Estimating Local Intrinsic Dimensionality Using Thresholding Techniques
The problem of determining the number of dominant (signal related) singular values in estimating Local Intrinsic Dimensionality (LID) using Singular Value Decomposition (SVD) is considered. Earlier a method for estimating the LID using the SVD was proposed when the observed data is corrupted by noise. Problems are encountered when the Signal to Noise Ratio (SNR) gets very high or very low. For noisy data the algorithm will produce higher dimensionality even when the observed system has low dimension. A signal/noise separation criterion is proposed based on the analysis of the perturbation matrix to identify the number of dominant singular values. Results are presented for some standard chaotic signals and compared to the previously used approach, showing the superiority of the criterion used at high SNR’s.
KeywordsChaotic System Singular Value Decomposition Data Matrix Separation Criterion Thresholding Technique
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