In order to generate e ective results, it is essential for a recommender system to model the information about the user interests in a pro le. Even though word embeddings (i.e., vector representations of textual descriptions) have proven to be e ective in many contexts, a content-based recommendation approach that employs them is still less e ective than collaborative strategies (e.g., SVD). In order to overcome this issue, we introduce a novel criterion to evaluate the word-embedding representation of the items a user rated. The proposed approach de nes a vector space in which the similarity between an unevaluated item and those in a user pro le is measured in terms of linear independence. Experiments show its e ectiveness to perform a better ranking of the items, w.r.t. collaborative ltering, both when compared to a latent-factor-based approach (SVD) and to a classic neighborhood user-based system. This work is partially funded by Regione Sardegna under project NOMAD (Next generation Open Mobile Apps Development), through PIA - Pacchetti Integrati di Agevolazione \Industria Artigianato e Servizi" (annualita 2013).
Recommender systems are essential for e-commerce
companies, to lter the huge amounts of items they can provide
and improve the quality and e ciency of the sales
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A user pro le represented by a unique vector of features allows a system to perform quick comparisons, e.g., in a content-based system, it can be easily compared to the vector that represents an item with a simple metric, like the cosine similarity. The idea behind this paper is to represent a user pro le as a matrix of word-embeddings, where each row is represented by an item a user positively evaluated, and to de ne a metric able to evaluate the correlation between an item not rated by a user and those in her matrix-based user pro le, in terms of linear independence.
We observe that if the vector representation of an unevaluated item is linearly dependent to the items in a user pro le that have been positively evaluated, their features match, thus it is similar to the user preferences. This leads to a higher accuracy of a recommender system w.r.t. collaborative approaches. 2.
Here, we present the steps our approach performs: Item Vectorization. Given a set I of items, we rst de ne and train a model by using the doc2vec neural net (by using as source the textual description of the items in I). The result is the vector representation of the items in I, where the cardinality of each vector (item) depends on the number L of features used in the doc2vec vectorization process. Given a user, the output of this step will be a matrix that contains the embeddings of the items positively evaluated by her (denoted as Iu), plus an empty row to employ during the ltering process to evaluate the items not yet evaluated by the user.
Linear Independence Rate. To evaluate the similarity between the items in the matrix-based user pro le and an 1http://deeplearning4j.org/word2vec unevaluated one, we de ne the Linear Independence Rate (LIR) coe cient. It is the average of the determinants of all square sub-matrices, de ned by decomposing the user pro le matrix in square sub-matrices of size jIuj jIuj (with jIuj L, otherwise we have only a matrix of size L L). We calculate the LIR value by moving on the entire user prole matrix, extracting the determinant of each sub-matrix, without overlaps. We can note that the maximum size of the square sub-matrices is the cardinality of the vectors, i.e., the L parameter used to build the doc2vec model. Through this compositional process, we evaluate the LIR of an item by placing its vector representation as last element of the user pro le. We consider closer to the preferences of a user the items with a LIR value as close as possible to zero.
Ranking Algorithm. The Algorithm 1 takes as input the items I, a user u, the items Iu she evaluated, and the number of features L in the vectors created by doc2vec (i.e., the layerSize parameter). It returns as output a list R of the items not evaluated by the user u (ranked by LIR value). Algorithm 1 Items evaluation and ranking Input: I=Set of items, u=User, Iu=Items of u, L=layerSize Output: R = List of ranked items 1: procedure GetRankedItems(I,u,Iu,L) 2: if jIuj > L then Iu=GetLastLItems(Iu; L) 3: end if 4: V =Doc2VecVectorization(I) 5: M=De neUserPro leMatrix(V ,Iu) 6: M=AddEmptyVectorAsLastRow(M); 7: for each i in I do 8: if i NOT IN Iu then 9: v=GetItemVector(V; i) 10: M=FillLastMatrixRow(M; v) 11: LIR=CalculateLIR(M) 12: R (i; LIR) 13: end if 14: end for 15: Return SortItemsByDescLIR(jRj) 16: end procedure
It should be noted that our approach is scalable by employing distributed computing models (e.g., MapReduce). Indeed, the computation of the LIR metric for each unevaluated item can be distributed over di erent machines.
We compared our approach with two collaborative ltering approaches: CF , which is based on a classic neighborhood model, and SV D, based on the latent factor model. The experiments have been performed by using a dataset that represents a standard benchmark for recommender systems, i.e., Movielens 1M, composed by 6,040 users, 3,900 items, and 1,000,209 ratings.
The criterion adopted for obtaining the training and the test sets was the K-fold cross validation with K = 3, and the independent-samples two-tailed Student's t-tests. The adopted metric is the Mean Reciprocal Rank (M RR), a statistical measure able to evaluate the ranking generated for a set of elements that belong to a certain domain.
The rst experiment evaluates the metric capability to measure the similarity between a user pro le and an item, in terms of linear independence (Figure 1: Top). On the basis of our approach, we rank all the items in decreasing order, by verifying that almost all of those in the test set have been placed in the top positions (i.e., 1 20), proving the LIR capability to e ectively rank the items. R0:15 R0:10 M0:05 62.02 %
26.68 % 01.63 % 09.67 %
CF SVD LIR (75)
(150) (225) T ested items ( 1000) (300)
The second experiment evaluates the metric capability to infer the future choices of the users (Figure 1: Bottom), by comparing the rank assigned to the items in the test set by using the LIR metric, with those assigned to the same items by the other state-of-the-art approaches taken into account.
The t-tests highlighted a statistical di erence between the results (p < 0:05). 4.
DISCUSSION AND CONCLUSIONS The experimental results show the e ectiveness of the compositional approach used by our LIR metric, as well as its capability to overcome the canonical state-of-the-art metrics, in terms of modeling of the user preferences. Indeed, we have a strong improvement in the process of rating of the unevaluated items, and this means that our metric assigns an higher score (w.r.t. the state-of-the-art approaches to which we compared) to the items positively evaluated by a user. The use of the LIR metric can be also extended to other contexts that do not use word embeddings, e.g., those based on a canonical term-document matrix.
Future work. We will consider our metric to evaluate the items negatively evaluated by the users, in order to obtain additional information in terms of unpreferred items, exploiting it to improve the recommendations accuracy, e.g., by verifying the preferences collision (i.e., very similar items rated both positively and negatively by a user).