Some Improvements Of Mahalanobis Distance Method And Its Application In Tourist Information Recommender System

The purpose of writing this paper is to work out an efficient intelligent recommendation method, which is working for Hong Kong University of Science and Technology's project"G-U229"– Virtual Computing Environment, Tourist Information Recommender System (TIRS) ). In order to do this, this paper mentions some mends of Mahalanobis Distance (MD) method, the first of which is the Weighted Mahalanobis Distance (WMD) method. WMD can give every variable a specific weight and take this into account. In the simulation, we can find that the matching rate of WMD is 66.7%, which is 5% higher than which of MD, cause the matching rate of MD is 61.1%.Furthermore, in order to utilize the scoring system well, the paper defines the Generalized Set and Fuzzy Generalized Set; gives some basic and statistical principles and their demonstrations. Based on which, the paper mentions Fuzzy Weighted Mahalanobis Distance (FWMD) method. In the simulation, we can find that the matching rates of FWMD of four indexes are 69.4%, 63.9%,58.3% and 81.8%, which are separately higher than those of WMD, cause the matching rates of WMD are 66.7%, 59.7%,51.9% and 80.6%.Finally, for the sake of improving MD, WMD and FWMD, because those methods only analyze the integrated distance between question samples and the expectation of each population, which could brings a lot of vulgar mistakes, this paper mentions a Multiple Discriminant method– Multiple Fuzzy Weighted Mahalanobis Distance (MFWMD) method. Except analyzing the integrated distance, MFWMD also takes some important variables into account. In the simulation, we can find that the matching rates of MFWMD for the four indexes are 94.4%,83.3%,71.3% and 84.3%, which are separately 25.0%, 19.4%,13.0% and 2.5% higher than the matching rates of FWMD, cause the matching rates of FWMD are 69.4%, 63.9%, 58.3% and 81.8%.Other than those, this paper provides the algorithms of MD, WMD, FWMD and MFWMD and testifies that their time complexities are all O(n~2). Besides, this paper also works out the Java procedures of MD, WMD, FWMD and MFWMD in order to do the simulation of them.