Abstract
Time series approximation techniques can provide approximate results for the data in another new space by dimensionality reduction or feature extraction. In this study, we propose a new time series approximation strategy based on the Fuzzy C-Means (FCM) clustering and elaborate on a comprehensive analysis of relationships between reconstruction error and classification performance when dealing with various representation (approximation) mechanisms of time series. Typically, time series approximation leads to the representation of original time series in the space of lower dimensionality compared to the dimensionality of the original input space. We reveal, quantify, and visualize the relationships between the reconstruction error and classification error (classification rate) for several commonly encountered representation methods. Through carefully structured experiments completed for sixteen publicly available datasets, we demonstrate experimentally and analytically that the classification error obtained for time series in the developed representation space becomes smaller than when dealing with original time series. It has been also observed that the reconstruction error decreases when increasing the dimensionality of the representation space. In addition, when compared with the state-of-the-art algorithms reported in the literature, experimental results show the efficiency of the proposed approach.