I present a hybrid matrix factorisation model representing users and items as linear combinations of their content features' latent factors. The model outperforms both collaborative and content-based models in cold-start or sparse interaction data scenarios (using both user and item metadata), and performs at least as well as a pure collaborative matrix factorisation model where interaction data is abundant. Additionally, feature embeddings produced by the model encode semantic information in a way reminiscent of word embedding approaches, making them useful for a range of related tasks such as tag recommendations.
Saveski @cite_12 perform joint factorisation of the user-item and item-feature matrices by using the same item latent feature matrix in both decompositions; the parameters are optimised by minimising a weighted sum of both matrices' reproduction loss functions. A weight hyperparameter governs the relative importance of accuracy in decomposing the collaborative and content matrices. A similar approach is used by McAuley @cite_4 for jointly modelling ratings and product reviews. Here, LightFM has the advantage of simplicity as its single optimisation objective is to factorise the user-item matrix.
@cite_4 @cite_12
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Recommender problems with large and dynamic item pools are ubiquitous in web applications like content optimization, online advertising and web search. Despite the availability of rich item meta-data, excess heterogeneity at the item level often requires inclusion of item-specific "factors" (or weights) in the model. However, since estimating item factors is computationally intensive, it poses a challenge for time-sensitive recommender problems where it is important to rapidly learn factors for new items (e.g., news articles, event updates, tweets) in an online fashion. In this paper, we propose a novel method called FOBFM (Fast Online Bilinear Factor Model) to learn item-specific factors quickly through online regression. The online regression for each item can be performed independently and hence the procedure is fast, scalable and easily parallelizable. However, the convergence of these independent regressions can be slow due to high dimensionality. The central idea of our approach is to use a large amount of historical data to initialize the online models based on offline features and learn linear projections that can effectively reduce the dimensionality. We estimate the rank of our linear projections by taking recourse to online model selection based on optimizing predictive likelihood. Through extensive experiments, we show that our method significantly and uniformly outperforms other competitive methods and obtains relative lifts that are in the range of 10-15 in terms of predictive log-likelihood, 200-300 for a rank correlation metric on a proprietary My Yahoo! dataset; it obtains 9 reduction in root mean squared error over the previously best method on a benchmark MovieLens dataset using a time-based train test data split. In this paper we introduce a novel linear precoding technique. The approach used for the design of the precoding matrix is general and the resulting algorithm can address several optimization criteria with an arbitrary number of antennas at the user terminals. We have achieved this by designing the precoding matrices in two steps. In the first step we minimize the overlap of the row spaces spanned by the effective channel matrices of different users using a new cost function. In the next step, we optimize the system performance with respect to specific optimization criteria assuming a set of parallel single- user MIMO channels. By combining the closed form solution with Tomlinson-Harashima precoding we reach the maximum sum-rate capacity when the total number of antennas at the user terminals is less or equal to the number of antennas at the base station. By iterating the closed form solution with appropriate power loading we are able to extract the full diversity in the system and reach the maximum sum-rate capacity in case of high multi-user interference. Joint processing over a group of multi-user MIMO channels in different frequency and time slots yields maximum diversity regardless of the level of multi-user interference. State-of-the-art item recommendation algorithms, which apply Factorization Machines (FM) as a scoring function and pairwise ranking loss as a trainer (PRFM for short), have been recently investigated for the implicit feedback based context-aware recommendation problem (IFCAR). However, good recommenders particularly emphasize on the accuracy near the top of the ranked list, and typical pairwise loss functions might not match well with such a requirement. In this paper, we demonstrate, both theoretically and empirically, PRFM models usually lead to non-optimal item recommendation results due to such a mismatch. Inspired by the success of LambdaRank, we introduce Lambda Factorization Machines (LambdaFM), which is particularly intended for optimizing ranking performance for IFCAR. We also point out that the original lambda function suffers from the issue of expensive computational complexity in such settings due to a large amount of unobserved feedback. Hence, instead of directly adopting the original lambda strategy, we create three effective lambda surrogates by conducting a theoretical analysis for lambda from the top-N optimization perspective. Further, we prove that the proposed lambda surrogates are generic and applicable to a large set of pairwise ranking loss functions. Experimental results demonstrate LambdaFM significantly outperforms state-of-the-art algorithms on three real-world datasets in terms of four standard ranking measures. Matrix factorization (MF) models and their extensions are standard in modern recommender systems. MF models decompose the observed user-item interaction matrix into user and item latent factors. In this paper, we propose a co-factorization model, CoFactor, which jointly decomposes the user-item interaction matrix and the item-item co-occurrence matrix with shared item latent factors. For each pair of items, the co-occurrence matrix encodes the number of users that have consumed both items. CoFactor is inspired by the recent success of word embedding models (e.g., word2vec) which can be interpreted as factorizing the word co-occurrence matrix. We show that this model significantly improves the performance over MF models on several datasets with little additional computational overhead. We provide qualitative results that explain how CoFactor improves the quality of the inferred factors and characterize the circumstances where it provides the most significant improvements. We derive a least-squares formulation for MDDMp technique.A novel multi-label feature extraction algorithm is proposed.Our algorithm maximizes both feature variance and feature-label dependence.Experiments show that our algorithm is a competitive candidate. Dimensionality reduction is an important pre-processing procedure for multi-label classification to mitigate the possible effect of dimensionality curse, which is divided into feature extraction and selection. Principal component analysis (PCA) and multi-label dimensionality reduction via dependence maximization (MDDM) represent two mainstream feature extraction techniques for unsupervised and supervised paradigms. They produce many small and a few large positive eigenvalues respectively, which could deteriorate the classification performance due to an improper number of projection directions. It has been proved that PCA proposed primarily via maximizing feature variance is associated with a least-squares formulation. In this paper, we prove that MDDM with orthonormal projection directions also falls into the least-squares framework, which originally maximizes Hilbert-Schmidt independence criterion (HSIC). Then we propose a novel multi-label feature extraction method to integrate two least-squares formulae through a linear combination, which maximizes both feature variance and feature-label dependence simultaneously and thus results in a proper number of positive eigenvalues. Experimental results on eight data sets show that our proposed method can achieve a better performance, compared with other seven state-of-the-art multi-label feature extraction algorithms. A hierarchical Bayes Gaussian Mixture Model (HBGMM) with adaptive sparsity is proposed.We impose our hierarchical Bayes prior on the entries of precision matrices in GMM to encourage sparsity.Our adaptive sparsity can reduce the dimensionality of the parameters in GMM to be estimated.Our HBGMM method does not involve any hyperparameters to be estimated, i.e., it is hyperparameter-free. Gaussian Mixture Model (GMM) has been widely used in statistics for its great flexibility. However, parameter estimation for GMM with high dimensionality is a challenge because of the large number of parameters and the lack of observation data. In this paper, we propose an effective method named hierarchical Bayes based Adaptive Sparsity in Gaussian Mixture Model (ASGMM) to estimate the parameters in a GMM by incorporating a two-layer hierarchical Bayes based adaptive sparsity prior. The prior we impose on the precision matrices can encourage sparsity and hence reduce the dimensionality of the parameters to be estimated. In contrast to the l 1 -norm penalty or Laplace prior, our approach does not involve any hyperparameters that must be tuned, and the sparsity adapts to the observation data. The proposed method is achieved by three steps: first, we formulate an adaptive hierarchical Bayes model of the precision matrices in the GMM with a Jeffrey's noninformative hyperprior, which expresses scale-invariance and, more importantly, is hyperparameter-free and unbiased. Second, we perform a Cholesky decomposition on the precision matrices to impose the positive definite property. Finally, we exploit the expectation maximization (EM) algorithm to obtain the final estimated parameters in the GMM. Experimental results on synthetic and real-world datasets demonstrate that ASGMM cannot only adapt the sparsity of high-dimensional data with small estimated error, but also achieve better clustering performance comparing with several classical methods. In this paper, two supervised methods for enhancing the classification accuracy of the Nonnegative Matrix Factorization (NMF) algorithm are presented. The idea is to extend the NMF algorithm in order to extract features that enforce not only the spatial locality, but also the separability between classes in a discriminant manner. The first method employs discriminant analysis in the features derived from NMF. In this way, a two-phase discriminant feature extraction procedure is implemented, namely NMF plus Linear Discriminant Analysis (LDA). The second method incorporates the discriminant constraints inside the NMF decomposition. Thus, a decomposition of a face to its discriminant parts is obtained and new update rules for both the weights and the basis images are derived. The introduced methods have been applied to the problem of frontal face verification using the well-known XM2VTS database. Both methods greatly enhance the performance of NMF for frontal face verification We show that the standard beam-search algorithm can be used as an efficient decoder for the global linear model of Zhang and Clark (2008) for joint word segmentation and POS-tagging, achieving a significant speed improvement. Such decoding is enabled by: (1) separating full word features from partial word features so that feature templates can be instantiated incrementally, according to whether the current character is separated or appended; (2) deciding the POS-tag of a potential word when its first character is processed. Early-update is used with perceptron training so that the linear model gives a high score to a correct partial candidate as well as a full output. Effective scoring of partial structures allows the decoder to give high accuracy with a small beam-size of 16. In our 10-fold cross-validation experiments with the Chinese Tree-bank, our system performed over 10 times as fast as Zhang and Clark (2008) with little accuracy loss. The accuracy of our system on the standard CTB 5 test was competitive with the best in the literature. We analyse the noise arising in collaborative filtering when formalised as a probabilistic matrix factorisation problem. We show empirically that modelling row- and column-specific variances is important, the noise being in general non-Gaussian and heteroscedastic. We also advocate for the use of a Student-t prior for the latent features as the standard Gaussian is included as a special case. We derive several variational inference algorithms and estimate the hyperparameters by type-II maximum likelihood. Experiments on real data show that the predictive performance is significantly improved. Finding latent factors of the data using matrix factorizations is a tried-and-tested approach in data mining. But finding shared factors over multiple matrices is more novel problem. Specifically, given two matrices, we want to find a set of factors shared by these two matrices and sets of factors specific for the matrices. Not only does such decomposition reveal what is common between the two matrices, it also eliminates the need of explaining that common part twice, thus concentrating the non-shared factors to uniquely specific parts of the data. This paper studies a problem called Joint Subspace Boolean Matrix Factorization asking exactly that: a set of shared factors and sets of specific factors. Furthermore, the matrix factorization is based on the Boolean arithmetic. This restricts the presented approach suitable to only binary matrices. The benefits, however, include much sparser factor matrices and greater interpretability of the results. The paper presents three algorithms for finding the Joint Subspace Boolean Matrix Factorization, an MDLbased method for selecting the subspaces’ dimensionality, and throughout experimental evaluation of the proposed algorithms. In this paper, we report our extension of the use of feature selection based on mutual information and feature fusion to improve gender classification of face images. We compare the results of fusing three groups of features, three spatial scales, and four different mutual information measures to select features. We also showed improved results by fusion of LBP features with different radii and spatial scales, and the selection of features using mutual information. As measures of mutual information we use minimum redundancy and maximal relevance (mRMR), normalized mutual information feature selection (NMIFS), conditional mutual information feature selection (CMIFS), and conditional mutual information maximization (CMIM). We tested the results on four databases: FERET and UND, under controlled conditions, the LFW database under unconstrained scenarios, and AR for occlusions. It is shown that selection of features together with fusion of LBP features significantly improved gender classification accuracy compared to previously published results. We also show a significant reduction in processing time because of the feature selection, which makes real-time applications of gender classification feasible. The essence of distantly supervised relation extraction is that it is an incomplete multi-label classification problem with sparse and noisy features. To tackle the sparsity and noise challenges, we propose solving the classification problem using matrix completion on factorized matrix of minimized rank. We formulate relation classification as completing the unknown labels of testing items (entity pairs) in a sparse matrix that concatenates training and testing textual features with training labels. Our algorithmic framework is based on the assumption that the rank of item-by-feature and item-by-label joint matrix is low. We apply two optimization models to recover the underlying low-rank matrix leveraging the sparsity of feature-label matrix. The matrix completion problem is then solved by the fixed point continuation (FPC) algorithm, which can find the global optimum. Experiments on two widely used datasets with different dimensions of textual features demonstrate that our low-rank matrix completion approach significantly outperforms the baseline and the state-of-the-art methods. Matrix factorization on user-item rating matrices has achieved significant success in collaborative filtering based recommendation tasks. However, it also encounters the problems of data sparsity and scalability when applied in real-world recommender systems. In this paper, we present the Localized Matrix Factorization (LMF) framework, which attempts to meet the challenges of sparsity and scalability by factorizing Block Diagonal Form (BDF) matrices. In the LMF framework, a large sparse matrix is first transformed into Recursive Bordered Block Diagonal Form (RBBDF), which is an intuitionally interpretable structure for user-item rating matrices. Smaller and denser submatrices are then extracted from this RBBDF matrix to construct a BDF matrix for more effective collaborative prediction. We show formally that the LMF framework is suitable for matrix factorization and that any decomposable matrix factorization algorithm can be integrated into this framework. It has the potential to improve prediction accuracy by factorizing smaller and denser submatrices independently, which is also suitable for parallelization and contributes to system scalability at the same time. Experimental results based on a number of real-world public-access benchmarks show the effectiveness and efficiency of the proposed LMF framework. Recently, many e-commerce websites have encouraged their users to rate shopping items and write review texts. This review information has been very useful for understanding user preferences and item properties, as well as enhancing the capability to make personalized recommendations of these websites. In this paper, we propose to model user preferences and item properties using convolutional neural networks (CNNs) with dual local and global attention, motivated by the superiority of CNNs to extract complex features. By using aggregated review texts from a user and aggregated review text for an item, our model can learn the unique features (embedding) of each user and each item. These features are then used to predict ratings. We train these user and item networks jointly which enable the interaction between users and items in a similar way as matrix factorization. The local attention provides us insight on a user's preferences or an item's properties. The global attention helps CNNs focus on the semantic meaning of the whole review text. Thus, the combined local and global attentions enable an interpretable and better-learned representation of users and items. We validate the proposed models by testing on popular review datasets in Yelp and Amazon and compare the results with matrix factorization (MF), the hidden factor and topical (HFT) model, and the recently proposed convolutional matrix factorization (ConvMF+). Our proposed CNNs with dual attention model outperforms HFT and ConvMF+ in terms of mean square errors (MSE). In addition, we compare the user item embeddings learned from these models for classification and recommendation. These results also confirm the superior quality of user item embeddings learned from our model. Collaborative Filtering(CF)-based recommendation algorithms, such as Latent Factor Models (LFM), work well in terms of prediction accuracy. However, the latent features make it difficulty to explain the recommendation results to the users. Fortunately, with the continuous growth of online user reviews, the information available for training a recommender system is no longer limited to just numerical star ratings or user item features. By extracting explicit user opinions about various aspects of a product from the reviews, it is possible to learn more details about what aspects a user cares, which further sheds light on the possibility to make explainable recommendations. In this work, we propose the Explicit Factor Model (EFM) to generate explainable recommendations, meanwhile keep a high prediction accuracy. We first extract explicit product features (i.e. aspects) and user opinions by phrase-level sentiment analysis on user reviews, then generate both recommendations and disrecommendations according to the specific product features to the user's interests and the hidden features learned. Besides, intuitional feature-level explanations about why an item is or is not recommended are generated from the model. Offline experimental results on several real-world datasets demonstrate the advantages of our framework over competitive baseline algorithms on both rating prediction and top-K recommendation tasks. Online experiments show that the detailed explanations make the recommendations and disrecommendations more influential on user's purchasing behavior. Many real-world problems, such as web image analysis, document categorization and product recommendation, often exhibit dual-heterogeneity: heterogeneous features obtained in multiple views, and multiple tasks might be related to each other through one or more shared views. To address these Multi-Task Multi-View (MTMV) problems, we propose a tensor-based framework for learning the predictive multilinear structure from the full-order feature interactions within the heterogeneous data. The usage of tensor structure is to strengthen and capture the complex relationships between multiple tasks with multiple views. We further develop efficient multilinear factorization machines (MFMs) that can learn the task-specific feature map and the task-view shared multilinear structures, without physically building the tensor. In the proposed method, a joint factorization is applied to the full-order interactions such that the consensus representation can be learned. In this manner, it can deal with the partially incomplete data without difficulty as the learning procedure does not simply rely on any particular view. Furthermore, the complexity of MFMs is linear in the number of parameters, which makes MFMs suitable to large-scale real-world problems. Extensive experiments on four real-world datasets demonstrate that the proposed method significantly outperforms several state-of-the-art methods in a wide variety of MTMV problems. We analyze skip-gram with negative-sampling (SGNS), a word embedding method introduced by , and show that it is implicitly factorizing a word-context matrix, whose cells are the pointwise mutual information (PMI) of the respective word and context pairs, shifted by a global constant. We find that another embedding method, NCE, is implicitly factorizing a similar matrix, where each cell is the (shifted) log conditional probability of a word given its context. We show that using a sparse Shifted Positive PMI word-context matrix to represent words improves results on two word similarity tasks and one of two analogy tasks. When dense low-dimensional vectors are preferred, exact factorization with SVD can achieve solutions that are at least as good as SGNS's solutions for word similarity tasks. On analogy questions SGNS remains superior to SVD. We conjecture that this stems from the weighted nature of SGNS's factorization. In this paper, we propose a rank minimization method to fuse the predicted confidence scores of multiple models, each of which is obtained based on a certain kind of feature. Specifically, we convert each confidence score vector obtained from one model into a pairwise relationship matrix, in which each entry characterizes the comparative relationship of scores of two test samples. Our hypothesis is that the relative score relations are consistent among component models up to certain sparse deviations, despite the large variations that may exist in the absolute values of the raw scores. Then we formulate the score fusion problem as seeking a shared rank-2 pairwise relationship matrix based on which each original score matrix from individual model can be decomposed into the common rank-2 matrix and sparse deviation errors. A robust score vector is then extracted to fit the recovered low rank score relation matrix. We formulate the problem as a nuclear norm and l 1 norm optimization objective function and employ the Augmented Lagrange Multiplier (ALM) method for the optimization. Our method is isotonic (i.e., scale invariant) to the numeric scales of the scores originated from different models. We experimentally show that the proposed method achieves significant performance gains on various tasks including object categorization and video event detection. 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. Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in statistics, machine learning, computer vision, as well as signal and image processing. In theory, this problem can be solved by the natural convex joint mixed relaxations (i.e., l 1 -norm and trace norm) under certain conditions. However, all current provable algorithms suffer from superlinear per-iteration cost, which severely limits their applicability to large-scale problems. In this paper, we propose a scalable, provable and structured robust bilinear factorization (RBF) method to recover low-rank and sparse matrices from missing and grossly corrupted data, i.e., robust matrix completion (RMC), or incomplete and grossly corrupted measurements, i.e., compressive principal component pursuit (CPCP). Specifically, we first present two small-scale matrix trace norm regularized bilinear factorization models for RMC and CPCP problems, in which repetitively calculating SVD of a large-scale matrix is replaced by updating two much smaller factor matrices. Then, we apply the alternating direction method of multipliers (ADMM) to efficiently solve the RMC problems. Finally, we provide the convergence analysis of our algorithm, and extend it to address general CPCP problems. Experimental results verified both the efficiency and effectiveness of our method compared with the state-of-the-art methods.