Property Testing of Data Dimensionality
Data dimensionality is a crucial issue in a variety of settings, where it is desirable to determine whether a data set given in a high-dimensional space adheres to a low-dimensional structure. We study this problem in the framework of property testing: Given a query access to a data set S, we wish t...
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| Main Authors: | , |
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| Format: | text |
| Language: | English |
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Institutional Knowledge at Singapore Management University
2003
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| Subjects: | |
| Online Access: | https://ink.library.smu.edu.sg/sis_research/1248 http://dl.acm.org/citation.cfm?id=644112 |
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| Institution: | Singapore Management University |
| Language: | English |
| Summary: | Data dimensionality is a crucial issue in a variety of settings, where it is desirable to determine whether a data set given in a high-dimensional space adheres to a low-dimensional structure. We study this problem in the framework of property testing: Given a query access to a data set S, we wish to determine whether S is low-dimensional, or whether it should be modified significantly in order to have the property. Allowing a constant probability of error, we aim at algorithms whose complexity does not depend on the size of S.We present algorithms for testing the low-dimensionality of a set of vectors and for testing whether a matrix is of low rank. We then address low-dimensionality in metric spaces. For vectors in the metric space l1, we show that low-dimensionality is not testable. For l2, we show that a data set can be tested for having a low-dimensional structure, but that the property of approximately having such a structure is not testable. |
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