Elsevier

Fuzzy Sets and Systems

Volume 278, 1 November 2015, Pages 98-117
Fuzzy Sets and Systems

Discovering user preferences using Dempster–Shafer theory

https://doi.org/10.1016/j.fss.2015.06.004Get rights and content

Abstract

This paper presents a model for discovering user preferences from item characteristics. Based on the theory of evidence, the model estimates a probability interval for an item represented by a set of features. This interval represents the item preference within a group of users and it is computed according to preferences expressed in the past. Additionally, a method for moving among different domains and fusing information is outlined. The issue of efficient search subsets of interest within the inclusion lattice is investigated and algorithms are presented.

Introduction

Research in Recommendation Systems has been exponentially growing since the development of the Internet, more precisely, with the development of e-commerce. A Recommender System (RS) usually provides a rating or a preference for each user. To provide this recommendation an RS requires information about the preferences of the user in relation to the website (movies, books, songs, hotels, etc.). This information can be acquired explicitly by asking the users to rate items or implicitly by monitoring users' behavior (booked hotels or heard songs). RS can also use other kinds of information as demographic features (e.g., age, gender) or social information. The research related to RS has been focused on movies, music and books recommendations [1], being music recommendation the most studied topic although, recently, it has been applied in other e-commerce domains [2].

No hassle of going from shop to shop to find that perfect dress on a snowy day, e-commerce not only provides convenience but also a much larger variety of products and lower prices. E-commerce works perfectly when you know exactly what you want: you browse through some online sites, compare prices and buy from the site offering the best deal. But what about random discovery when you are undecided about what you want to buy?

For example, we all have our preferred clothing style: sporty, casual, classic, floral, vintage etc. In an offline world scenario we would walk into a shop and tell one store employee what we were exactly looking for: a red maxi dress with a floral print. This request can be replicated partially by filters on an eCommerce store. Dress: Yes. Style: Maxi. Color: Red. Number of Results: 200+. Then, we browse through the numerous pages with all the visible results to find one dress with a floral print. Whereas, in the store the employee would have asked you a few more questions about the style you are seeking: androgynous, feminine, vintage, etc., and presented you with limited options (<10) filtered to your taste and preferences from the 200+ available in the store. This illustrates a limitation in the online world, where it is hard to understand your specific style and get direct feedback to filter according to a user preference. The employee can then repeat the process to further cross-sell products that would go well with the dress to complete the outfit: a bag, a pair of shoes, jewelry, maybe even a hat! This employee has made the overwhelming task of discovery when you are unsure of what a consumer needs to buy much easier. In the online world the selection would depend on the user browsing through the sites hoping that they are accessorising correctly.

To bridge this offline-online gap in discovering products, RS comes to the rescue. By understanding users' browsing and purchase history, via implicit and explicit actions, we can recommend them products with the higher probability of being preferred. In the example above, about searching for the red floral maxi dress, after having analyzed users style preferences in the 200+ results, we can push up to the top of the results page these products having the higher probability of being bought by the user, according to the RS. Similarly, further understanding about this user and other users preferences on the product can make the RS recommend a set of items that the dress can be worn with. Over time, with continuous improvement, the RS understands users preferences better, in order to predict more precisely the selection of the products.

In this paper, we face the problem of filtering from an e-shop catalogue a set of products which might be interesting for the customer on the basis of preferences expressed by a group of users within a market segment. This problem is studied from a theoretical point of view by means of Dempster–Shafer Theory of Evidence (D–S Theory). The purpose of this work is to show how the D–S Theory can be used in the context of RS. The first approach of this type was introduced by Zhang and Li [3]. They suggested to use D–S Theory as a mean to combine recommendations from different systems, each one considered as an independent source of information. Instead, we focus on how to use D–S Theory internally in a recommendation system. This approach goes generally with skepticism of dealing with combinations of items, which might not fit real world inventories. In this paper we propose to move from items to features in order to (i) reduce problem dimensionality and (ii) to infer user preferences even when they are not made explicit. Preferences induced by each feature are considered as an independent source of information, then combined by a rule. In the second part of this paper, it is studied how to explore the subset inclusion lattice, once Belief and Plausibility are mapped over it. We outline some efficient algorithms to perform such an exploration.

The remainder of this contribution is organized as follows: Section 2 provides some preliminaries regarding RS and D–S theory, Section 3 outlines the model adopted and describes the model application by means of an example. Sections 4 and 5 are focused on studying some questions related to complexity. Finally, Section 5 draws conclusions and future directions.

Section snippets

Recommender systems

RS were created out of the user needs to handle the increasing volume of information that is available in the world wide web [1]. The definition of a RS depends on several issues. The type of data available to provide the recommendation is the first issue to take into account. For example, it is possible to find ratings, information provided by the user when registration, or social relationships. The data can be provided both explicitly and implicitly. Explicit data are given by a customer (for

Discovering item sets using D–S theory

In this section it is studied how to identify item sets of interest using D–S Theory.

Some properties of the item set lattice

In order to complete the model presented in Section 3, this section shows how to explore in an efficient way the item subset lattice in order to find the elements of our interest. Therefore, some questions regarding complexity are analyzed.

Complexity is twofold: on one side the number of item subsets increase exponentially. This makes unfeasible to list all possible subsets in order to compute their Belief and Plausibility, and then to select those of interest, even for small inventories. The

Efficient exploration of the item set lattice

A major issue concerns the efficient exploration of the item set lattice. However, monotonicity of Belief and Plausibility with respect to inclusion enables branch and bound searching strategies. This also holds if we employ any convex combination of the Belief and Plausibility, that is, if we considerDes(X)=σPl(X)+(1σ)Bel(X)σ[0,1],X2Ω where σ represents the conservatism degree (being σ=0 full conservative, σ=1 the opposite). We will call Des(X) the desirability of the subset X.

Obviously Ω

Conclusions and future work

The D–S Theory of Evidence provides a rich and not yet fully explored framework to build RS. In this paper we presented a preliminary example of application, in which votes expressed by users on some items are considered as proxies of which features are more appealing and which less for the whole item set. After, information provided with respect to different product characteristic are combined in order to answer complex questions, such as what is the most appropriate set of products to propose

References (22)

  • M.J. Pazzani

    A framework for collaborative, content-based and demographic filtering

    Artif. Intell. Rev.

    (1999)
  • Cited by (0)

    1

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