Dimension Estimation Using Weighted Correlation Dimension Method
Dimension reduction is an important tool for feature extraction and has been widely used in many fields including image processing, discrete-time systems, and fault diagnosis. As a key parameter of the dimension reduction, intrinsic dimension represents the smallest number of variables which is used...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/837185 |
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| Summary: | Dimension reduction is an important tool for feature
extraction and has been widely used in many fields including image processing, discrete-time systems, and fault diagnosis. As
a key parameter of the dimension reduction, intrinsic dimension
represents the smallest number of variables which is used to describe a complete dataset. Among all the dimension estimation
methods, correlation dimension (CD) method is one of the most
popular ones, which always assumes that the effect of every point
on the intrinsic dimension estimation is identical. However, it is
different when the distribution of a dataset is nonuniform. Intrinsic
dimension estimated by the high density area is more reliable than
the ones estimated by the low density or boundary area. In this
paper, a novel weighted correlation dimension (WCD) approach is
proposed. The vertex degree of an undirected graph is invoked to
measure the contribution of each point to the intrinsic dimension
estimation. In order to improve the adaptability of WCD estimation, k-means clustering algorithm is adopted to adaptively select
the linear portion of the log-log sequence (logδk,logC(n,δk)).
Various factors that affect the performance of WCD are studied.
Experiments on synthetic and real datasets show the validity and
the advantages of the development of technique. |
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| ISSN: | 1026-0226 1607-887X |