A histogram-valued observation is a specific type of symbolic objects that represents its value by a list of bins (intervals) along with their corresponding relative frequencies or probabilities. In the literature, the raw data in bins of all histogram-valued data have been assumed to be uniformly distributed. A new representation of such observations is proposed in this paper by assuming that the raw data in each bin are linearly distributed, which are called trapezoid-valued data. Moreover, new definitions of union and intersection between trapezoid-valued observations are made. This study proposes the k-nearest neighbour technique for classifying histogram-valued data using various dissimilarity measures. Further, the limiting behaviour of the computational complexities based on the performed dissimilarity measures are compared. To study the effect of using a distance instead of a dissimilarity measure, the Wasserstein distance is also used and the accuracy of the classification is compared. Some simulations are done to study the performance of the proposed procedures. Also, the results are applied to three various real data sets. Eventually, some conclusions are stated.

Keywords