Source-linked AI summary
Multi-Domain Collaborative Filtering
Yu Zhang, Bin Cao, Dit-Yan Yeung
TL;DR
Sparse rating matrices motivate jointly learning collaborative-filtering tasks across multiple domains. The paper proposes probabilistic matrix factorization with adaptively learned domain correlations and a link-function extension, and reports effectiveness across recommendation datasets. The method is scoped by assumptions including a common link function and special handling of uncorrelated domains.
Problem
Collaborative filtering suffers from extremely sparse rating matrices, motivating joint modeling of multiple domain-specific rating prediction tasks.
Method
The paper uses probabilistic matrix factorization for each domain, learns correlations among domain-specific user features, and optionally transforms ratings with a link function.
Results
Experiments on several recommendation datasets demonstrate the effectiveness of the proposed methods.
Takeaways & Limitations
Modeling domain correlations enables shared rating information to be adaptively transferred across domains within the multi-domain collaborative-filtering framework.
Takeaways & Limitations
The link-function extension assumes different domains share the same link function, while uncorrelated domains reduce the user-feature update to single-domain factorization.
Abstract
from arXiv · showhide
Collaborative filtering is an effective recommendation approach in which the preference of a user on an item is predicted based on the preferences of other users with similar interests. A big challenge in using collaborative filtering methods is the data sparsity problem which often arises because each user typically only rates very few items and hence the rating matrix is extremely sparse. In this paper, we address this problem by considering multiple collaborative filtering tasks in different domains simultaneously and exploiting the relationships between domains. We refer to it as a multi-domain collaborative filtering (MCF) problem. To solve the MCF problem, we propose a probabilistic framework which uses probabilistic matrix factorization to model the rating problem in each domain and allows the knowledge to be adaptively transferred across different domains by automatically learning the correlation between domains. We also introduce the link function for different domains to correct their biases. Experiments conducted on several real-world applications demonstrate the effectiveness of our methods when compared with some representative methods.
1 Introduction
Collaborative filtering predicts preferences from users with similar interests, but sparse ratings limit its effectiveness. The paper addresses this by jointly modeling multiple domains and adaptively transferring knowledge between correlated rating tasks.
- Motivation: Collaborative filtering predicts user preferences from the past activities of users with similar interests.These activities include transaction histories and ratings.
- Motivation: Memory-based collaborative filtering requires dense rating data to estimate similarities accurately, an unrealistic condition in many applications.
- Problem: Data sparsity makes rating matrices extremely sparse and is the paper’s central problem.
- Approach: The proposed multi-domain collaborative filtering problem jointly models rating tasks from domains such as books and electronics.
- Approach: The probabilistic framework uses probabilistic matrix factorization and learns domain correlations to transfer shared knowledge adaptively.
2 Multi-Domain Collaborative Filtering
The method factorizes each domain’s rating matrix into user and item features while modeling relationships among domain-specific user features. Its objective combines rating fit with complexity penalties and reduces to single-domain factorization when domains are uncorrelated.
- Model: Each domain has a rating matrix with domain-specific latent user and item feature matrices.The user and item features represent users and items in a shared latent dimension.
- Model: Observed ratings are modeled conditionally using a Gaussian distribution based on latent user–item interactions.An indicator function identifies which user–item entries are observed.
- Model: The model places a matrix-variate normal prior on domain-specific user features to learn correlations between domains.The column covariance matrix Ω represents relationships between domains.
- Optimization: The parameters are learned by alternating optimization of a negative log-posterior for latent features, noise terms, prior parameters, and domain covariance.The procedure obtains MAP estimates for latent features and MLE estimates for other model parameters.
- Special case: When domains are uncorrelated, the user-feature update degenerates to single-domain matrix factorization.
- Objective: The objective balances empirical loss on observed ratings against penalties on model complexity, latent-feature ranks, and singular values.
3 Incorporation of Link Function
The link-function extension transforms discrete ratings before applying the Gaussian model, addressing the mismatch between integral ratings and Gaussian likelihoods. The transformation is learned jointly with the original model parameters under monotonicity and mapping constraints.
- Motivation: The link-function variant transforms original ratings into latent variables before applying the probabilistic model.This modification addresses the suitability of Gaussian likelihood for discrete integral ratings.
- Design: Each domain’s link function must be monotonically increasing and map onto the whole real line to preserve the probability measure.
- Design: For simplicity, the model assumes all domains share one common link function.
- Learning: The link-function parameters and original model parameters are learned simultaneously by maximizing the log-posterior with alternating optimization.
- Implementation: The experiments use the monotonically increasing form g(x) = a ln(bx + c) + d with a, b, c > 0 and d ∈ ℝ.
4 Related Work
Related work includes collective matrix factorization and transfer collaborative filtering. The proposed model differs by allowing domain-specific user features and jointly improving rating prediction across all domains.
- Collective matrix factorization: Collective matrix factorization shares one common latent user feature matrix across domains, making it a restricted case of the proposed model.The restriction requires all domain-specific user feature matrices to be identical.
- Transfer collaborative filtering: Transfer collaborative filtering uses one rating problem to improve another, whereas this paper jointly improves rating prediction across all domains.The related transfer model is described as targeting two domains.
5 Experiments
The experiments evaluate the proposed methods on two real-world recommendation datasets and analyze their results.
- Experiments use two real-world recommendation datasets and include analysis of the results.
5.1 Experimental Settings
The experiments evaluate multi-domain recommendation methods on MovieLens and Book-Crossing, using RMSE to compare performance across heterogeneous domains. The study compares independent and joint matrix-factorization approaches under repeated train/test splits.
- Datasets: The experiments use MovieLens and Book-Crossing datasets whose items are divided into multiple heterogeneous domains.MovieLens provides genre information, while Book-Crossing uses available book categories.
- Datasets: MovieLens contains 100,000 ratings from 943 users on 1,682 movies, while the Book-Crossing subset contains 56,148 ratings from 28,503 users on 9,009 books.MovieLens ratings use a 1–5 scale; Book-Crossing ratings use a 1–10 scale.
- Data preparation: Five popular movie genres and five general book categories define the domains, with 80% of ratings used for training and the remainder for testing.Each experimental configuration is iterated 10 times.
- Evaluation: Performance is evaluated with root mean squared error (RMSE), where smaller scores indicate better rating prediction.RMSE compares ground-truth and predicted ratings over the tested ratings.
- Compared methods: The proposed models are compared with independent probabilistic matrix factorization and collective matrix factorization.Independent PMF treats rating-prediction problems in different domains separately, whereas CMF handles multiple matrix-factorization tasks jointly.
- Proposed methods: The paper refers to its Section 2 method as MCF and its Section 3 link-function variant as MCF-LF.These names are used throughout the reported experiments.
5.2 Experimental Results
Across MovieLens and Book-Crossing, MCF and MCF-LF achieve the strongest reported performance, while learned domain correlations broadly align with intuitive relationships. The link function consistently improves performance across MovieLens domains.
- Parameter setting: The latent dimensionality has little effect on RMSE after d reaches 10, so the experiments set d to 10.The probabilistic model requires only the latent dimensionality as a parameter to set.
- Dataset results: MCF and MCF-LF achieve the best performance among the compared methods on both MovieLens and Book-Crossing.On MovieLens, models incorporating multiple domains outperform independent PMF; on Book-Crossing, CMF performs worse than PMF.
- MovieLens results: MCF outperforms CMF on MovieLens because it learns similarities between different rating-prediction problems.The comparison is presented as evidence of the effectiveness of learning domain relationships.
- MovieLens results: The link function improves performance consistently over all MovieLens domains when comparing MCF-LF with MCF.MCF-LF is the variant that includes the link function.
- Book-Crossing results: On Book-Crossing, CMF performs worse than PMF despite jointly considering multiple domains.The text relates this result to uncorrelated domain pairs that conflict with CMF’s shared-latent-factor assumption.
- Learned correlations: MCF-LF learns intuitive MovieLens correlations, including the smallest correlation between Comedy and Thriller and the largest between Romance and Drama.For Action, the learned ordering is Thriller, Romance, Drama, then Comedy.
- Learned correlations: On Book-Crossing, Mystery & Thrillers and Business & Investing, and Science Fiction & Fantasy and Business & Investing, show nearly zero correlation.Science and Religion & Spirituality have the largest reported correlation.
6 Conclusion
The paper addresses multi-domain collaborative filtering with a probabilistic model that learns relationships between domains, and reports effective performance across recommendation datasets. It also identifies active learning as a direction for future work.
- The proposed model jointly learns multiple rating prediction problems while considering correlations between domains.It leverages rating data across domains through a probabilistic model.
- The experiments evaluate methods on MovieLens and Book-Crossing using domain-specific and total-testing-data RMSE over ten trials.The reported tables compare mean RMSE values across five domains and overall test data.
- Future work proposes incorporating active learning into the probabilistic model to further address data sparsity.Active learning is described as a way to select unlabeled data for querying an oracle or domain expert.