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Optimal Distance Function for Locally Weighted Average Prediction of Just‐in‐Time Methods
Author(s) -
Fujimoto Yusuke,
Maruta Ichiro,
Sugie Toshiharu
Publication year - 2018
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1698
Subject(s) - mahalanobis distance , function (biology) , focus (optics) , mathematics , regular polygon , mathematical optimization , computer science , algorithm , key (lock) , statistics , geometry , physics , evolutionary biology , optics , biology , computer security
This paper discusses the optimal distance function for Just‐in‐Time prediction. We focus on the standard Locally Weighted Average (LWA) prediction with Mahalanobis distance, and find the optimal distance which minimizes the prediction error. The key idea of this work is to introduce an integral which works as a model of the LWA prediction. This integral approximates the LWA prediction, and it becomes easier to discuss analytically. The main result of this paper is to show that the optimal distance function for such integral is constructed through a convex optimization. A numerical example and an experiment with a motor are shown to demonstrate the validity of the proposed distance function.