There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Item recommendation is the task of predicting a personalized ranking on a set of items (e.g. websites, movies, products). In this paper, we investigate the most common scenario with implicit feedback (e.g. clicks, purchases). There are many methods for item recommendation from implicit feedback like matrix factorization (MF) or adaptive k-nearest-neighbor (kNN). Even though these methods are designed for the item prediction task of personalized ranking, none of them is directly optimized for ranking. In this paper we present a generic optimization criterion BPR-Opt for personalized ranking that is the maximum posterior estimator derived from a Bayesian analysis of the problem. We also provide a generic learning algorithm for optimizing models with respect to BPR-Opt. The learning method is based on stochastic gradient descent with bootstrap sampling. We show how to apply our method to two state-of-the-art recommender models: matrix factorization and adaptive kNN. Our experiments indicate that for the task of personalized ranking our optimization method outperforms the standard learning techniques for MF and kNN. The results show the importance of optimizing models for the right criterion.

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BPR: Bayesian personalized ranking from implicit feedback

In this paper, we introduce Factorization Machines (FM) which are a new model class that combines the advantages of Support Vector Machines (SVM) with factorization models. Like SVMs, FMs are a general predictor working with any real valued feature vector. In contrast to SVMs, FMs model all interactions between variables using factorized parameters. Thus they are able to estimate interactions even in problems with huge sparsity (like recommender systems) where SVMs fail. We show that the model equation of FMs can be calculated in linear time and thus FMs can be optimized directly. So unlike nonlinear SVMs, a transformation in the dual form is not necessary and the model parameters can be estimated directly without the need of any support vector in the solution. We show the relationship to SVMs and the advantages of FMs for parameter estimation in sparse settings. On the other hand there are many different factorization models like matrix factorization, parallel factor analysis or specialized models like SVD++, PITF or FPMC. The drawback of these models is that they are not applicable for general prediction tasks but work only with special input data. Furthermore their model equations and optimization algorithms are derived individually for each task. We show that FMs can mimic these models just by specifying the input data (i.e. the feature vectors). This makes FMs easily applicable even for users without expert knowledge in factorization models.

Factorization Machines

Recommender systems are an important component of many websites. Two of the most popular approaches are based on matrix factorization (MF) and Markov chains (MC). MF methods learn the general taste of a user by factorizing the matrix over observed user-item preferences. On the other hand, MC methods model sequential behavior by learning a transition graph over items that is used to predict the next action based on the recent actions of a user. In this paper, we present a method bringing both approaches together. Our method is based on personalized transition graphs over underlying Markov chains. That means for each user an own transition matrix is learned - thus in total the method uses a transition cube. As the observations for estimating the transitions are usually very limited, our method factorizes the transition cube with a pairwise interaction model which is a special case of the Tucker Decomposition. We show that our factorized personalized MC (FPMC) model subsumes both a common Markov chain and the normal matrix factorization model. For learning the model parameters, we introduce an adaption of the Bayesian Personalized Ranking (BPR) framework for sequential basket data. Empirically, we show that our FPMC model outperforms both the common matrix factorization and the unpersonalized MC model both learned with and without factorization.

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Factorizing personalized Markov chains for next-basket recommendation

Building a successful recommender system depends on understanding both the dimensions of people's preferences as well as their dynamics. In certain domains, such as fashion, modeling such preferences can be incredibly difficult, due to the need to simultaneously model the visual appearance of products as well as their evolution over time. The subtle semantics and non-linear dynamics of fashion evolution raise unique challenges especially considering the sparsity and large scale of the underlying datasets. In this paper we build novel models for the One-Class Collaborative Filtering setting, where our goal is to estimate users' fashion-aware personalized ranking functions based on their past feedback. To uncover the complex and evolving visual factors that people consider when evaluating products, our method combines high-level visual features extracted from a deep convolutional neural network, users' past feedback, as well as evolving trends within the community. Experimentally we evaluate our method on two large real-world datasets from Amazon.com, where we show it to outperform state-of-the-art personalized ranking measures, and also use it to visualize the high-level fashion trends across the 11-year span of our dataset.

Ups and Downs: Modeling the Visual Evolution of Fashion Trends with One-Class Collaborative Filtering

Many applications of collaborative filtering (CF), such as news item recommendation and bookmark recommendation, are most naturally thought of as one-class collaborative filtering (OCCF) problems. In these problems, the training data usually consist simply of binary data reflecting a user's action or inaction, such as page visitation in the case of news item recommendation or webpage bookmarking in the bookmarking scenario. Usually this kind of data are extremely sparse (a small fraction are positive examples), therefore ambiguity arises in the interpretation of the non-positive examples. Negative examples and unlabeled positive examples are mixed together and we are typically unable to distinguish them. For example, we cannot really attribute a user not bookmarking a page to a lack of interest or lack of awareness of the page. Previous research addressing this one-class problem only considered it as a classification task. In this paper, we consider the one-class problem under the CF setting. We propose two frameworks to tackle OCCF. One is based on weighted low rank approximation; the other is based on negative example sampling. The experimental results show that our approaches significantly outperform the baselines.

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One-Class Collaborative Filtering

Cross-validation is a mainstay for measuring performance and progress in machine learning. There are subtle differences in how exactly to compute accuracy, F-measure and Area Under the ROC Curve (AUC) in cross-validation studies. However, these details are not discussed in the literature, and incompatible methods are used by various papers and software packages. This leads to inconsistency across the research literature. Anomalies in performance calculations for particular folds and situations go undiscovered when they are buried in aggregated results over many folds and datasets, without ever a person looking at the intermediate performance measurements. This research note clarifies and illustrates the differences, and it provides guidance for how best to measure classification performance under cross-validation. In particular, there are several divergent methods used for computing F-measure, which is often recommended as a performance measure under class imbalance, e.g., for text classification domains and in one-vs.-all reductions of datasets having many classes. We show by experiment that all but one of these computation methods leads to biased measurements, especially under high class imbalance. This paper is of particular interest to those designing machine learning software libraries and researchers focused on high class imbalance.

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Apples-to-apples in cross-validation studies: pitfalls in classifier performance measurement

One-Class Collaborative Filtering (OCCF) is a task that naturally emerges in recommender system settings. Typical characteristics include: Only positive examples can be observed, classes are highly imbalanced, and the vast majority of data points are missing. The idea of introducing weights for missing parts of a matrix has recently been shown to help in OCCF. While existing weighting approaches mitigate the first two problems above, a sparsity preserving solution that would allow to efficiently utilize data sets with e.g., hundred thousands of users and items has not yet been reported. In this paper, we study three different collaborative filtering frameworks: Low-rank matrix approximation, probabilistic latent semantic analysis, and maximum-margin matrix factorization. We propose two novel algorithms for large-scale OCCF that allow to weight the unknowns. Our experimental results demonstrate their effectiveness and efficiency on different problems, including the Netflix Prize data.

Mind the gaps: weighting the unknown in large-scale one-class collaborative filtering

Linear classifiers have been shown to be effective for many discrimination tasks. Irrespective of the learning algorithm itself, the final classifier has a weight to multiply by each feature. This suggests that ideally each input feature should be linearly correlated with the target variable (or anti-correlated), whereas raw features may be highly non-linear. In this paper, we attempt to re-shape each input feature so that it is appropriate to use with a linear weight and to scale the different features in proportion to their predictive value. We demonstrate that this pre-processing is beneficial for linear SVM classifiers on a large benchmark of text classification tasks as well as UCI datasets.

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Feature shaping for linear SVM classifiers

One embodiment is a method that determines at a client computer a relevancy of information received with respect to a user profile. The method then adjusts a ranking of the information according to the relevancy and displays a selected portion of the adjusted information on the client computer.

Martin B. Scholz

Papers

One-Class Collaborative Filtering

Apples-to-apples in cross-validation studies: pitfalls in classifier performance measurement

Mind the gaps: weighting the unknown in large-scale one-class collaborative filtering

Feature shaping for linear SVM classifiers

Adjusting Content To User Profiles