The rapidly growing of Location-based Social Networks (LBSNs) provides a vast amount of check-in data, which enables many services, e.g., point-of-interest (POI) recommendation. In this paper, we study the next new POI recommendation problem in which new POIs with respect to users' current location are to be recommended. The challenge lies in the difficulty in precisely learning users' sequential information and personalizing the recommendation model. To this end, we resort to the Metric Embedding method for the recommendation, which avoids drawbacks of the Matrix Factorization technique. We propose a personalized ranking metric embedding method (PRME) to model personalized check-in sequences. We further develop a PRME-G model, which integrates sequential information, individual preference, and geographical influence, to improve the recommendation performance. Experiments on two real-world LBSN datasets demonstrate that our new algorithm outperforms the state-of-the-art next POI recommendation methods.

We address an ensemble clustering problem, where reliable clusters are locally embedded in given multiple partitions. We propose a new nonnegative matrix factorization (NMF)-based method, in which locally reliable clusters are explicitly considered by using instance-wise weights over clusters. Our method factorizes the input cluster assignment matrix into two matrices H and W, which are optimized by iteratively 1) updating H and W while keeping the weight matrix constant and 2) updating the weight matrix while keeping H and W constant, alternatively. The weights in the second step were updated by solving a convex problem, which makes our algorithm significantly faster than existing NMF-based ensemble clustering methods. We empirically proved that our method outperformed a lot of cutting-edge ensemble clustering methods by using a variety of datasets.

The rapidly growing of Location-based Social Networks (LBSNs) provides a vast amount of check-in data, which enables many services, e.g., point-of-interest (POI) recommendation. In this paper, we study the next new POI recommendation problem in which new POIs with respect to users' current location are to be recommended. The challenge lies in the difficulty in precisely learning users' sequential information and personalizing the recommendation model. To this end, we resort to the Metric Embedding method for the recommendation, which avoids drawbacks of the Matrix Factorization technique. We propose a personalized ranking metric embedding method (PRME) to model personalized check-in sequences. We further develop a PRME-G model, which integrates sequential information, individual preference, and geographical influence, to improve the recommendation performance. Experiments on two real-world LBSN datasets demonstrate that our new algorithm outperforms the state-of-the-art next POI recommendation methods.

In this paper we investigate the use of coactive learning in a multitask setting. In coactive learning, an expert presents the learner with a problem and the learner returns a candidate solution. The expert then improves on the solution if necessary and presents the improved solution to the learner. The goal for the learner is to learn to produce solutions which cannot be further improved by the expert while minimizing the average expert effort. In this paper, we consider the setting where there are multiple experts (tasks), and in each iteration one expert presents a problem to the learner. While the experts are expected to have different solution preferences, they are also assumed to share similarities, which should enable generalization across experts. We analyze several algorithms for this setting and derive bounds on the average expert effort during learning. Our main contribution is the balanced Perceptron algorithm, which is the first coactive learning algorithm that is both able to generalize across experts when possible, while also guaranteeing convergence to optimal solutions for individual experts. Our experiments in three domains confirm that this algorithm is effective in the multitask setting, compared to natural baselines.

Principal component analysis (PCA) is an unsupervised method for learning low-dimensional features with orthogonal projections. Multilinear PCA methods extend PCA to deal with multidimensional data (tensors) directly via tensor-to-tensor projection or tensor-to-vector projection (TVP). However, under the TVP setting, it is difficult to develop an effective multilinear PCA method with the orthogonality constraint. This paper tackles this problem by proposing a novel Semi-Orthogonal Multilinear PCA (SO-MPCA) approach. SO-MPCA learns low-dimensional features directly from tensors via TVP by imposing the orthogonality constraint in only one mode. This formulation results in more captured variance and more learned features than full orthogonality. For better generalization, we further introduce a relaxed start (RS) strategy to get SO-MPCA-RS by fixing the starting projection vectors, which increases the bias and reduces the variance of the learning model. Experiments on both face (2D) and gait (3D) data demonstrate that SO-MPCA-RS outperforms other competing algorithms on the whole, and the relaxed start strategy is also effective for other TVP-based PCA methods.

Gaussian processes (GPs) provide a nonparametric representation of functions. However, classical GP inference suffers from high computational cost for big data. In this paper, we propose a new Bayesian approach, EigenGP, that learns both basis dictionary elements — eigenfunctions of a GP prior — and prior precisions in a sparse finite model. It is well known that, among all orthogonal basis functions, eigenfunctions can provide the most compact representation. Unlike other sparse Bayesian finite models where the basis function has a fixed form, our eigenfunctions live in a reproducing kernel Hilbert space as a finite linear combination of kernel functions. We learn the dictionary elements — eigenfunctions — and the prior precisions over these elements as well as all the other hyperparameters from data by maximizing the model marginal likelihood. We explore computational linear algebra to simplify the gradient computation significantly. Our experimental results demonstrate improved predictive performance of EigenGP over alternative sparse GP methods as well as relevance vector machines.

Large sparse datasets are common in many real-world applications. Linear SVM has been shown to be very efficient for classifying such datasets. However, it is still unknown how data sparseness would affect its convergence behavior. To study this problem in a systematic manner, we propose a novel approach to generate large and sparse data from real-world datasets, using statistical inference and the data sampling process in the PAC framework. We first study the convergence behavior of linear SVM experimentally, and make several observations, useful for real-world applications. We then offer theoretical proofs for our observations by studying the Bayes risk and PAC bound. Our experiment and theoretic results are valuable for learning large sparse datasets with linear SVM.

Microarray experiments are capable of measuring the expression level of thousands of genes simultaneously. Dealing with this enormous amount of information requires complex computation. Support Vector Machines (SVM) have been widely used with great efficiency to solve classification problems that have high dimension. In this sense, it is plausible to develop new feature selection strategies for microarray data that are associated with this type of classifier. Therefore, we propose, in this paper, a new method for feature selection based on an ordered search process to explore the space of possible subsets. The algorithm, called Admissible Ordered Search (AOS), uses as evaluation function the margin values estimated for each hypothesis by a SVM classifier. An important theoretical contribution of this paper is the development of the projected margin concept. This value is computed as the margin vector projection on a lower dimensional subspace and is used as an upper bound for the current value of the hypothesis in the search process. This enables great economy in runtime and consequently efficiency in the search process as a whole. The algorithm was tested using five different microarray data sets yielding superior results when compared to three representative feature selection methods.

In this paper we focus on the greedy matrix completion problem. A simple atom selection strategy is proposed building upon an alternating minimization procedure. Based on this per-iteration strategy, we devise a greedy algorithm OAMC and establish an upper bound of the approximation error. To evaluate different weight refinement methods, several variants of OAMC are designed. We prove that OAMC and three of its variants have the property of linear convergence. Experiments of Recommendation and Image Recovery are conducted to make empirical evaluation. Results are promising. We report that our algorithm takes only 700 seconds to process Yahoo Music dataset in PC, yet achieves a root mean square error 24.5 on test set.

User interest inference from social networks is a fundamental problem to many applications. It usually exhibits dual-heterogeneities: a user's interests are complementarily and comprehensively reflected by multiple social networks; interests are inter-correlated in a nonuniform way rather than independent to each other. Although great success has been achieved by previous approaches, few of them consider these dual-heterogeneities simultaneously. In this work, we propose a structure-constrained multi-source multi-task learning scheme to co-regularize the source consistency and the tree-guided task relatedness. Meanwhile, it is able to jointly learn the task-sharing and task-specific features. Comprehensive experiments on a real-world dataset validated our scheme. In addition, we have released our dataset to facilitate the research communities.