; (3) promote
collaborative learning and foster critical thinking through
student involvement in the PI's research projects; (4) build a
firm foundation for the PI in contributing to a
well-integrated research and education program in the theory,
computation and application of mixture models and related
areas; (5) impart education that will train a new generation
of scientists and engineers capable of developing mixture
models tools to solve important problems arising from new
frontiers of biology, engineering and medicine; (6) result in
offering an interdisciplinary course in mixture models and
applications to graduate students, enabling and promoting
interactions between statistics and allied fields; (7) enhance
multidisciplinary research experience for students through the
PI's collaborations and partnerships with the U.S. Navy and
international scientists.
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