A Geometric View of Similarity Measures in Data Mining

The main objective of data mining is to acquire information from a set of data for prospect applications using a measure. The concerning issue is that one often has to deal with large scale data. Several dimensionality reduction techniques like various feature extraction methods have been developed to resolve the issue. However, the geometric view of the applied measure, as an additional consideration, is generally neglected. Since each measure has its own perspective to the data, different interpretations may achieved on data depending on the used measure. While efforts are often focused on adjusting the feature extraction techniques for mining the data, choosing a suitable measure regarding to the nature or general characteristics of the data or application is more appropriate. Given a couple of sequences, a specific measure may consider them as similar while another one may quantify them as dissimilar. The goal of this research is twofold: evincing the role of feature extraction in data mining and revealing the significance of similarity measures geometric attributes in detecting the relationships between data. Differrent similarity measures are also applied to three synthetic datasets and a real set of ECG time series to examine their performance.