Confidence Intervals of Six Distance Indices Estimated by Numerical Simulations

An important task in signal processing is to estimate the correlation between two signals by distance indices, which directly restricts the validity and reliability of the analysis results. This paper firstly studies the fundamental characteristics of six distance indices, i.e., the Manhattan distance, Euclidean distance, Chebyshev distance, Wasserstein distance, dynamic time warping (DTW), and maximal information coefficient (MIC) distance. Secondly, their confidence intervals are calculated by numerical simulations. The test signal is a standard normal distribution variable plus a deterministic function, i.e., a step (position), a ramp (velocity), a parabola (acceleration) function respectively. A wider range of confidence intervals implied a great uncertainty of a distance index. Simulations show that the Euclidean distance, Chebyshev distance and Wasserstein distance are usually better than the others. Lastly, as an example, using distance values calculated from the moving time window, the optimal lag time between the atmospheric pressure difference from Tianjin to Guangzhou and Guangzhou wind speed is generated, and the future Guangzhou wind speeds can be predicted reliably around the optimal lag time.