Matching Media Contents with User Profiles by means of the Dempster-Shafer Theory Luigi Troiano Irene D´ıaz Ciro Gaglione University of Sannio Oviedo University Sky Italia Department of Engineering Computer Science Department Interactive Tv Lab Benevento, Italy Gij´on, Spain Milan, Italy Email: [email protected] Email: [email protected] Email: [email protected] Abstract—The media industry is increasingly personalizing the new entities, along a self-growing process. Predictiveness of offering of contents in attempt to better target the audience. models make them also suitable to support the acquisition of This requires to analyze the relationships that goes established new contents and customers. between users and content they enjoy, looking at one side to the content characteristics and on the other to the user profile, These models are at the core logic of recommender sys- in order to find the best match between the two. In this paper tems (RS), that obtained large attention once Netflix showed we suggest to build that relationship using the Dempster-Shafer’s potentiality of algorithms in developing and supporting their Theory of Evidence, proposing a reference model and illustrating streaming platform [1]. Recommender systems gained large its properties by means of a toy example. Finally we suggest application because of the e-commerce diffusion. They are possible applications of the model for tasks that are common in the modern media industry. generally grouped in different types, including Content-based recommenders [2], Collaborative recommenders [3], Demo- I. INTRODUCTION graphic recommenders [4], and Hybrid recommenders [5]. The purpose of a recommender system is to provide a Digital technologies are radically changing the way of suggestion, regarding available alternatives, by scoring and performing business in media industry, with new possibilities ranking them according to the user preferences. In order to ac- of tailoring the catalog so that everybody has the chance complish its task, a recommender system requires information of enjoying contents that best fit his/her interests, often on regarding the user profile and habits with respect to the differ- demand, at the time that is most appropriate for each user. ent alternatives that can be proposed to him. This information Such a change is requiring to reformulate the way of building can be acquired explicitly by asking the users to rate items the content offering. Data collected from customers regarding or implicitly by monitoring users’ behavior (booked hotels or their profile and preferences become central, so models able heard songs). RS can also use other kinds of information as to interpret and to reason about data. demographic features (e.g, age, gender) or social information. These models aims to discover and exploit the relationship The research related to RS has been focused on movies, music that stands between users and media contents they enjoy. Here and books [6], being music recommendations the most studied the problem is not to ask directly the user what are his/her topic, although later it has been applied to other e-commerce interests and preferences, but to infer them by looking at those domains [7]. contents they access and to the feedback they provide about Similar to RS, we need data about user likings regarding them. The ultimate goal is to learn a model from data able to catalog items such as movies, series and shows. Such infor- arXiv:1704.03048v1 [cs.AI] 10 Apr 2017 link user to the vast catalog of contents made available by a mation can be gathered by asking the user to rate the items, large media company. e.g., by using stars or likes, or implicitly by monitoring the Looking at past interactions is useful to help users to customer behavior, e.g., which item enjoyed fully an which discover contents that they would appreciate as valuable part of partially, how often they accessed the content description, etc. the product they paid for. This means to improve the customer In addition we need other information regarding demographics retention and foster their upgrade towards more profitable such age, gender, family members, job, etc. The objective is to products. The benefits coming from the implementation and relate user profiles to content descriptors. Different techniques use of these models go beyond existing contents and cus- have been experimented in order to discover and exploit this tomers. They also help to propose new contents to existing relationship. Most of them take the form of information fusion. customers, and on the other way to support new customers Following the idea explored by [8], and more concretely in discovering existing contents. Soon, new contents and new the model developed in [9], we aim to build a relationship customers become part of the model, enriching the dataset of model based on the Dempster-Shafer’s Theory of Evidence (D- S theory) [10], [11] and to use it to make inference regarding DISCLAIMER. This article was prepared or accomplished by Ciro Gaglione in his personal capacity. The opinions expressed in this paper the relationship between users and contents. The reminder of are the authors’ own and do not reflect the view of Sky Italia. this paper is organized as follows: Section II provides some preliminaries regarding D-S Theory; Section III describes the model; Section IV outlines some examples of application; Section V draws conclusions and future directions. II. PRELIMINARIES The Dempster-Shafer theory, also known as the Theory of Evidence [10], [11], is used as basis for the preference model presented in [9]. In D-S theory, basic probabilities are allocated to subsets, instead of elements, according to the following definitions. Definition 1. A function m : 2Ω −→ [0, 1] over a set Ω is called a basic probability assignment if Fig. 1. The Boolean lattice of item subsets from Ω = {A,B,C,D} with m(∅)=0 and X m(A)=1 focal elements F (Ω) = {C,BC,AD.} [9] A∈2Ω Definition 2. Let Ω be a set, then A ⊆ Ω is a focal element if m(A) > 0. In addition, F (Ω) ⊂ 2Ω represents the set of constant as far as we move to nodes that do not a probability focal elements induced by m. mass assigned to them. As consequence of this property, we can identify regions of connected nodes, each assuming a Definition 3. Let m be a basic probability assignment function specific value of Belief or Plausibility, as illustrated by Fig. 2. over a set Ω. The Belief of A ⊆ Ω induced by m is defined In this example, focal elements are C, BC and AD with the as follows associated basic probability assignments mC , mBC and mAD Bel(A)= X m(B) (1) (assuming mC + mBC + mAD = 1). This leads to identify B⊆A 8 groups in the lattice, each with Belief and Plausibility Definition 4. Let m be a basic probability assignment function depending from a focal subset of F (Ω). Fig. 2 outlines these over a set Ω. The Plausibility of A ⊆ Ω induced by m is regions for both Belief and Plausibility. we can observe how defined as follows all portions of lattice associated to a given value of Belief or Plausibility are connected. Pl(A)= X m(B) (2) B∩A6=∅ The relationship between Plausibility and Belief is given by the following equation: Pl(A)=1 − Bel(A) (3) where A is the complement of A to Ω. When the probability basic assignments are given by differ- ent sources, it is possible to combine them. The first and most common combination method is known as the Dempster’s rule, that is defined as follows: Definition 5. Let m1 and m2 be two basic probability as- signments, the joint basic probability assignment is computed as 1 m1 2(A)= m1(B) · m2(C) (4) , 1 − Z X B∩C=A where Z = X m1(B) · m2(C) (5) B∩C=∅ is a measure of conflict between the two basic probability assignment sets. In addition, it is assumed m1,2(∅)=0. Fig. 2. Belief (top) and Plausibility (bottom) regions induced by F (Ω) = Belief and Plausibility are monotonic functions with respect {C,BC,AD} [9] to inclusion. This means that if we consider the lattice of Ω subsets, as shown in Fig. 1, Belief and Plausibility will If we sort the Belief (or Plausibility) values in ascending increase from bottom (Bel(∅)= Pl(∅)=0)to top(Bel(Ω) = order, we get a sequence of levels, each grouping the nodes Pl(Ω) = 1). In particular Belief and Plausibility will be kept into those that are below the level and over the level. For For instance, according to the example in Fig. 1 F (Ω) = {C,BC,AD}, we have Cr(BCD) = {C,BC} = Cr(BC) and Su(ABD) = Su(BD) = Su(AB) = {BC,AD}. It is straightforward that Cr(A) ⊆ Su(A), for all A ⊆ Ω. The core and support represent the basis for computing respectively the Belief and the Plausibility of A. The core and the support are able to group the subsets of Ω into classes of equivalence as (a) (b) the following definition states. Definition 8 (Cr− and Su− Equivalence). Two sets A and B are said to be Cr-equivalent if and only if Cr(A)= Cr(B)= Cr. A Cr-equivalence class is defined as the collection def ECr == {A ⊆ Ω | Cr(A)= Cr} (8) In addition, A and B are Su-equivalent if and only if Su(A)= Su(B) = Su. The Su-equivalence class obtained from this relation. is defined as (c) (d) def ESu == {A ⊆ Ω | Su(A)= Su} (9) Fig. 4(a) provides an example of Cr-equivalence class assuming as core Cr = {BC,C}.