As opposed to manual feature engineering which is tedious and difficult to scale, network representation learning has attracted a surge of research interests as it automates the process of feature learning on graphs. The learned low-dimensional node vector representation is generalizable and eases the knowledge discovery process on graphs by enabling various off-the-shelf machine learning tools to be directly applied. Recent research has shown that the past decade of network embedding approaches either explicitly factorize a carefully designed matrix to obtain the low-dimensional node vector representation or are closely related to implicit matrix factorization, with the fundamental assumption that the factorized node connectivity matrix is low-rank. Nonetheless, the global low-rank assumption does not necessarily hold especially when the factorized matrix encodes complex node interactions, and the resultant single low-rank embedding matrix is insufficient to capture all the observed connectivity patterns. In this regard, we propose a novel multi-level network embedding framework BoostNE, which can learn multiple network embedding representations of different granularity from coarse to fine without imposing the prevalent global low-rank assumption. The proposed BoostNE method is also in line with the successful gradient boosting method in ensemble learning as multiple weak embeddings lead to a stronger and more effective one. We assess the effectiveness of the proposed BoostNE framework by comparing it with existing state-of-the-art network embedding methods on various datasets, and the experimental results corroborate the superiority of the proposed BoostNE network embedding framework.
Ensemble methods have shown to be effective in improving the performance of single matrix factorization models, especially in the context of collaborative filtering. DeCoste @cite_14 made one of the first attempts to use ensemble methods to improve the prediction results of a single Maximum Margin Matrix Factorization (MMMF) model. In the sequel, the effectiveness of ensemble models is further validated on the Nystr "o m method @cite_48 and Divide-and-Conquer matrix factorization @cite_45 . The winner of Netflix Prize @cite_19 @cite_21 advanced the performance of recommendation by capitalizing the advantages of memory-based models and latent factor models. @cite_20 proposed a feature induction algorithm that works in conjunction with stagewise least-squares, and the combination with induced features is superior to existing methods. Most of the existing efforts on matrix factorization are fundamentally based on the prevalent assumption that the given matrix is low-rank, which is often too restrict in practice. developed a novel framework LLORMA model @cite_33 @cite_37 to combine the factorization results from multiple locally weighted submatrices, with the assumption that only the local submatrices are low-rank. The success of LLORMA is further extended to other related problems, including social recommendation @cite_46 , topic discovery @cite_36 and image processing @cite_38 .
@cite_38 @cite_37 @cite_14 @cite_33 @cite_36 @cite_48 @cite_21 @cite_19 @cite_45 @cite_46 @cite_20
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Fast gradient-based methods for Maximum Margin Matrix Factorization (MMMF) were recently shown to have great promise (Rennie & Srebro, 2005), including significantly outperforming the previous state-of-the-art methods on some standard collaborative prediction benchmarks (including MovieLens). In this paper, we investigate ways to further improve the performance of MMMF, by casting it within an ensemble approach. We explore and evaluate a variety of alternative ways to define such ensembles. We show that our resulting ensembles can perform significantly better than a single MMMF model, along multiple evaluation metrics. In fact, we find that ensembles of partially trained MMMF models can sometimes even give better predictions in total training time comparable to a single MMMF model. Matrix approximation is a common tool in recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the partially observed matrix is of low-rank. We propose a new matrix approximation model where we assume instead that the matrix is locally of low-rank, leading to a representation of the observed matrix as a weighted sum of low-rank matrices. We analyze the accuracy of the proposed local low-rank modeling. Our experiments show improvements in prediction accuracy over classical approaches for recommendation tasks. Nonnegative matrix factorization (NMF) has beenwidely applied in many domains. In document analysis, it hasbeen increasingly used in topic modeling applications, where aset of underlying topics are revealed by a low-rank factor matrixfrom NMF. However, it is often the case that the resulting topicsgive only general topic information in the data, which tends notto convey much information. To tackle this problem, we proposea novel ensemble model of nonnegative matrix factorizationfor discovering high-quality local topics. Our method leveragesthe idea of an ensemble model, which has been successfulin supervised learning, into an unsupervised topic modelingcontext. That is, our model successively performs NMF givena residual matrix obtained from previous stages and generatesa sequence of topic sets. Our algorithm for updating the inputmatrix has novelty in two aspects. The first lies in utilizing theresidual matrix inspired by a state-of-the-art gradient boostingmodel, and the second stems from applying a sophisticatedlocal weighting scheme on the given matrix to enhance thelocality of topics, which in turn delivers high-quality, focusedtopics of interest to users. We evaluate our proposed method bycomparing it against other topic modeling methods, such as afew variants of NMF and latent Dirichlet allocation, in termsof various evaluation measures representing topic coherence, diversity, coverage, computing time, and so on. We also presentqualitative evaluation on the topics discovered by our methodusing several real-world data sets. Recommender systems provide users with personalized suggestions for products or services. These systems often rely on Collaborating Filtering (CF), where past transactions are analyzed in order to establish connections between users and products. The two more successful approaches to CF are latent factor models, which directly profile both users and products, and neighborhood models, which analyze similarities between products or users. In this work we introduce some innovations to both approaches. The factor and neighborhood models can now be smoothly merged, thereby building a more accurate combined model. Further accuracy improvements are achieved by extending the models to exploit both explicit and implicit feedback by the users. The methods are tested on the Netflix data. Results are better than those previously published on that dataset. In addition, we suggest a new evaluation metric, which highlights the differences among methods, based on their performance at a top-K recommendation task. The collaborative filtering approach to recommender systems predicts user preferences for products or services by learning past user-item relationships. In this work, we propose novel algorithms for predicting user ratings of items by integrating complementary models that focus on patterns at different scales. At a local scale, we use a neighborhood-based technique that infers ratings from observed ratings by similar users or of similar items. Unlike previous local approaches, our method is based on a formal model that accounts for interactions within the neighborhood, leading to improved estimation quality. At a higher, regional, scale, we use SVD-like matrix factorization for recovering the major structural patterns in the user-item rating matrix. Unlike previous approaches that require imputations in order to fill in the unknown matrix entries, our new iterative algorithm avoids imputation. Because the models involve estimation of millions, or even billions, of parameters, shrinkage of estimated values to account for sampling variability proves crucial to prevent overfitting. Both the local and the regional approaches, and in particular their combination through a unifying model, compare favorably with other approaches and deliver substantially better results than the commercial Netflix Cinematch recommender system on a large publicly available data set.