An Explicit Analytical Estimation of the Validity of the Tanimoto Similarity by Confidence Intervals in Mathematical Statistics

In order to evaluate the validity of the Tanimoto similarity in the fields of machine learning and data mining rigorously, the “validity” is interpreted as the term of confidence intervals of a point estimation in mathematical statistics, if the sets inputted into Tanimoto similarity are extended to two finite random variable samples. The range of confidence intervals (the lower bound subtracts from the upper bound) gets smaller, the validity gets more valid. Based on the existing references, an explicit analytical expression from the Pearson correlation coefficient to the Tanimoto similarity is deduced. The Fisher transformation is employed to estimate the confidence intervals of the sample Pearson correlation coefficient. Then the confidence intervals of the Tanimoto similarity are generated, if the lower bound and the upper bound is substituted into the explicit analytical expression respectively. Numerical experiments confirm the veracity of the explicit analytical expression. In the ultra-short term wind speed prediction by spatial correlation, the root mean square error of wind speed prediction is decreased by about 17%, if substitute the Tanimoto similarity for the Pearson correlation coefficient to sort out the most similar neighbors in the k-nearest neighbor prediction model. To improve the accuracy and reliability of wind power prediction in the green renewable energy field, the Tanimoto similarity is much better than the Pearson correlation coefficient in the correlation estimation between the wind speeds.