SOFIANE ABBAR, HABIBUR RAHMAN, SARAVANA N THIRUMURUGANATHAN, CARLOS CASTILLO, G AUTAM DAS QATAR COMPUTING RESEARCH INSTITUTE UNIVERSITY OF TEXAS AT ARLINGTON Ranking Item Features by Mining Online User-Item Interactions

Outline Introduction Motivation and Challenge Model and Extensions Experimental Evaluation Related Works Conclusion

Business owners relies on user's feedback for the success of their businesses. It is important for them to understand what are the features which makes an item popular. User's put feedback on items in the form of reviews, tags, likes or +1's etc. Can we leverage this information to and the ranking of features in an item ? Can we and the global ranking or popularity of the features?

Introduction The main focus in this paper is the investigation of a novel-problem: how to rank the features of each item from user-item interactions. The principal problem investigated in this paper is stated as FEATURE RANKING(FR) PROBLEM: Where a set of features, and rudimentary user-item interactions (either at aggregate or individual level) is given, and how to identify the most important features per item (alternatively, a ranked list of features per item).

In this paper, the approach propose a probabilistic model that describes user-item interactions in terms of user preference distribution over feature and a feature-item transition matrix that determine the probability that an item will be chosen, given a feature.

This paper, used a database of items, where each item is des cribed by a set of attributes, some of which are multi valued. We refer to each of the distinct attribute values of an item as features(or equivalently, an item can be described as a set of features) Sparsity assumption. This paper assumes that among all the ℓ features available, each user expresses preference over a relatively small fraction of them:

Motivation For example Netflix, a simple user-item interaction would Involve whether the user watched the movie. While some users could have watched the movie because it starred Tom Hanks, others could have watched it because, in addition it was also directed by Steven Spielberg. Similarly, while some users might buy a car due to its manufacturer, others might buy it for the model and transmission type.

Example

Challenges

Models A ranking is a relationship between a set of items such that, for any two items, the first is either “ranked higher than”, “ranked lower than” or “ranked equal” ranking is the popularity of items features and suggesting popular item features.

Feature Ranking with Aggregate interaction information This model assumed that user u first picked a single feature j based on their individual preference vector h u and then selected an item i containing j with probability proportional to W ij

FR-AGG-W Algorithm: Input: Database D and aggregate visit vector v 1: W = Estimate feature item transition matrix 2: constraints = { ∀ i ∈ [1, n] hi ≥ 0, ||h||1= 1 } 3: h = argmin Error(v,Wh) subject to constraints h 4: Compute Xi = Wi· ◦ h ∀ i ∈ [1, n] 5: return X = {X1,X2,...,Xn}

FR-AGG-h Algorithm : Input: Database D and aggregate visit vector v 1: W = Estimate feature-item presence matrix 2: h = Estimate aggregate preference vector 3: constraints = { W ≤ W and ∀ j||W·j ||1= 1 and ∀ i, jWij ≥ 0 } 4: W = argmin Error(v,Wh) subject to constraints W 5: Compute Xi = Wi· ◦ h ∀ i ∈ [1, n] 6: return X = {X1,X2,...,Xn}

Variant Problem 1: (FR-AGG): Given a database D and Aggregate interaction Vector v, estimate the item-featurevis it vector X (where Xi=Wi·◦h) For each item I such that Error (v, W h) is minimized. Variant Problem 2 (FR-INDIV): Given a database D and ind ividual interaction matrix V, estimate the item-feature vi sit vector Xi for each item i (where Xi = Wi· ◦ h, is the average of columns of H) such that Error (V, W H) is minimized.

Network Flow In this, they consider a graph-based representation of t he problem that maps to the element. This algorithm finds feature to item transition matrix (W) by minimizing |V-Wh| error

Extensions Feature Ranking with Composite Features. Baselines. Algorithms - FR-AGG-W-LS - FR-AGG-h-LS - FR-AGG-h-NF Evaluation Metrics Ranking quality

Proposed method(FR-INDIV-MNMF) We choose Kullback-Leibler divergence D(V||W H) in order to measure the reconstruction error Between V and W H. This choice (instead of other Measures such as L2 distance) allows us to design an algorithm that preserves the column stochasticity constraints in the solution. In what follows, They propose a four-step algorithm to solve the problem of ranking item features in the presence of individual interaction matrix.

Step 1: Imposing sparsity constraints over H. They impose a (row) sparsity constraint over the factor W by assuming a sparse binary matrix W such that W ≤ W An entry(W)ij = 0 iff item I does not contain feature j A seemingly similar approach can be used to also impose (column) sparsity constraints over the Factor H by defining a sparse binary matrix H such that H ≤ H, where an entry (H) jk= 0 if user k has not visited any item that contains feature j However, this straightforward approach may not generate adequate sparsity constraints, since the union of distinct features of the items that a user has visited may be quite large

Step 2: Iterative algorithm with multiplicative update rules. In the second step, they propose modifications to the algorithm to discover factors W and H such that the Reconstruction error D (V ||W H)is minimized

Step 3: Imposing stochastic constraints on W and H The matrices W and H produced by Step 2 satisfy the sparsity requirements, however, they may not satisfy the col- umn stochastic constraints, which requires that the weights of each column of W and H sum to 1. In this step we describe a procedure for further modifying W and H such that the stochastic constraints are satisfied. We make use of the following theorem by Ho and Dooren

Step 4: Computing item-feature visit vectors Xi. Once the feature-item transition matrix W and individual preference matrix H are obtained, then the feature ranking of any Item can be computed as follows. First, compute the aggregate preference vector h by averaging all column-wise vectors H.j ∈, then perform a component wise multiplication between the item’s feature transition vector Wi. And h,i.e. Xi = Wi. ◦ h.

FR-INDIV-MNMF Algorithm: Input: Database D and individual interaction matrix V 1: W = Estimate feature-item presence matrix 2: H0 = Initialize a column-wise sparse individual preferen ce matrix using setCover (Step 1) 3: Compute W1, H1 = M-NMF(W, H0) (Step 2) 4: W, H = Impose stochastic constraints (Step 3) 5: Compute h = average (H) 6: Compute Xi = Wi oh ∀ I ∈ [1, n](Step 4) 7: return X ={X1, X2,..., Xn}

Experiment They conduct a comprehensive set of experiments to evaluate the effectiveness and efficiency of various Methods for ranking item features. The ranking quality measured within two scenarios: prediction of the most prominent feature and overall ranking of item features Dataset: MovieLens joint with cast data from IMDB

Result

Related Work Nonnegative Matrix Factorization (NMF) Attributes ranking Feature Ranking.

Conclusion In this paper, they consider the feature ranking problem that ranks features of an item by only considering user-item interaction information such as visits., defined two variants problem based on the granularity of the interaction information available and proposed different algorithms (based on constrained convex optimization, network flow approximation and marginal NMF) to solve these variants. In the future, they wish to investigate a variant where users can choose an item through a weighted combination of features.

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