The k-nearest Neighbor Classification of Histogram- and Trapezoid-Valued Data

Statistics, Optimization and Information Computing

article

Mostafa Razmkhah¹  FathimahAl-Ma¹  Sohrab Effati¹ 

[1] Ferdowsi University of Mashhad

关键词: Dissimilarity measure;    Histogram-valued data (HVD);    Supervised learning;    Trapezoid-valued data (TVD);    Wasserstein distance.;   

DOI  :  10.19139/soic-2310-5070-1451

来源: Istituto Superiore di Sanita

【 摘 要 】

‎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 neighbor technique for classifying histogram-valued data using various dissimilarity measures‎. ‎Further‎, ‎the limiting behavior of the computational complexities based on the performed dissimilarity measures are 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.

【 授权许可】

Unknown