Learning to Approximate a Bregman Divergence

Bregman divergences generalize measures such as the squared Euclidean distance and the KL divergence, and arise throughout many areas of machine learning. In this paper, we focus on the problem of approximating an arbitrary Bregman divergence from supervision, and we provide a well-principled approach to analyzing such approximations. We develop a formulation and algorithm for learning arbitrary Bregman divergences based on approximating their underlying convex generating function via a piecewise linear function. We provide theoretical approximation bounds using our parameterization and show that the generalization error $O_p(m^{-1/2})$ for metric learning using our framework matches the known generalization error in the strictly less general Mahalanobis metric learning setting. We further demonstrate empirically that our method performs well in comparison to existing metric learning methods, particularly for clustering and ranking problems.Comment: 19 pages, 4 figure

Hierarchical Metric Learning for Optical Remote Sensing Scene Categorization

We address the problem of scene classification from optical remote sensing (RS) images based on the paradigm of hierarchical metric learning. Ideally, supervised metric learning strategies learn a projection from a set of training data points so as to minimize intra-class variance while maximizing inter-class separability to the class label space. However, standard metric learning techniques do not incorporate the class interaction information in learning the transformation matrix, which is often considered to be a bottleneck while dealing with fine-grained visual categories. As a remedy, we propose to organize the classes in a hierarchical fashion by exploring their visual similarities and subsequently learn separate distance metric transformations for the classes present at the non-leaf nodes of the tree. We employ an iterative max-margin clustering strategy to obtain the hierarchical organization of the classes. Experiment results obtained on the large-scale NWPU-RESISC45 and the popular UC-Merced datasets demonstrate the efficacy of the proposed hierarchical metric learning based RS scene recognition strategy in comparison to the standard approaches.Comment: Undergoing revision in GRS

RandomBoost: Simplified Multi-class Boosting through Randomization

We propose a novel boosting approach to multi-class classification problems, in which multiple classes are distinguished by a set of random projection matrices in essence. The approach uses random projections to alleviate the proliferation of binary classifiers typically required to perform multi-class classification. The result is a multi-class classifier with a single vector-valued parameter, irrespective of the number of classes involved. Two variants of this approach are proposed. The first method randomly projects the original data into new spaces, while the second method randomly projects the outputs of learned weak classifiers. These methods are not only conceptually simple but also effective and easy to implement. A series of experiments on synthetic, machine learning and visual recognition data sets demonstrate that our proposed methods compare favorably to existing multi-class boosting algorithms in terms of both the convergence rate and classification accuracy.Comment: 15 page

Socially Constrained Structural Learning for Groups Detection in Crowd

Modern crowd theories agree that collective behavior is the result of the underlying interactions among small groups of individuals. In this work, we propose a novel algorithm for detecting social groups in crowds by means of a Correlation Clustering procedure on people trajectories. The affinity between crowd members is learned through an online formulation of the Structural SVM framework and a set of specifically designed features characterizing both their physical and social identity, inspired by Proxemic theory, Granger causality, DTW and Heat-maps. To adhere to sociological observations, we introduce a loss function (G-MITRE) able to deal with the complexity of evaluating group detection performances. We show our algorithm achieves state-of-the-art results when relying on both ground truth trajectories and tracklets previously extracted by available detector/tracker systems

Minimum Density Hyperplanes

Associating distinct groups of objects (clusters) with contiguous regions of high probability density (high-density clusters), is central to many statistical and machine learning approaches to the classification of unlabelled data. We propose a novel hyperplane classifier for clustering and semi-supervised classification which is motivated by this objective. The proposed minimum density hyperplane minimises the integral of the empirical probability density function along it, thereby avoiding intersection with high density clusters. We show that the minimum density and the maximum margin hyperplanes are asymptotically equivalent, thus linking this approach to maximum margin clustering and semi-supervised support vector classifiers. We propose a projection pursuit formulation of the associated optimisation problem which allows us to find minimum density hyperplanes efficiently in practice, and evaluate its performance on a range of benchmark datasets. The proposed approach is found to be very competitive with state of the art methods for clustering and semi-supervised classification

Large-Margin Determinantal Point Processes

Determinantal point processes (DPPs) offer a powerful approach to modeling diversity in many applications where the goal is to select a diverse subset. We study the problem of learning the parameters (the kernel matrix) of a DPP from labeled training data. We make two contributions. First, we show how to reparameterize a DPP's kernel matrix with multiple kernel functions, thus enhancing modeling flexibility. Second, we propose a novel parameter estimation technique based on the principle of large margin separation. In contrast to the state-of-the-art method of maximum likelihood estimation, our large-margin loss function explicitly models errors in selecting the target subsets, and it can be customized to trade off different types of errors (precision vs. recall). Extensive empirical studies validate our contributions, including applications on challenging document and video summarization, where flexibility in modeling the kernel matrix and balancing different errors is indispensable.Comment: 15 page