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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| _version_ | 1832567934100176896 |
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| author | Yuanhong Liu Zhiwei Yu Ming Zeng Shun Wang |
| author_facet | Yuanhong Liu Zhiwei Yu Ming Zeng Shun Wang |
| author_sort | Yuanhong Liu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-4c73b6dc49c9447b87b740c3ca8b3e07 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-4c73b6dc49c9447b87b740c3ca8b3e072025-02-03T01:00:02ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/837185837185Dimension Estimation Using Weighted Correlation Dimension MethodYuanhong Liu0Zhiwei Yu1Ming Zeng2Shun Wang3Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin 150001, ChinaSpace Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin 150001, ChinaSpace Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin 150001, ChinaSpace Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin 150001, ChinaDimension 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.http://dx.doi.org/10.1155/2015/837185 |
| spellingShingle | Yuanhong Liu Zhiwei Yu Ming Zeng Shun Wang Dimension Estimation Using Weighted Correlation Dimension Method Discrete Dynamics in Nature and Society |
| title | Dimension Estimation Using Weighted Correlation Dimension Method |
| title_full | Dimension Estimation Using Weighted Correlation Dimension Method |
| title_fullStr | Dimension Estimation Using Weighted Correlation Dimension Method |
| title_full_unstemmed | Dimension Estimation Using Weighted Correlation Dimension Method |
| title_short | Dimension Estimation Using Weighted Correlation Dimension Method |
| title_sort | dimension estimation using weighted correlation dimension method |
| url | http://dx.doi.org/10.1155/2015/837185 |
| work_keys_str_mv | AT yuanhongliu dimensionestimationusingweightedcorrelationdimensionmethod AT zhiweiyu dimensionestimationusingweightedcorrelationdimensionmethod AT mingzeng dimensionestimationusingweightedcorrelationdimensionmethod AT shunwang dimensionestimationusingweightedcorrelationdimensionmethod |