Advances in Artificial Intelligence

Volume 2016 (2016), Article ID 9386368, 10 pages

http://dx.doi.org/10.1155/2016/9386368

## Effect of Collaborative Recommender System Parameters: Common Set Cardinality and the Similarity Measure

^{1}Computer Engineering Department, College of Computer Science, King Khalid University, P.O. Box 394, Abha, Saudi Arabia^{2}Electrical Engineering Department, Faculty of Engineering and Architecture, Ibb University, Ibb, Yemen

Received 25 March 2016; Revised 13 May 2016; Accepted 22 May 2016

Academic Editor: Theo Van Der Weide

Copyright © 2016 Mohammad Yahya H. Al-Shamri. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Recommender systems are widespread due to their ability to help Web users surf the Internet in a personalized way. For example, collaborative recommender system is a powerful Web personalization tool for suggesting many useful items to a given user based on opinions collected from his neighbors. Among many, similarity measure is an important factor affecting the performance of the collaborative recommender system. However, the similarity measure itself largely depends on the overlapping between the user profiles. Most of the previous systems are tested on a predefined number of common items and neighbors. However, the system performance may vary if we changed these parameters. The main aim of this paper is to examine the performance of the collaborative recommender system under many similarity measures, common set cardinalities, rating mean groups, and neighborhood set sizes. For this purpose, we propose a modified version for the mean difference weight similarity measure and a new evaluation metric called users’ coverage for measuring the recommender system ability for helping users. The experimental results show that the modified mean difference weight similarity measure outperforms other similarity measures and the collaborative recommender system performance varies by varying its parameters; hence we must specify the system parameters in advance.

#### 1. Introduction

Today, Web users face an abundance of choices when they surf the Web. Hence, recommender systems (RSs) as many Web personalization tools become necessary to offer Web users personalized items they may like. These systems become available in many Web sites that cover social networks, e-commerce, e-business, e-tourist, and many others [1, 2]. A recent survey for the applications of the recommender systems and their classifications is given in [2].

Basically, RS compares users based on a suitable similarity measure which plays an important rule for the success of the whole system. However, different similarity measures often lead to different sets of neighbors for a given active user. A good similarity measure will produce a close set of neighbors for a given active user [3]. Actually, many of the existing similarity measures for collaborative recommender systems rely on the overlapping between users. Nevertheless, the size of this overlapping is not explored in detail where most of the previous work studied similarity measures based on a predefined number of common items [3–8].

This motivates us to study the cardinality effect of the common set on the performance of different similarity measures for collaborative recommender systems. The proximity between two users based upon a single commonly rated item is surely weaker than that of 20 common rated items. Moreover, the second case is more reliable because close sets of neighbors are guaranteed. This paper studies the effect of three parameters, namely, cardinality of the common rated items, the rating mean group, and the number of neighbors on the performance of the collaborative recommender system. The contributions of this paper are threefold:(1)The notion of users’ coverage is introduced as opposed to items’ coverage.(2)We proposed a modified version for mean difference weights similarity measure.(3)Our experiments are implemented on both synthetic and real data sets.

The rest of this paper is organized as follows: a literature review is given in Section 2 and an introduction to collaborative recommender systems is given in Section 3. The effect of the cardinality of the common set on the performance of different similarity measures is introduced in Section 4. Section 5 presents the experimental methodology used for examining many similarity measures while Section 6 discusses the results of the conducted experiments. Finally, we conclude our work in Section 7.

#### 2. Literature Review

Many papers have discussed and proposed many similarity measures, but they fixed the lowest number of the common items in advance and examined their proposals based on that predefined number [3–9]. For example, Al-Shamri [3] examined traditional approaches and proposed a power coefficient as a similarity measure but he assumed the common set size is greater than or equal to five. Breese et al. [9] did empirical analysis for many similarity measures used for collaborative filtering and realized the effect of a low size of common set. Therefore, they suggested default voting for unrated items to enhance the system performance. The same approach is used by many authors to overcome the low number of common items [10]. This is in agreement with the findings of [11] where they showed that participants of their system were more confident in their choices when the recommender had a high rating overlap with the decision maker. However, default voting approach may not reflect the actual user taste for unrated items.

Usually, active users correlate highly with neighbors having very small number of corated items. These neighbors are terrible predictors because they were based on tiny samples of common items. Authors of [12, 13] devalue similarity weights that were based on a small number of corated items by adding a correlation significance-weighting factor of to the original weight, where is the number of corated items. Thus, a full contribution will be only for those users having greater than 50 common items with the active user. However, for many cases it is impossible to find this much of common items.

Vozalis and Margaritis [14] tested Pearson correlation coefficient (PCC) with a fixed number of common items of 25. Later, they tested the same system under many threshold values of common items, namely, 1, 10, 20, 30, and 40. They assumed that the best common item threshold is 20. However, they fixed the number of neighbors and did not consider the user mean rating group in their work. Moreover, all experiments they carried out tested only one similarity measure, PCC. Our paper studies the system performance under varying similarity measure and three other parameters, namely, cardinality of the common set, user mean rating group, and the number of neighbors for the active user. These parameters are tested using synthetic and real datasets. Five choices of common items are tested; the first choice assumes at least one common item and then at least 5, 10, 15, and 20 common items for the remaining choices.

#### 3. Collaborative Recommender System

Many types of recommender systems are proposed based on the way they build user models and their work principle [1]. Systematically, any recommender system passes through five phases to perform its job, namely, data collection, profile formulation, similarity computation, neighborhood set selection, and predictions and recommendations. The effect of each phase on the RS performance depends on its position on the RS stack. The early phases affect the RS more because the performance of the next stages depends on them. The most popular RS is the collaborative recommender system (CRS) which relies on the opinions of possible similar users and hence allows the system to recommend out-of-the-box items [4, 5].

Formally, CRS has users, , rating explicitly or implicitly items, and , such as news, Web pages, books, movies, or CDs. Each user has rated a subset of items . The declared rating of user for an item is denoted by and the user’s average rating is denoted by [4].

During similarity computation phase, the RS matches the active user to the available database of the training users according to a suitable similarity measure. This value is a measure of how closely two users resemble each other. Once similarity values are computed, the system ranks users according to their similarity values with the active user to extract a set of neighbors for him. After that the CRS assigns a predicted rating to all the items seen by the neighborhood set and not by the active user. The predicted rating, , indicates the expected interestingness of the item to the user [3, 8].

#### 4. Common Set Cardinality and the Similarity Measure

Similarity computation is the third phase for building a recommender system. Obviously, the accuracy and the reliability of this phase rely largely on the two phases below it. This paper concentrates on the similarity computation phase and assumes that all remaining phases are fixed and accurate except changing the number of neighbors for some experiments. For similarity computation, many similarity measures are used in literature and this paper will examine only three of them. The first similarity measure is Pearson correlation coefficient (PCC) [3–5, 14] which is the most popular similarity function for memory-based CRS:

PCC computes the similarity between two users based on the common ratings, , both users have declared: where is the cardinality of the common set, . Logically, as the common set becomes large, we expect that the computed similarity reflects the true value of similarity between any two users.

The second similarity measure we examined is called cosine similarity measure [1, 3]. This measure treats each user as a vector in the items’ space and finds the cosine of the angle between the two vectors as a measure for the similarity between them:

Again, the common set is the core for this calculation. A third similarity measure is called mean difference weights (MDW) similarity measure proposed by Bobadilla et al. [7]. They used genetic algorithm (GA) learning for evolving the weights for the rating differences between users. However, these weights can be assumed to be fixed to the mean of each difference weight interval that has been proposed in [7]. For our experiments, we set as done by Al-Shamri and Al-Ashwal [8]:

We took into account the point raised by [8] about dividing formula (4) by the difference between the maximum and minimum values of the rating scale. They argued that this factor is not necessary because formula (4) already divides the weights by their number. The numerator cannot exceed in any way since . The only effect this factor has is to reduce the similarity values, which in turn will reduce the contribution of each neighbor’s rating in the aggregation process.

##### 4.1. Modified Mean Difference Weights Similarity Measure

The mean difference weights similarity measure does not take the user’s mean into consideration because it was proposed for learning algorithms like GA. However, a correction factor based on the rating means of the two users in consideration can be added when we fix the weights and rely on the direct calculations without a learning algorithm. In this paper, we propose the following correction factor:

The modified mean difference weights similarity measure is simply formula (4) multiplied by the correction factor that takes the mean of each user into consideration:

Because of the correction factor, this measure does not give high similarity value for users with one common item if their rating means are different. This similarity measure is called modified mean difference weights (MMD).

##### 4.2. User Coverage

By increasing the cardinality of the common set, we expect that the recommender system could not help all the active users. Therefore, we have to measure the system ability to help the intended users through a measure we call it users’ coverage or penetration, which is different from that of items’ coverage (this will be discussed later). This metric is defined by the following definition.

*Definition 1 (users coverage). *The users’ coverage of a given recommender system with a minimum predefined cardinality of the common set is the number of users benefitting from the recommender system (who can get neighbors and hence predictions) over all the active users of the system:where is the number of active users getting predictions from the system with a given cardinality of the common set (CS) and is the total number of the active users.

This measure helps us to study the effect of increasing the cardinality of the common set on the usability of the system. Low value of the users’ coverage means that the system could not help many users because they have low overlapping between them.

##### 4.3. Sample Dataset for Empirical Analysis

We construct a sample dataset in Table 1 for 19 users with 12 items. The first user is the active user and the remaining 18 users are training users. The zero value for an item indicates that this item has not been rated yet by the user and therefore can be suggested for him. The sample data set has the following specifications:(i)It should cover many cardinalities of the common set. Therefore, we take many values 1, 2, 5, 8, and 10.(ii)It should cover three rating mean groups (small, medium, and high).(iii)The sample data is arranged such that one opposite-minded user and three users with different rating means (low, medium, and high) are available for each cardinality of the common set.(iv)The last two users represent opposite-minded users to the active user with two different common items, 8 and 10.(v)For each rating mean group, the user with the bigger cardinality of the common set inherits the same items of the user with the lower cardinality to see the effect of increasing the cardinality of the common set without changing the previous set of items.