In this section, we will discuss definitions of serendipity and diversity, and overview algorithms that improve these properties.
Definition of serendipity
The term serendipity was coined by Horace Walpole by referencing a Persian fairytale, “The Three Princess of Serendip,” in 1758. In the fairytale, the three princes of the country Serendip ventured out to explore the world and made many unexpected discoveries on their way.Footnote 1 In his letter, Horace Walpole mentioned that the princes were “always making discoveries, by accidents & sagacity, of things which they were not in quest of” .
The dictionary definition of serendipity is “the faculty of making fortunate discoveries by accident”.Footnote 2 However, there is no consensus on the definition of serendipity in recommender systems. Some researchers require items to be relevant and unexpected to be considered serendipitous [19, 22], whereas other researchers suggest that serendipitous items are novel and unexpected [19, 32]. However, the most common definition of serendipity includes all three components: relevance, novelty and unexpectedness [17, 18].
Novelty and unexpectedness also have multiple definitions, which results in eight variations of serendipity . Novelty has two variations: strict novelty—the user has never heard about an item; and motivational novelty—the user had not thought of consuming an item, before this items was recommended to him/her. Unexpectedness has four variations: unexpectedness (relevant)—the user does not expect to enjoy the item; unexpectedness (find)—the user does not expect to find the item on his/her own; unexpectedness (implicit)—the item is very dissimilar to what the user usually consumes; and unexpectedness (recommend)—the user does not expect the item to be recommended to him/her. Relevance has one variation and indicates how much the user enjoys consuming the item. Since serendipity consists of relevance, novelty and unexpectedness, relevance has one variation, novelty has two variations and unexpectedness has four variations, there are eight variations of serendipity (proposed in ): strict serendipity (relevant), strict serendipity (find), strict serendipity (implicit), strict serendipity (recommend), motivational serendipity (relevant), motivational serendipity (find), motivational serendipity (implicit) and motivational serendipity (recommend). We employ these variations in this study.
There are three categories for serendipity-oriented algorithms : (a) reranking algorithms (these algorithms change the order of items in recommendation lists using relevance scores provided by accuracy-oriented algorithms); (b) serendipity-oriented modifications (these algorithms are based on particular accuracy-oriented algorithms); and (c) novel algorithms (these algorithms are not based on any common accuracy-oriented algorithms, but rather utilize different techniques to improve serendipity).
Reranking algorithms improve serendipity by changing the order of the output of accuracy-oriented algorithms . These algorithms often use relevance scores to filter out potentially irrelevant items first and then use other techniques to promote potentially serendipitous ones. For example, the algorithm proposed by Adamopoulos and Tuzhilin first filters out items likely to be irrelevant and obvious to a user and then orders items based on their overall utility for the user. The latter is based on how different an item is to users’ expectations and on relevance scores for this item provided by an accuracy-oriented algorithm . Another example is the algorithm proposed by Zhang et al. Auralist . The algorithm consists of the three other algorithms: Basic Auralist, which is responsible for relevance scores, Listener Diversity, which is responsible for diversity, and Declustering, which is responsible for unexpectedness. The algorithm orders items in the recommendation list according to the final score, which is represented by a linear combination of the scores provided by the three algorithms.
Serendipity-oriented modifications refer to common accuracy-oriented algorithms modified with a purpose of increasing serendipity . The main difference between reranking algorithms and modifications is that modifications are always based on particular accuracy-oriented algorithms, whereas a particular reranking process can be applied to any accuracy-oriented algorithm, which provides relevance scores. For example, Nakatsuji et al. modified a common user-based collaborative filtering algorithm (k-nearest neighbor algorithm)  by replacing the user similarity measure with relatedness. It is calculated using random walks with restarts on a user similarity graph . The graph consists of nodes corresponding to users and edges corresponding to similarities based on an item taxonomy. By utilizing the relatedness, for a target user, the algorithm picks a neighborhood of users who are not necessarily similar, but who are in some way related to the target user . Another example of modifications is the algorithm proposed by Zheng et al. The algorithm is based on PureSVD (a variation of the singular value decomposition algorithm) . The main difference between PureSVD and its modification is that the objective function of the modification includes components responsible for unexpectedness, whereas the objective function of PureSVD lacks these components .
Novel serendipity-oriented algorithms neither fall into reranking nor into modifications categories, as they are not based on any common accuracy-oriented algorithms and do not use relevance scores provided by any accuracy-oriented algorithms . For example, TANGENT recommends items using relevance scores and bridging scores, where both kinds of scores are inferred using a bipartite graph . The graph contains nodes that represent users and items, and edges that represent ratings. The algorithm calculates relevance scores using random walks with restarts and bridging scores based on the calculated relevance scores . Another example of an algorithm that belongs to the category of novel algorithms is random walk with restarts enhanced with knowledge infusion . The algorithm orders items in recommendation lists according their relatedness to a user profile. The relatedness is calculated using random walks with restarts on an item similarity graph, where nodes correspond to items, and edges correspond to similarities between these items. To calculate the similarities, the authors used the spreading activation network based on Wikipedia and WordNet .
Most existing algorithms have been designed to achieve serendipity measured by artificial evaluation metrics due to the lack of publicly available datasets containing user feedback regarding serendipity. The results of artificial evaluation metrics might be misleading, as the assumptions that these metrics are based on might not correspond to the reality due to the lack of ground truth . Furthermore, performance of most existing algorithms is not compared with that of others . In this article, we propose a reranking algorithm and compare it with state-of-the-art algorithms in evaluation conducted on the first publicly available dataset containing serendipity ground truth.
Definition of diversity
Diversity is a property of a recommendation list or a set of them composed by one or several recommender systems. It reflects how dissimilar items are to each other in the list [4, 14]. To measure diversity inside a list, researchers often calculate an average pairwise dissimilarity of items in a recommendation list [4, 14], where dissimilarity can be represented by any metric, which reflects how dissimilar items are to one another. A dissimilarity metric is often based on attributes of items. The higher the average pairwise dissimilarity, the higher the diversity of the list.
Diversity is considered as a desirable property of a recommender system, as it was proven to improve user satisfaction , and by diversifying the recommendation results, we are likely to suggest an item satisfying a current need of a target user . A fan of the movie The Matrix is likely to prefer a recommendation list of movies similar to The Matrix, including this movie, rather than a recommendation list consisting of The Matrix sequels only.
Diversity is not always related to dissimilarity of items in a particular recommendation list. The term can also refer to diversity of recommendations provided by different recommender systems , diversity across recommendation lists suggested to all the users of a particular system , or diversity of recommendations to the same user in a particular system over time . In these cases one needs a more complicated diversity measure than the pairwise average diversity of items inside one recommendation list.
Greedy reranking algorithms are very common in improving diversity of recommendation lists. They create two lists of items (a candidate list and a recommendation list), and iteratively move items from the candidate list to the recommendation list [4, 14]. In each iteration, these algorithms calculate different scores, which depend on the algorithm. Based on these scores, the algorithms pick an item from the candidate list to be moved to the recommendation list [4, 14]. For example, the TD algorithm, which our algorithm is based on, calculates in each iteration average similarities between each item in the candidate list and items in the recommendation list and uses the obtained scores to pick an item that is the most relevant but at the same time the most dissimilar to the items already added to the recommendation list .
Another group of the algorithms optimized for diversity take diversity into account in the process of generating recommendations. For example, Su et al. proposed an algorithm that integrates diversification in a traditional matrix factorization model . Another example of an algorithm falling into this category is diversified collaborative filtering algorithm (DCF) that employs a combination of support vector machine and parametrized matrix factorization to generate accurate and diversified recommendation lists .
To the best of our knowledge, studies that focus on both serendipity and diversity are very limited. In this article, we propose an algorithm that improves both serendipity and diversity.