Ergodic theorems arising in correlation dimension estimation

1996 ◽  
Vol 85 (1-2) ◽  
pp. 25-40 ◽  
Author(s):  
Regis J. Serinko
Keyword(s):  
Correlation Dimension ◽  
Ergodic Theorems ◽  
Dimension Estimation

INVESTIGATION OF CORRELATION DIMENSION ESTIMATION IN HEARTBEAT TIME SERIES

2006 ◽  
Vol 16 (09) ◽  
pp. 2481-2498
Author(s):  
STAVROS NIKOLOPOULOS ◽  
GEORGE MANIS ◽  
ANASTASIA ALEXANDRIDI
Keyword(s):  
Heart Rate ◽  
Time Series ◽  
Heart Rate Variability ◽  
Data Acquisition ◽  
Correlation Dimension ◽  
Specific Problem ◽  
Euclidean Norm ◽  
Application Process ◽  
Dimension Estimation ◽  
Sensitive Method

The Correlation Dimension estimation is an especially sensitive method which allows for important information to be extracted from the signal under investigation. However, due to its sensitivity, its parameters as well as details of the application process must be chosen carefully and customized to each specific problem. In this paper, we examine the application of the Correlation Dimension estimation in the case of heart rate variability signals. Specifically, we investigate issues which are not discussed in other similar studies or which are chosen differently, such as the use of the Euclidean norm and the Theiler window. We also document with detail the method of data acquisition and make a case for the importance of proper recordings the lack of which leads to controversial results.

scholarly journals Dimension Estimation Using Weighted Correlation Dimension Method

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Yuanhong Liu ◽  
Zhiwei Yu ◽  
Ming Zeng ◽  
Shun Wang
Keyword(s):  
Dimension Reduction ◽  
Correlation Dimension ◽  
Clustering Algorithm ◽  
Estimation Methods ◽  
Intrinsic Dimension ◽  
Boundary Area ◽  
Dimension Estimation ◽  
Complete Dataset ◽  
Correlation Dimension Method ◽  
Weighted Correlation

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(log⁡δk,log⁡C(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.

A vectorized algorithm for correlation dimension estimation

1997 ◽  
Vol 229 (6) ◽  
pp. 375-378 ◽  
Author(s):  
Eran Toledo ◽  
Sivan Toledo ◽  
Yael Almog ◽  
Solange Akselrod
Keyword(s):  
Correlation Dimension ◽  
Dimension Estimation
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