| Summary: | 碩士 === 國立臺灣大學 === 資訊工程學研究所 === 89 === The decomposition method
is currently one of the major
methods for solving
support vector machines (SVM).
An important issue of this method
is the selection of working sets.
In the first part of this thesis through the design of
decomposition methods
for bound-constrained SVM formulations
and from the experimental analysis
we propose a simple
selection of the working set
which leads to faster
convergences for difficult cases.
Numerical experiments on different
types of problems are conducted
to demonstrate the viability of the
proposed method.
The second part of this thesis focuses on decomposition methods
for multi-class SVM.
As SVM was originally
designed for binary classification,
how to effectively extend it for
multi-class classification is still
an on-going research issue.
Several methods have been proposed where
typically we construct a multi-class classifier
by combining several binary classifiers. Some
authors also proposed methods that consider all
classes of data at once. As it is computationally
more expensive on solving multi-class problems,
comparisons on these methods using large-scale
problems have not been seriously conducted.
Especially for methods solving multi-class SVM
in one step, a much larger optimization
problem is required
so up to now experiments
are limited to small data sets.
In this thesis we give decomposition
implementation for
two such ``all-together" methods:
\cite{VV98a,JW98a} and
\cite{KC00a}. We then
compare their
performance with three methods
based on binary classification:
``one-against-all,'' ``one-against-one,''
and DAGSVM \cite{JP00a}.
Our
experiments indicate that the ``one-against-one'' and DAG
methods are
more suitable for practical use than the
other methods.
Results also show that for large problems
methods by considering all data at once in general need
fewer support vectors.
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