Dimension Estimation Using Weighted Correlation Dimension Method

Algorithm 1

The calculating procedure of WCD.

Input: Signal dataset .

Output: Intrinsic dimension .

(1) Normalize the dataset between 0 and 1, then the distance matrix can be constructed by .

(2) Construct the similarity matrix . Where is the variance

of the dataset. The vertex degree, that is the weighted vector is defined as .

(3) The scale sequences are computed by

, . Where is the number of the scale .

(4) Compute the local bulk at point . , .

(5) In the scale , the global bulk is computed .

(6) The linear part of the log-log sequence is selected by -means

method and a curve is fitted using linear part by the linear least square method.

(7) Correlation dimension is calculated by the slope of the curve. .