Active learning aims to obtain a classifier of high accuracy by using fewer label requests in comparison to passive learning by selecting effective queries. Many active learning methods have been developed in the past two decades, which sample queries based on informativeness or representativeness of unlabeled data points. In this work, we explore a novel querying criterion based on statistical leverage scores. The statistical leverage scores of a row in a matrix are the squared row-norms of the matrix containing its (top) left singular vectors and is a measure of influence of the row on the matrix. Leverage scores have been used for detecting high influential points in regression diagnostics and have been recently shown to be useful for data analysis and randomized low-rank matrix approximation algorithms. We explore how sampling data instances with high statistical leverage scores perform in active learning. Our empirical comparison on several binary classification datasets indicate that querying high leverage points is an effective strategy.

Subspace models play an important role in a wide range of signal processing tasks, and this paper explores how the pairwise geometry of subspaces influences the probability of misclassification. When the mismatch between the signal and the model is vanishingly small, the probability of misclassification is determined by the product of the sines of the principal angles between subspaces. When the mismatch is more significant, the probability of misclassification is determined by the sum of the squares of the sines of the principal angles. Reliability of classification is derived in terms of the distribution of signal energy across principal vectors. Larger principal angles lead to smaller classification error, motivating a linear transform that optimizes principal angles. The transform presented here (TRAIT) preserves some specific characteristic of each individual class, and this approach is shown to be complementary to a previously developed transform (LRT) that enlarges inter-class distance while suppressing intra-class dispersion. Theoretical results are supported by demonstration of superior classification accuracy on synthetic and measured data even in the presence of significant model mismatch.

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.

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.

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.

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.