Towards Understanding Latent Factors and User Profiles by Enhancing Matrix Factorization with Tags

Abstract

With the interactive recommending approach we have recently proposed, users are given more control over modelbased Collaborative Filtering while the results are perceived as more transparent. Integrating the latent factors derived by Matrix Factorization with tags users provided for the items has, however, even more advantages. In this paper, we show how general understanding of the abstract factor space, and of user and item positions inside it, can bene t from the semantics introduced by considering additional information. Moreover, our approach allows us to explain the user's (former latent) preference pro le by means of tags.

-

1. INTRODUCTION

Complementing Matrix Factorization (MF) with further data, e.g. implicit feedback, temporal information or predened metadata, has widely been accepted to increase algorithmic accuracy [ 4 ]. In line with others, we have shown that this is also true when user-provided tags are taken into account [ 1 ]. As part of a comprehensive user study of tag-enhanced Recommender Systems (RS), we could con rm that the recommendation quality perceived by users benets as well [ 2 ]. However, latent factor models derived by MF have rarely been exploited for purposes other than improving e ectiveness or performance. Few exceptions rely on the factor space to elicit user preferences in a choicebased manner [ 5, 3 ] or to visualize e.g. item characteristics [ 6 ]. Although considered particularly di cult from a system-perspective [ 4 ], in [ 8 ], a rst step towards relating the factors to an intelligible meaning has been taken. Still, latent factors are overall hard to explain. It is also a more general problem that users often lack a deeper understanding in model-based Collaborative Filtering (CF) systems.

By enhancing standard SVD-like MF with tags users provided for the items, we however not only proposed novel interaction possibilities, especially for cold-start situations, but have also shown that introducing the easy-to-understand semantics of tags to a latent factor model positively a ects perceived recommendation transparency [ 2 ]. In this paper, we demonstrate that our approach has even more advantages. It allows us to get a general understanding of the factor space and how users and items are positioned inside it. Furthermore, users can be presented with textual tags explicitly explaining their preference pro le they have expressed implicitly in the (intransparent) latent factor space. 2.

UNDERSTANDING LATENT FACTORS AND EXPLAINING USER PROFILES With the steps described in [ 1 ], we have integrated itemspeci c tag relevance information into a MF algorithm in order to derive corresponding user-tag relevance scores as well as tag-factor relations. Since the matrix holding these general relations, T, is a square diagonalizable matrix, we can use eigendecompositon to represent it in terms of eigenvalues and eigenvectors:

R uA T iAT = uAV VT iAT (1)

The diagonal matrix contains the eigenvalues of T in non-increasing order. The eigenvectors in V hold the importance of every tag with respect to a certain direction. Since T is symmetric, eigenvectors are chosen orthogonal to each other. Latent factors are thus incorporated into the tag information space by stretching it along the directions of the eigenvectors to the amount of corresponding eigenvalues.

This way considering tag information in model-based CF o ers us the opportunity to access the previously abstract user-factor and item-factor vectors in a much more comprehensible way. As the tag concept is easily understood, this allows us to both explain a user's vector, i.e. his or her preference pro le, and to let users actively adjust it. We have described the latter in our previous work [ 1, 2 ]. Now, we will concentrate on how enhancing MF with additional information allows to gain a better understanding of users, items and the latent factor space itself, and in particular to express a latent preference pro le through explicit tags.

Understanding the Factor Space: Applying eigendecomposition as described above provides us information on the importance of each dimension of the factor space and their relationship to the tags. By looking at the most positively/negatively related tags, this gives us a more general understanding of what is expressed by factors derived automatically by MF. For instance, using the con guration from [ 1, 2 ] with MovieLens 10M and Tag Genome dataset, Table 1 shows that the rst latent factor is best described by tags such as \twist ending" or \psychology", the second by \time travel" or \comedy". Consequently, we found movies such as \Seven" or \Back to the Future" having highest values for the respective factors in the actual item-factor matrix iAV 1=2. twist ending (0.50), romance (-0.40), psychology (0.38), . . . quirky (-0.30), classic (0.34) sci- (-0.23)

Seven, The Machinist, . . . time travel (0.36), vis. appealing (-0.54), dystopia (0.31), . . . stylized (-0.35), comedy (0.27) romance (-0.23) Bill & Ted's Excellent Advent., Back to the Future, . . .

sci- (0.43), dark (-0.53), vis. appealing (0.24), . . . surreal (-0.38), twist ending (0.24) violence (-0.19)

Planet of the Apes, When Worlds Collide, . . . psychology (0.36), classic (-0.32), dystopia (0.30), . . . vis. appealing (-0.29), romance (0.28) based on a book (-0.27)

A Life Less Ordinary, Splendor, . . . dystopia (0.29), psychology (-0.41), violence (0.23), . . . time travel (-0.41), sci- (0.20) based on a book (-0.37)

Nausicaa, Robocop, . . .

The regression-constrained formulation also allows us to gain insights on how users and items are positioned inside the information space. For items, Figure 1 illustrates this in an example with two tags, which are then used to enhance a two-factorical MF for demonstration purposes. The original tag-related item positions are represented by row vectors of iA. In the left plot, movies are shown accordingly with respect to tag relevances. The in uence of latent information can then be examined by considering the item-factor matrix iAV 1=2 which is used eventually for generating recommendations by MF, i.e. usually by calculating dot products. Consequently, the right plot in Figure 1 shows how items are arranged with respect to the resulting factors. Similarities between movies in terms of tag relevance can still be found when considering the latent information, especially in this case where we used the same amount of tags and factors. 1.0 0.5

Comedy

Bill and Ted's ...

Splendor A Life Less Ordinary

Back to the ... 1.0 Robocop

Factor 2

When Worlds Collide Planet of the Apes

Nausicaa Back to the Future Bill and Ted's Excellent Adventure

The Machinist Seven 0.5 Splendor A Life Less Ordinary

Robocop SeTvhene MachiniNstausicaa PlanWethoefnthWeoArlpdess...

0.5 1.0 Sci-Fi 0.5 1.0 Factor 1 Figure 1: Normalized movie positions with respect to tag relevance (left) and latent factors (right).

Explaining User Pro les: By enhancing MF, preference pro les now comprise information related to both tags and latent factors. Thus, we can utilize uA to explain the user's pro le by means of those tags considered most important to him or her. In an extension of our web-based movie RS, a dialog comprising a tag cloud enables users to inspect their existing pro le by means of such tags (Figure 2). Individual preferences expressed implicitly with respect to the factor space, e.g. by rating items, can thus be presented more explicitly. When uA is derived according to our approach [ 1 ], this is independent of the tags users actually have assigned. We can thereby present the tag cloud even in the common case where the current user never tagged any items. 3. CONCLUSIONS AND OUTLOOK

Enhancing MF with tags improves accuracy [ 1 ] as well as subjective perception of RS [ 2 ]. In this paper, we have proposed that such additional data may also be leveraged for the purpose of explaining latent factors. In particular, our approach seems promising to present users with an explicit description of their|in model-based CF usually intransparent|preference pro le. However, it will be subject of our future work to examine this contribution in more detail, for instance, by determining the information theoretic value as in [ 7 ] or by conducting user studies to compare with other approaches that explain recommendations using tags, e.g. [ 9 ]. We also aim to investigate how latent factor models can be better semantically enriched, e.g. by exploiting further data. Finally, there is also room left for improvement especially regarding visual explanations.

References

[1] T. Donkers , B. Loepp , and J. Ziegler . Merging latent factors and tags to increase interactive control of recommendations . In Poster Proc. RecSys '15 , 2015 .

[2] T. Donkers , B. Loepp , and J. Ziegler . Tag-enhanced collaborative ltering for increasing transparency and interactive control . In Proc. UMAP '16 , pages 169 { 173 . ACM, 2016 .

[3] M. P. Graus and M. C. Willemsen. Improving the user experience during cold start through choice-based preference elicitation . In Proc. RecSys '15 , pages 273 { 276 . ACM, 2015 .

[4] Y. Koren , R. M. Bell , and C. Volinsky . Matrix factorization techniques for recommender systems . IEEE Computer , 42 ( 8 ): 30 { 37 , 2009 .

[5] B. Loepp , T. Hussein , and J. Ziegler . Choice-based preference elicitation for collaborative ltering recommender systems . In Proc. CHI '14 , pages 3085 { 3094 . ACM, 2014 .

[6] B. Nemeth , G. Takacs, I. Pilaszy , and D. Tikk . Visualization of movie features in collaborative ltering . In Proc. SoMeT '13 , pages 229 { 233 , 2013 .

[7] T. T. Nguyen and J. Riedl . Predicting users' preference from tag relevance . In Proc. UMAP '10 , pages 274 { 280 . Springer, 2013 .

[8] M. Rossetti , F. Stella , and M. Zanker . Towards explaining latent factors with topic models in collaborative recommender systems . In Proc. DEXA '13 , pages 162 { 167 , 2013 .

[9] J. Vig , S. Sen , and J. Riedl . Tagsplanations: Explaining recommendations using tags . In Proc. IUI '09 , pages 47 { 56 . ACM, 2009 .