Time series labeling based on nearest fuzzy representation of data distribution

In this study, three new time series labeling methods have been generated. Fuzzy c-means clustering which is an unsupervised learning method have been used in these methods. Each cluster has been labeled regard to its center magnitude. Observations have been assigned to the clusters with respect to their distances to the cluster?s centers. Hence, the time series of labels have been extracted from time series of observations. As a next step, -nearest neighbor rule have been performed on time series of labels to obtain smoother curve of labels. As difference from classical method, instead of distance, the previous and next labels of data have been considered in the determination of neighbors. The efficiency of offered methods has been tested on bispectral index data sets which are related with brain activity and it has been proved that the application of KNN rule on time domain satisfies an increasing on average of classification accuracies.Considering increasing effect of membership function on classification accuracies, four new theorems about nearest fuzzy representations of data distributions have been offered, as second part of this study. Two perspectives have been followed in the constructions of theorems. In the first perspective, five points of data distribution have been matched with five points of parametric triangular and trapezoidal type membership functions. In the second perspective, frequency tables have been used. The objective functions have been constructed considering the normalized percentages and midpoints of frequency tables. Parametric triangular and exponential membership functions which are consistent with histogram of data have been evaluated via minimization problem. The classification processes have been performed on bispectral index data sets to see whether the offered theorems have increasing effects on classification accuracies or not. The obtained classification accuracies are compared by other ones which are evaluated by using another approach that previously used in the literature. At the end of the analysis of data sets, it has been proved that the membership function approaches offered in this thesis have increasing effects on average of classification accuracies.