Merging Latent Factors and Tags to Increase Interactive Control of Recommendations

Abstract

We describe a novel approach that integrates user-generated tags with standard Matrix Factorization to allow users to interactively control recommendations. The tag information is incorporated during the learning phase and relates to the automatically derived latent factors. Thus, the system can change an item's score whenever the user adjusts a tag's weight. We implemented a prototype and performed a user study showing that this seems to be a promising way for users to interactively manipulate the set of items recommended based on their user pro le or in cold-start situations.

1. INTRODUCTION

Optimizing the objective accuracy of algorithms that generate recommendations has led to considerable advances, but does not necessarily increase user satisfaction [ 3 ]. Hence, letting users in uence the recommendation process is increasingly considered an important goal in Recommender Systems (RS) research. Interactive RS have been proposed that use metadata such as user-provided tags for this purpose [ 5 ]. This has the advantage of using concepts that are meaningful to users without requiring explicit item descriptions. Using tags to express user preferences thus seems promising to improve user control and comprehension. However, attempts to increase interactivity (e. g. [ 5 ]) are typically independent of conventional Collaborative Filtering (CF) techniques and consequently do not consider existing user proles based on e. g. previous ratings. Moreover, the availability of precise and e cient algorithms such as Matrix Factorization (MF) [ 4 ] is not exploited. What is lacking, thus, are techniques that combine the accuracy-related bene ts of model-based RS with the easy-to-understand semantics of tags. We therefore propose an interactive recommending approach that integrates latent factors derived by standard SVD-like MF with tags users provided for the items. 2.

CONCEPT & PROTOTYPE

A range of techniques is available for integrating supplemental data into MF which has been shown to increase accuracy. These techniques, however, are typically very limited regarding user control. In addition, after being learned, the factors often exhibit no interpretable association with the supplemental information, which thus cannot be accessed by the user. In contrast, in [ 1 ], the data is explicitly used to establish a content-related association: Using a regressionconstrained formulation, the factors are considered as functions of content attributes. We initially follow this approach closely for incorporating item-speci c tag relevance information: For a set T of tags we de ne uA 2 RjUj jT j and iA 2 RjIj jT j representing their relationship with users U and items I, and rede ne the original MF model:

R PQT = uAu (iAi )T, (1) with u and i being the factor-tag matrices corresponding to users and items, respectively. However, explicit supplemental information may only be available either for users or for items. Generally, we act on the assumption that tagitem relevance scores have been calculated separately and iA is known a priori. Speci cally, we exploit tag relevance scores [ 5 ]: ait 2 [ 0, 1 ] describes the extent to which tag t is relevant for item i. In contrast, the corresponding matrix for users, uA, is considered to be unknown. Thus, we treat the whole term uAu implicitly at this step by just learning the user-factor matrix P as known from standard MF. With this constrained equation, we formulate the minimization problem as in [ 1 ] and apply gradient descent.

A user's u (calculated) interest in a particular factor f is numerically expressed by entry puf of P while entry qif of Q describes the extent to which item i possesses this factor. Although in our case tag relevance scores are only known for items, we can establish a relation between users and tags as well: Under the assumption that f re ects a certain characteristic which has the same semantic meaning for users and items [ 4 ], we extend the approach of [ 1 ] and transfer the learned relationship between tags and latent factors to the user side. In fact, we assume that the regression coe cients stored in i are equivalent to the implicitly assumed entries of the corresponding matrix u , such that: u = i =: . Thus, according to (1) we solve for uA:

P = uA , P = uAU

VT , uA = PV +UT , uA = P +

Since is generally not a square matrix, we rst calculate its pseudo-inverse + using SVD. Regarding the regression(2) constrained approximation of R in (1), this gives us: R uA uAU

T iAT uAU

TUT iAT TUT iAT

G

HT (3)

G 2 RjUj jT j basically stores all vectors for the users and summarizes uAU. Conversely, H 2 RjIj jT j holds the item vectors. 2 RjT j jT j is a diagonal matrix containing positive eigenvalues of T. The general interest of a certain user regarding all tags is now expressed by vector au of uA, which is basically the counterpart of the tag-item relevance scores. Since they also comprise the latent factors, the gu vectors can then be used to generate recommendations.

The previously abstract user-factor and item-factor vectors can now both be accessed in a much more comprehensible way. The tag concept is easily understood by users and can be used to actively adjust their own user vector, i. e. their pro le. In particular, users can in uence the recommendations by searching, selecting and weighting tags, thus indirectly determining their preferences in the latent factor space. A weight vector wu 2 [ 0, 1 ]jT j therefore holds the user feedback regarding the tags, where 0 means no and 1 very strong interest in a particular tag. Integrating the weights into the calculation of recommendations leads to: r~ui = (gu + (4) where 2 R represents the extent to which the weight information should be considered. r~ui is a combination of the user's general preference structure gu, with the operationalization of the user's current mood or interest wu. Initially, all values of wu are set to 0. When users start to interact with the system by manipulating the values of wu, for example by means of sliders, the resulting set of recommendations is continuously adapted in realtime.

Figure 1 shows a web-based prototype movie RS we have implemented to demonstrate this approach: At the top, an area is shown where the users can place the tags they select and adjust their weight by manipulating the sliders attached to them. Users can also search for tags with the input eld underneath. Below, the system shows some suggested tags. Alongside each recommendation the three most relevant tags for this movie are shown. In addition, users could also rate the recommended movies to further adapt their pro le.

EVALUATION & DISCUSSION

We performed an evaluation using a standard SVD-like MF algorithm1 as a baseline, and extended this algorithm according to our approach considering a number of the most popular tags as additional training data. We used the wellknown MovieLens 10M dataset for ratings and the MovieLens Tag Genome dataset for tag-item relevance scores. Figure 2 shows the results of one of our o ine experiments. 0.85 0.80 0.65 5

Number of latent factors 15 10 20

In line with others (e. g. [ 1 ]), it seems bene cial to include metadata into MF. However, we also performed a user study with 46 participants (33 female; age: M = 22.89, = 6.88) who had to interact with our prototype RS in di erent conditions, with and without tags. We used a questionnaire comprising among others items from [ 2 ]. Results from our and other o ine experiments could be con rmed, as subjective perception of recommendation quality was higher with (M = 3.65, = 0.69) than without (M = 3.16, = 0.73) tags (t(45) = 3.98, p < .001), also prior to interaction. Outlining some further results, participants were also very satis ed with the movie they nally selected from the recommendations (M = 4.35, = 0.09) and stated a good usability (78 on SUS). In general, users liked the interaction via tags while perceiving the interaction e ort to be acceptable (M = 3.64, = 0.74). In the tag condition, initial preferences were elicited by only selecting a small number of tags instead of rating items rst. Since this led to particularly promising results in terms of e. g. perceived recommendation quality, our tag-supported approach seems also to be useful in cold-start situations. In future work, we plan to evaluate the users' perception of di erences between conventional MF and our prototype integrating tags in more detail, and to exploit the integration of additional data more extensively. 1Mahout ParallelSGDFactorizer (20 fact., 40 iter., = .001)

References

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