A New Similarity Measure for the Profiles Management Ahmed Belkhirat Department of Information Systems College of Computer and Information Sciences King Saud University Riyadh, Saudi Arabia belkhirat@ksu.edu.sa Abdelkader Belkhir Dept. of computer science USTHB University Algiers, Algeria belkhir@lsi-usthb.dz Abdelghani Bouras Industrial Engineering Dept. College of engineering King Saud University Riyadh, Saudi Arabia bouras@ksu.edu.sa Abstract— The measure of similarity is necessary for the study of several problems such as: the multimedia adaptation, detection of intrusion based behavior, adaptation of web services …. In this article, the definition of a new measure of similarity that deals with the shared objects properties, their values and the weight of each property is proposed. Keywords- similarity measure; Jaccard factor; user profil; characteristic weight I. INTRODUCTION The objects identification is a recurrent problem in several applications. This identification is applied in security [1, 2], adaptation in multimedia systems, or in web service [3], and auto configuration (domestic network) [4]. Thus, every object (user, web service, multimedia document) is represented by a profile that describes the object [5] thanks to its features. For this reason, we can use a similarity measure [6, 7] in order to determine the resemblance of two objects. This resemblance can be dictated by the common properties of two objects. However, the practice shows that the objects’ properties are quantified. It requires the representation of the similarity measure in terms of the shared properties and their values. In several cases, it is necessary to take into account the relevance of some object properties. In case of predominance of some properties in the object description, we must refine the similarity measure in terms of properties, their values and their relevance. This article is organized as follows: the section 2 presents a measure inspired from Jaccard similarity measure [5] while taking into account the quantization or atomization of properties. We demonstrate that the proposed measure verifies the properties of a similarity measure. Then, we give the equivalent distance as well as its properties. Section 3 presents a refinement of the measure presented in section 2. In a similar manner, we will verify the properties of this measure. Again, we provide the equivalent distance measure and verify its properties. Section 4 presents two properties of our measure face to usual measures. Then we conclude on the importance of the new similarity measure. II. SIMILARITY MEASURE Let P be a set of objects profiles (individuals, documents, web sites …). These profiles, noted x, are described by n characteristics x i : x= ( ) n x x x ,..., , 2 1 . A similarity measure, noted sim is defined by an application from ) ( IN P P P ⊆ × into [ ] 1 , 0 . [ ] 1 , 0 : → × P P sim It verifies the following properties: ( ) 0 , : , ) 1 ( ≥ ∈ ∀ y x sim P y x P ( ) ( ) ( ) y x sim y y sim x x sim P y x P , , , : , ) 2 ( ≥ = ∈ ∀ ( ) ( ) x y sim y x sim P y x P , , : , ) 3 ( = ∈ ∀ We note that the more the objects have features in common, the more they are similar. The similarity is maximal for two identical objects. Inversely, it decreases when most of features are different. A measure of distance, noted dist , is a defined application from P P × into [ ] 1 , 0 . [ ] 1 , 0 : → × P P dist It verifies the following properties: ( ) 0 , : , ) 4 ( ≥ ∈ ∀ y x dist P y x P ( ) 0 , : , ) 5 ( = ∈ ∀ x x dist P y x P ( ) ( ) x y dist y x dist P y x P , , : , ) 6 ( = ∈ ∀ 2011 UKSim 13th International Conference on Modelling and Simulation 978-0-7695-4376-5/11 $26.00 © 2011 IEEE DOI 10.1109/UKSIM.2011.55 255