Estimations of Confidence Intervals for Six Common Similarity Indices by Numerical Simulations
Zhengling Yang, Ru-Xue Wang, Bo-Feng Shi, Di Wang, Jun Zhang · 2020
In the fields of big data, signal analysis and smart grid, the calculations of similarity or distance between two time series are commonly employed. Most of the signals (time series) in the real world are fluctuating and noised. The similarity between the two signals is usually a compound outcome synthesized from their fluctuating components and deterministic components. For example, the well-known Pearson correlation coefficient is mainly the similarity between the fluctuating components in the two actual signals, and has a large confidence interval. In this paper, the basic properties of six common similarity indices, i.e., the Pearson correlation coefficient, the cosine similarity, the Tanimoto similarity, the Dice similarity, the mutual information and the maximal information coefficient (MIC), are studied. Their confidence intervals for the signals with a standard normal distribution random component are numerically simulated. If the original signals are z-score normalized, the confidence intervals of the Tanimoto similarity and the Dice similarity are often smaller than those of the Pearson correlation coefficient, the cosine similarity, the mutual information and the maximal information coefficient. As a practical example of their applications, for a horizontal axis wind turbine, the optimal statistical time period of "wind speed - output electrical power" time series obtained by the six similarity indices is consistent with that obtained by the mechanism analysis.