Solution of Constrained Clustering Problems through Homotopy Tracking

Modern machine learning methods are dependent on active optimization research to improve the set of methods available for the efficient and effective extraction of information from large datasets. This, in turn, requires an intense and rigorous study of optimization methods and their possible applications to crucial machine learning applications in order to advance the potential benefits of the field. This thesis provides a study of several modern optimization techniques and supplies a mathematical inquiry into the effectiveness of homotopy methods to attack a fundamental machine learning problem, effective clustering under constraints. The first part of this thesis provides an empirical survey of several popular optimization algorithms, along with one approach that is cutting-edge. These algorithms are tested against deeply challenging real-world problems with vast numbers of local minima, and compares and contrasts the benefits of each when confronted with problems of different natures. The second part of this thesis proposes a new homotopy map for use with constrained clustering problems. This thesis explores the connections between the map and the problem, providing several theorems to justify the use of the map and making use of modern homotopy tracking software to compare an optimization that employs the map with several modern approaches to solving the same problem.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Computer Science and Applications

Department dc:contributor.department

Computer Science

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2015

Author dc:creator

• Easterling, David R.

Chair dc:contributor.committeechair

• Watson, Layne T.

Committee members dc:contributor.committeemember

• Ramakrishnan, Naren
• Cao, Yang
• Borggaard, Jeffrey T.
• Cameron, Kirk W.
• Thacker, William Ivanhoe

• Multiobjective optimization
• stochastic optimization
• deterministic op- timization
• biomechanics
• quadratic optimization
• DIRECT
• QNSTOP
• KNITRO
• SPAN
• simulated annealing
• homotopy
• constrained clustering

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:3901

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/51189