Dimension Estimation Using Weighted Correlation Dimension Method

Abstract EN

Dimension reduction is an important tool for featureextraction and has been widely used in many fields including image processing, discrete-time systems, and fault diagnosis.

Asa key parameter of the dimension reduction, intrinsic dimensionrepresents the smallest number of variables which is used to describe a complete dataset.

Among all the dimension estimationmethods, correlation dimension (CD) method is one of the mostpopular ones, which always assumes that the effect of every pointon the intrinsic dimension estimation is identical.

However, it isdifferent when the distribution of a dataset is nonuniform.

Intrinsicdimension estimated by the high density area is more reliable thanthe ones estimated by the low density or boundary area.

In thispaper, a novel weighted correlation dimension (WCD) approach isproposed.

The vertex degree of an undirected graph is invoked tomeasure the contribution of each point to the intrinsic dimensionestimation.

In order to improve the adaptability of WCD estimation, k-means clustering algorithm is adopted to adaptively selectthe 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 andthe advantages of the development of technique.