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Manifold Integration: Data Integration on Multiple Manifolds

In data analysis, data points are usually analyzed based on their relations to
other points (e.g., distance or inner product). This kind of relation can be analyzed
on the manifold of the data set. Manifold learning is an approach to understand
such relations. Various manifold learning methods have been developed and their
effectiveness has been demonstrated in many real-world problems in pattern recognition and signal processing. However, most existing manifold learning algorithms
only consider one manifold based on one dissimilarity matrix. In practice, multiple
measurements may be available, and could be utilized. In pattern recognition systems, data integration has been an important consideration for improved accuracy
given multiple measurements. Some data integration algorithms have been proposed
to address this issue. These integration algorithms mostly use statistical information
from the data set such as uncertainty of each data source, but they do not use the
structural information (i.e., the geometric relations between data points). Such a
structure is naturally described by a manifold.
Even though manifold learning and data integration have been successfully used
for data analysis, they have not been considered in a single integrated framework.
When we have multiple measurements generated from the same data set and mapped
onto different manifolds, those measurements can be integrated using the structural
information on these multiple manifolds. Furthermore, we can better understand the
structure of the data set by combining multiple measurements in each manifold using data integration techniques.
In this dissertation, I present a new concept, manifold integration, a data integration method using the structure of data expressed in multiple manifolds. In order
to achieve manifold integration, I formulated the manifold integration concept, and
derived three manifold integration algorithms. Experimental results showed the algorithms' effectiveness in classification and dimension reduction. Moreover, for manifold
integration, I showed that there are good theoretical and neuroscientific applications.
I expect the manifold integration approach to serve as an effective framework for
analyzing multimodal data sets on multiple manifolds. Also, I expect that my research
on manifold integration will catalyze both manifold learning and data integration
research.

Identiferoai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2010-05-7735
Date2010 May 1900
CreatorsChoi, Hee Youl
ContributorsChoe, Yoonsuck
Source SetsTexas A and M University
Languageen_US
Detected LanguageEnglish
Typethesis, text
Formatapplication/pdf

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