 Research
 Open Access
A method for evaluating discoverability and navigability of recommendation algorithms
 Daniel Lamprecht^{1}Email authorView ORCID ID profile,
 Markus Strohmaier^{2, 3} and
 Denis Helic^{1}
 Received: 12 February 2017
 Accepted: 3 October 2017
 Published: 11 October 2017
Abstract
Recommendations are increasingly used to support and enable discovery, browsing, and exploration of items. This is especially true for entertainment platforms such as Netflix or YouTube, where frequently, no clear categorization of items exists. Yet, the suitability of a recommendation algorithm to support these use cases cannot be comprehensively evaluated by any recommendation evaluation measures proposed so far. In this paper, we propose a method to expand the repertoire of existing recommendation evaluation techniques with a method to evaluate the discoverability and navigability of recommendation algorithms. The proposed method tackles this by means of first evaluating the discoverability of recommendation algorithms by investigating structural properties of the resulting recommender systems in terms of bow tie structure, and path lengths. Second, the method evaluates navigability by simulating three different models of information seeking scenarios and measuring the success rates. We show the feasibility of our method by applying it to four nonpersonalized recommendation algorithms on three data sets and also illustrate its applicability to personalized algorithms. Our work expands the arsenal of evaluation techniques for recommendation algorithms, extends from a oneclickbased evaluation towards multiclick analysis, and presents a general, comprehensive method to evaluating navigability of arbitrary recommendation algorithms.
Keywords
 Navigation
 Recommender systems
 Decentralized search
Background
Websites with large collections of items need to support three ways of information retrieval: (1) retrieval of familiar items; (2) retrieval of items that cannot be explicitly described, but will be recognized once retrieved; and (3) serendipitous discovery [1]. For a website with a large collection of items, such as an ecommerce website or a video platform, (1) can be enabled with a fulltext search function. For (2) and (3), however, a search function is generally not sufficient. These types of information retrieval are, therefore, often supported by recommendations that connect items and enable discovery and navigation.
The links generated by a recommender system are, by their very conception, meant to be navigated and used for exploration and navigation. When a website provides recommendations along with each item, the items and the associated recommendations form a recommendation network—an implicit view of a recommender system, where items are nodes and recommendations are edges. Figure 1 shows an example of such a network. This type of recommendations is frequent on ecommerce websites, such as Amazon’s “customers who bought this also bought”.
Knowing more about recommendation networks would give website operators the possibility to assess the effects of recommendations and help to produce recommendations that make it easier for users to discover and explore items. While a few studies have already looked at recommendation networks and provided first important insights into the nature and structure of these networks [8–11], there is no systematic approach to evaluating the network effects of recommendation algorithms both statically (discoverability) and dynamically (navigability).
The main contribution of this paper is a general method for evaluating navigability of arbitrary recommendation networks via both topological analysis and the evaluation of navigation models by simulation. The application of established techniques from network science allows us to present a novel method that extends common evaluation measures towards a pathbased evaluation and expands the arsenal of existing recommendation evaluation techniques with two dimensions that have not received sufficient attention so far.
The method consists of two parts: first, we analyze discoverablity, the property of a recommendation algorithm to enable users to reach items. We evaluate it by looking at aspects of the recommendation network topology, namely, components, bow tie structure and path lengths.
Second, we investigate navigability, which measures the degree to which a recommendation algorithm is able to assist users to actually navigate and explore an item collection. We evaluate the practical navigability of a recommendation network using simulations based on three navigation models established in the literature, namely, pointtopoint navigation [12], navigation via berrypicking [13], and navigation via information foraging [14].
This method is an extension of an evaluation method for navigability of recommendation algorithms of the previous work by the authors [15].
We show the feasibility of this method by applying it to four nonpersonalized recommendation algorithms on three data sets and investigate their properties. However, our method is not limited to evaluating nonpersonalized recommendation algorithms, but can be applied to any recommendation algorithms including personalized instances. We, therefore, illustrate the general suitability of our method and report initial results on personalized recommendations.
Related work
Related work to this paper can be grouped into three parts: evaluation of recommeder systems, network science, and networktheoretic evaluation of recommender systems.
Evaluation of recommender systems
Initially, recommender systems were mostly evaluated in terms of prediction accuracy [16]. However, the focus on accuracy has been found to neglect other import applications of recommender systems such as support for the discovery of novel items, browsing, or learning about diverse recommendations from related genres, and may lead to a bias towards popular items [9, 17] or a filter bubble effect [18]. For these reasons, a vast array of evaluation metrics for additional properties of recommender systems has been developed.
Prediction accuracy
The prediction accuracy is measured by comparing ratings predicted by the recommendation algorithm to a withheld set of actual user ratings and computing the deviation, for example, with the rootmean squared error (RMSE). Accuracy metrics have traditionally received the most attention in the evaluation of recommender systems [16].
Diversity
A recommendation list consisting only of very similar (e.g., all Star Trek films) can have a high prediction accuracy, but actually a low utility for users. Diversity measures the difference among a set of jointly shown recommendations and can be regarded as the opposite of similarity [19, 20]. Diversified recommendations have been found to lead to increased user satisfaction [21].
Novelty
Much like a lack of diversity, recommending only wellknown (popular) items to users is of little use. Metrics for novelty refer to the difference between past and present experiences [16, 20, 22] and measure the degree of recommendations leading to unfamiliar items.
Serendipity
Serendipity, or pleasant surprise, measures the fraction of recommendations that are both novel (surprising) and relevant (interesting) [2, 16, 23].
Coverage
Coverage describes how many items a system can generate recommendations for (prediction coverage), and how many items are effectively ever recommended to users (catalog coverage) [2, 16, 23]. As such, coverage is a simple measures that shows how many items a recommendation algorithm renders discoverable.
Network science
To evaluate discoverability and navigability, we make use of approaches from network science. Ever since Milgram’s smallworld experiments [24], researchers have been making efforts to understand navigability and in particular efficient navigation in networks. Kleinberg [12, 25] and Watts [26] formalized the property that a navigable network requires short paths between all (or almost all) nodes. Formally, such a network has a low diameter bounded by a polynomial in log(n), where n is the number of nodes in the network, and a giant component containing almost all the nodes exists. In other words, because the majority of network nodes are connected, it is possible to reach all or almost all of the nodes, given global knowledge of the network. The low diameter and the existence of a giant component constitute necessary topological conditions for network navigability. In this paper, we apply a set of standard networktheoretic measures to assess if a network satisfies them.
Kleinberg also found that an efficiently navigable network possesses certain structural properties that make it possible to design efficient local search algorithms (i.e., algorithms that only have local knowledge of the network) [12]. The delivery time (the expected number of steps to reach an arbitrary target node) of such algorithms is then sublinear in n. In this paper, we investigate the efficient navigability of networks through the simulation of a range of search and navigation models.
Networktheoretic evaluation of recommender systems
The static topology of recommendation networks has been extensively studied for the case of music recommenders. Their corresponding recommendation networks have been found to exhibit heavytail degree distributions and smallworld properties [8], implying that they are efficiently navigable with local search algorithms. Celma and Herrera [9] found that collaborative filtering provided the most accurate recommendations, while at the same time made it harder for users to navigate to items in the long tail. A hybrid recommendation approach and contentbased methods were able to provide better novel recommendations. These results suggest that a tradeoff exists between accuracy and other evaluation metrics. For movie recommendations, Mirza et al. [27] proposed to measure discoverability in the bipartite recommendation graph of users and items as an evaluation measure.
A first study [10] has already explored the discoverability and reachability of the recommender systems of IMDb using an analysis method similar to the one presented in this work. The corresponding recommendation networks were shown to generally lack support for navigation scenarios. However, the use of diversified recommendations was able to substantially improve this and lead to more navigable recommendation networks. While these analyses have shown certain topological properties and first aspects of navigability, we still know very little about the dynamics of actually using recommendations to find navigational paths through a recommender system.
Methods
In the following, we describe the general approach, the data sets, recommendation algorithms we use and how we derive the corresponding recommendation networks.
General approach
 1.
Discoverability Discoverability is the property of a recommendation algorithm to enable users to reach items. To evaluate it, we examine the static topology of a recommendation network and evaluate the discoverability by means of the bow tie structure and path lengths.
 2.
Navigability Navigability measures the degree to which a recommendation algorithm is able to assist users to actually navigate and explore an item collection. We evaluate the practical navigability of recommendation networks using simulations based on three different navigation models established in the literature: (a) pointtopoint navigation [12] as an example of goaloriented navigation with a single fixed goal; (b) navigation via berrypicking [13] as an example of goaloriented navigation with multiple and variable goals; and (c) navigation via information foraging [14] as an example of exploration.
Data sets
We use two types of items (namely, books and movies) from three data sets for this paper.
MovieLens ^{2} is a film recommender system maintained by GroupLens Research at the University of Minnesota. For this work, we use the data set consisting of one million ratings^{3} from 6000 users on 4000 movies. Each user in the data set has rated at least 20 movies.
BookCrossing is a book exchange platform.^{4} For this work, we use a 2005 crawl of the website [21]. As a preprocessing step, we filter out implicit ratings and combine the ratings of duplicate books with identical titles and authors. Furthermore, to be able to obtain meaningful results from the recommendation algorithms, we condense the data set and only keep ratings from users who rated at least five books and books which were at least rated 20 times. This leaves us with roughly 50,000 ratings by 1088 users on 3637 books.
IMDb is a database about movies and TV shows.^{5} We use a 2015 crawl of the website [10], from which we use all items published in the years of 2013 and 2014. We again condense the data set and only keep ratings from users who rated at least five books and books which were at least rated 20 times. This yields a data set of 2,254,873 ratings for 6690 titles by 37,216 users.
Recommendation algorithms
We calculate recommendations in the following way: for a given set of items I and a recommendation algorithm R, we use R to compute the pairwise similarities for all pairs of items \((i, j) \in I\). For each item \(i \in I\), we then define the set of the topN most similar items to i as \(L_{i, N}\). We investigated \(N \in \left[ 1, 20\right]\), which we consider a plausible range for recommender systems. We then create a directed topN recommendation network \(G\left( V, N, E\right)\), where \(V = I\), N is the number of recommendations available for each item and \(E = \{ \left( i, j\right)  i \in I, j \in L_{i, N}\}\). This method leads to recommendation networks with constant outdegree and varying indegree—representing a typical setting for topN recommendations such as Amazon.com’s Customers Who Bought This Item Also Bought.
For simplicity’s sake, we investigate recommendation algorithms based on nonpersonalized recommendations. The similarities these recommendations are based on, however, are directly taken from the similarities used in the recommendation algorithms. They, therefore, represent the recommendations (and the recommendation networks) as an unregistered or newly registered user would see them. For most websites, the vast majority of visitors does not contribute or register—this is known as the participation inequality or the 9091 Rule (90% lurkers, 9% intermittent contributers, and 1% heavy contributers) [28–30]. It seems likely that, for example, YouTube only has little preference information from about 90% of its visitors and, therefore, frequently needs to show nonpersonalized recommendations. However, our method is general and also applicable to personalized recommendation algorithms. We exemplarily demonstrate this in section and report first results.
We use each of the following four recommendation algorithms in this work.
Association rules (AR)
Association rules are based on the marketbasket model, where, in this case, we put all items rated by the same user into a basket and regard ratings as binary only (i.e., rated/not rated). For every ordered pair of items (i, j), we then evaluate a simple algorithm inspired by the Apriori algorithm [31] and rank all items by how much more likely an item is to be consumed if another item was consumed. Specifically, we compute the fraction of coratings of i and j over the total ratings of i (i.e., the fraction users who rated both i and j, out of those who rated i). Let \(U_i\) be the set of users who rated item i. We can then compute this as as \(\frac{U_i \cap U_j}{U_i}\). This is also known as the confidence of an association rule. To compensate for the popularity of j, we then divide by the fraction of users who did not rate i but still rated j. Let \(\overline{U}_i\) be the set of users who did not rate item i. We can then divide by \(\frac{\overline{U}_i \cap U_j}{\overline{U}_i}\) to counter the effect of highly popular items that are likely to be corated with every item, but would not be very useful as a recommendation. We then take the topN items most likely to be corated with an item by this measure.
Collaborative fltering (CF)
Interpolation weights (IW)
Matrix factorization (MF)
Evaluating discoverability
The first step of our proposed evaluation method assesses the discoverability of a recommendation algorithm, which measures the static reachability of items in a recommender system and represents a prerequisite for efficient navigability. We evaluate discoverability in two parts: effective discoverability (bow tie structure) and efficient discoverability (path lengths).
Effective discoverability
Description
The analysis of the partition with the bow tie model allows us to assess the effective discoverability of a recommendation algorithm. This model is a prominent model for the partitioning of a directed network, originally developed for the analysis of the Web [34]. The model partitions a network into three major components: the largest strongly connected component (SCC), wherein all nodes are mutually reachable, a component of all nodes from which SCC can be reached (IN) and a component of all nodes reachable from SCC (OUT). Figure 2 shows the model in more details and explains the components. Note that the components of the bow tie model do not necessarily correspond to components in a networktheoretic sense: while the SCC does form a strongly connected component, for example, the IN component generally consists of multiple components. This implies that the SCC is reachable from any node in IN, but not all nodes within IN are mutually reachable. The IN component of the bow tie model, therefore, represents oneway navigational flows in the network.
Results and interpretation
Figure 3 shows the bow tie membership over N (i.e., the number of recommendations available at each item). In general, the size of the SCC (i.e., the largest strongly connected component) in the recommendation networks grows with N. This follows from the increasing density in the network—in fact, as N increases, at some point, all items are bound to end up in the SCC. The size of the SCC is related to catalog coverage [23], which measures the fraction of items which are recommended. However, it also measures the size of the largest set of items that are not only recommended but also mutually reachable and, therefore, discoverable.
In realworld examples, the number of immediately visible recommendations typically lies between 4 and 12. For instance, Amazon recommends between five and eight items (depending on screen resolution), YouTube recommends 12 videos and IMDb lists six related films. If our examples generalize to these data sets, this comparison shows that standard recommendation approaches with five recommendations at each item allow users to explore between 11 and 99% of all items (cf. Fig. 3). For 20 recommendations, the sizes of the SCCs increase to 43–100%. Discoverability, therefore, depends on both the number of recommendations and the choice of algorithm.
The recommendations generated by association rules result in an SCC of \(11\%\) (MovieLens), \(59\%\) (BookCrossing) and \(14\%\) (IMDb) for five recommendations. With 20 recommendations at each item, this percentage somewhat improves to 34, 84, and 43%. For the other algorithms at \(N=5\) recommendations, the SCC sizes range from 75 to 99%, thus providing better effective discoverability in the resulting networks. For \(N=20\), the sizes further increase. Overall, the recommendations generated by matrix factorization perform best and lead to close to \(100\%\) of items in the SCC for all values of \(N \ge 5\).
The recommendations for the IMDb data set lead to a visibly more fragmented bow tie structure of the networks. A potential explanation for this lies in the sparsity of the data set: the rating matrix for IMDb contained just \(0.91\%\) of all possible entries, whereas for the other data sets, this was the case for \(4.16\%\) (MovieLens) and \(1.26\%\) (BookCrossing). Furthermore, the larger number of users in the IMDb data set leads to a substantially smaller fraction of possible coratings between items being present, thus making it more difficult for the association rules, collaborative filtering, and interpolation weights algorithms, which rely on coratings to generate the recommendations. As a result, the recommendation networks also show a substantially larger clustering coefficient than the other data sets. This does not occur as strongly for the matrix factorization algorithm, as this algorithm learns associations between items and latent factors. Therefore, if two items were never corated by any user, but still share a strong association with common factors, they are still deemed similar and can be recommended. However, the recommendation networks for IMDb generated by matrix factorization do also show larger clustering coefficients than the other data sets, indicating the presence of a number of densely interconnected (clustered) regions.
Even when a larger number of recommendations is present, users tend to prefer the ones at the top of a list [35].
For this reason, we also look at the results for \(1\ldots 4\) recommendations. The first thing that stands out is the stronger fragmentation of these networks. For just one recommendation, discovery of items in the networks is hardly possible, as one recommendation per item is not enough to form connected components. For two recommendations, discovery is at least partially enabled, in particular for matrix factorization, where for BookCrossing (\(53\%\)) and MovieLens (\(40\%\)), a substantial share of the items is already in a mutually reachable component. For all algorithms except association rules, four or five recommendations lead to fairly navigable networks for all investigated data sets. This suggests that when decluttering interfaces, a minimum of four or five recommendations should be kept to keep the system discoverable.
Apart from the SCCs, Fig. 3 shows that, overall, the dominant components are IN and SCC, except for fewer than five recommendations, where the networks are more fragmented. This implies that the network mainly consists of a core and items with recommendations leading to it. A detailed analysis of where links from IN component lead to underlines this intuition: In all networks for \(N=5\), more than \(68\%\) of all links from items in IN point to the SCC, and for \(N=20\) , this is the case for more than \(74\%\). From a navigational perspective, this means that items in the SCC can be directly reached from most items, but items in IN are in many cases only reachable by direct selection, e.g., via search results. We also find that for collaborative filtering and interpolation weights, the items in the SCC have a higher number of ratings than the ones in the remainder of the network. This could contribute to explaining a popularity bias identified in recommender systems [9, 17].
In addition, the OUT component include a relevant number of nodes for some combinations of algorithms and data sets. For the case of collaborative filtering and BookCrossing for \(N = 5\), two separate strongly connected components with different sizes emerge: SCC and OUT. An explanation for this situation could again be found in the average number of ratings for items, which was substantially higher for items in the SCC. As collaborative filtering recommendations are calculated based on the centered cosine similarity, items with few coratings are more likely to reciprocate their recommendations for other items with only few ratings, and popular items with many coratings are more likely to recommend other popular items. This makes items in OUT more likely to remain in that component.
Likewise, for the IMDb networks, the items in the OUT component again were also rated less frequently than the ones in the SCC. To improve discoverability for collaborative filtering, the bow tie analysis could be used to introduce specific recommendations to better connect the network.
Findings
We find that the discoverability depends on both the number of recommendations shown (the more the better) and on the recommendation algorithm, where matrix factorization perform best. In terms of the bow tie structure, we find that the networks are dominated by a strongly connected core of items together with an IN component leading to it. This implies that items in the core are reachable from most items. Constructing navigable recommender systems could potentially be facilitated with the help of a modified algorithm to specifically recommend items based on this analysis.
Efficient discoverability
Description
As the second step in evaluating discoverability, we investigate how efficiently recommendation algorithms enable item discovery.
Results and interpretation
Figure 4 plots the distribution of the median path lengths of all nodes in the largest components for \(N = 5\) and \(N = 20\) recommendations for MovieLens. The other data sets are qualitatively very similar. Overall, we find that increasing the number of recommendations leads to smaller distances in the recommendation networks. This confirms that the number of recommendations shown has a substantial influence on discoverability.
For all recommendation networks we investigate, the sizes of the largest strongly connected component (within which the path lengths were computed) increase as N is raised from 5 to 20. For example, for the recommendations for BookCrossing generated by association rules, the size of the largest strongly connected component increases from 59 to 80% of all items. Despite this, the median path length decreases from 7 to 4. However, this phenomenon has actually been observed for many types of graphs [36]. A possible explanation can be found in the increasing density of the networks: even though the largest strongly connected component increases in size, the number of recommendations for each item also strongly increases. This enables additional paths between items.
The diameters (the maximum path lengths in the SCCs) they range from 12 to 38 for \(N=5\) and 7 to 25 for \(N=20\). Large distances between pairs of nodes in a recommendation network such as these raise the question of whether users would actually undergo click sequences of this length to navigate the items. Analysis of Wiki game data, where players actively try to find shortest paths, has shown that humans need an average of three clicks more than the shortest possible paths [37]. To compare, the maximum of medians range from 7 to 28 for \(N = 5\) and 4 to 17 for \(N = 20\).
In terms of recommendation algorithm, matrix factorization leads to the shortest paths, followed by interpolation weights. To investigate the influence of path lengths further, we now turn our attention to the evaluation of navigability and its practical aspects.
Findings
We examine the distributions of shortest paths between nodes in the largest components and find that the number of recommendations exerts a strong influence on the resulting path lengths. Some of the distances between nodes (up to 38 hops) are potentially too long for reasonably efficient navigation. Matrix factorization and interpolation weights lead to the shortest distances.
Evaluating navigability
Personalized recommendations
In the previous sections, we have demonstrated the application of our proposed evaluation method to nonpersonalized recommendation algorithms. However, our method is not limited to them, but can be applied to any recommendation algorithm. To illustrate this, we now demonstrate the general suitability of our method to personalized recommendation approaches and report initial results.
Description

Pure We compute a candidate set of similar items for an item—these are simply the nonpersonalized recommendations. Then, we select the N items from this set that have the highest predicted rating for the specific user.

Mixed We again compute the set of similar items as for the pure recommendations, but only use the N / 2 recommendations with the highest predictions and the N / 2 top nonpersonalized recommendations (without introducing duplicates).
Results and interpretation
Findings
Discussion
We have presented a novel evaluation method that expands the repertoire of recommendation evaluation measures with a technique to evaluate discoverability and navigability. Our method is based on an evaluation conducted in two steps: the first step evaluates the discoverability by looking at the bow tie structure and path lengths. The second step evaluates the navigation dynamics of recommendation networks by simulating three different navigation models, namely, pointtopoint navigation, navigation via berrypicking, and navigation via information foraging.
This method presents a comprehensive approach to evaluating the discovery and navigation dynamics in recommender systems. Particularly for websites such as Netflix or YouTube, where no clear ordering of items exists, recommendations play a vital part of the interface. For these websites, discoverability and navigability are critical aspects that cannot be properly captured by any of the previously proposed evaluation measures. Conducting the evaluation method proposed in this paper broadens our understanding of recommendation algorithms and leads to a more complete characterization of their properties.
To demonstrate the feasibility of our method, we applied it to three exemplary data sets and highlighted differences in discoverability and navigability for four different, nonpersonalized, recommendation algorithms. In general, we find that the number of recommendations available at each item has a substantial influence. For five recommendations, we find that the recommendation algorithms we investigate considerably limit the discoverability and navigability. With distances in the recommendation networks up to 38 hops, path lengths could be too long for users. In terms of navigation dynamics, our results show that five recommendations also severely restrict the retrieval of items. However, we also find that both properties can be improved by raising the number of recommendations. For the three navigation scenarios, we investigate we find that the explorative scenarios inspired by berrypicking and information foraging lead to the best retrieval performance, while the scenario based on pointtopoint navigation was less well supported. While increasing the number of recommendations represents a simple solution, a large number of recommendations could potentially clutter the interface and overwhelm users [35]. This shows that there is still a substantial potential to improve recommendation algorithms to better support navigation dynamics.
As for the recommendation algorithms, we find that the recommendations generated by an interpolation weights and matrix factorization performed best overall. The association rule recommendations we investigated did not support discoverability and navigability very well and led to very fragmented recommendation networks. This suggests that exploiting the collective knowledge present in interaction of items and latent factors as done by interpolation weights and matrix factorization leads to more easily navigable recommender systems. However, more work is necessary to confirm these findings.
The recommendation algorithms selected for this work are established in the literature. Their selection was naturally arbitrary, but they serve the purpose of illustrating the evaluation and, therefore, do not limit our main contribution of presenting a novel evaluation method. We have shown the suitability of our method for nonpersonalized recommendation algorithms and thereby effectively inspected recommendation networks for users who are either new to the system or simply browsing without being registered. There is evidence that a large share of web users is not registered users and, therefore, only interacts with nonpersonalized recommendations. We also illustrated the applicability of our method for personalized recommendations by reporting the results of a sample combination of parameters and showed that perhaps, a bit counterintuitively, increased personalization leads to less discoverable networks.
The navigation models applied in this method are wellestablished in the research community and cover a wide range of typical user interaction scenarios with information systems in general, and recommender systems in particular. Greedy search, the basis for our navigation scenarios based on these models, has been used in the previous work to analyze navigation dynamics in networks [39, 40] and has been found to produce comparable results to human navigation patterns [41, 42]. The navigation models we used do, however, have limitations and were deliberately kept simple, as the focus of our work was not on the information seeking models and their validity but on the properties of the recommendation algorithms. However, this does not limit our work, as our evaluation method does not depend on this particular model, which can easily be adapted or exchanged in future work. Possible enhancements to the navigation models could include a teleportation element modeling jumps between items without recommendations like in PageRank. This could be useful to represent the interplay with search function that also enables users to directly switch (jump) to arbitrary items. To model familiarization with a system, a learning component (e.g., for memorizing preferred paths) could be included. However, it should be noted that simplistic navigational models have been proven to be useful in many applications, such as PageRank.
In realworld information systems, recommendations are typically used in conjunction with other navigational links such as a navigational menu. Websites may also make use of other dynamically generated links such as trending items or news items. To study the navigational dynamics of sites of this type, it is necessary to look at the combination of all navigational aids. For example, it would easily be possible to add a navigational menu to the evaluations presented in this paper. This would likely have the effect of always leading to a fully connected network, as every page would then be connected to the home page. As this would also mask any navigational inefficiencies in the network, we believe that testing the recommendation algorithm on its own is still a useful addition to the toolkit for website operators.
Conclusions
Our work extends common evaluation measures of recommendation algorithms towards a pathbased evaluation. The presented method estimates the discoverability of items and assesses the navigability of the resulting recommendation network. Just as the evaluation of recommender systems has been shifting from accuracybased measures towards diversification, coverage and timedependent evaluations, we believe that our method helps push the frontier of recommendation algorithms towards producing recommendations that make it easier for users to discover and explore items.
While the results of our experiments are limited to the data sets, our method to evaluating the discoverability and navigability of recommendation networks is general. We have demonstrated our method extensively for nonpersonalized algorithms, but also shown its usefulness for personalized algorithms. It can be applied to arbitrary recommendation networks, thereby acting as a novel tool of measurement for an increasingly important dimension of recommendation systems.
Declarations
Authors' contributions
All authors contributed equally to the analyses performed in this paper. DL wrote the code. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Availability of data and materials
The code used for the analyses in this paper is available at https://github.com/lamda/RecNet. The data set for MovieLens is available at https://grouplens.org/datasets/movielens/100k/ and the data set for BookCrossing is available at http://www2.informatik.unifreiburg.de/~cziegler/BX. The data set for IMDb was crawled by the authors in a previous study and cannot be shared for legal reasons.
Consent for publication
Not applicable.
Ethics approval and consent to participate
Not applicable.
Funding
This research was supported by a Grant from the Austrian Science Fund (FWF) [P24866].
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Authors’ Affiliations
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