Ordered Sets for Data Analysis
This book dwells on mathematical and algorithmic issues of data analysis based on generality order of descriptions and respective precision. To speak of these topics correctly, we have to go some way getting acquainted with the important notions of relation and order theory. On the one hand, data of...
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| Main Author | |
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| Format | Journal Article |
| Language | English |
| Published |
27.08.2019
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| Subjects | |
| Online Access | Get full text |
| DOI | 10.48550/arxiv.1908.11341 |
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| Summary: | This book dwells on mathematical and algorithmic issues of data analysis
based on generality order of descriptions and respective precision. To speak of
these topics correctly, we have to go some way getting acquainted with the
important notions of relation and order theory. On the one hand, data often
have a complex structure with natural order on it. On the other hand, many
symbolic methods of data analysis and machine learning allow to compare the
obtained classifiers w.r.t. their generality, which is also an order relation.
Efficient algorithms are very important in data analysis, especially when one
deals with big data, so scalability is a real issue. That is why we analyze the
computational complexity of algorithms and problems of data analysis. We start
from the basic definitions and facts of algorithmic complexity theory and
analyze the complexity of various tools of data analysis we consider. The tools
and methods of data analysis, like computing taxonomies, groups of similar
objects (concepts and n-clusters), dependencies in data, classification, etc.,
are illustrated with applications in particular subject domains, from
chemoinformatics to text mining and natural language processing. |
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| DOI: | 10.48550/arxiv.1908.11341 |