A Survey on Metric Learning for Feature Vectors and Structured Data

The need for appropriate ways to measure the distance or similarity between data is ubiquitous in machine learning, pattern recognition and data mining, but handcrafting such good metrics for specific problems is generally difficult. This has led to the emergence of metric learning, which aims at automatically learning a metric from data and has attracted a lot of interest in machine learning and related fields for the past ten years. This survey paper proposes a systematic review of the metric learning literature, highlighting the pros and cons of each approach. We pay particular attention to Mahalanobis distance metric learning, a well-studied and successful framework, but additionally present a wide range of methods that have recently emerged as powerful alternatives, including nonlinear metric learning, similarity learning and local metric learning. Recent trends and extensions, such as semi-supervised metric learning, metric learning for histogram data and the derivation of generalization guarantees, are also covered. Finally, this survey addresses metric learning for structured data, in particular edit distance learning, and attempts to give an overview of the remaining challenges in metric learning for the years to come.Comment: Technical report, 59 pages. Changes in v2: fixed typos and improved presentation. Changes in v3: fixed typos. Changes in v4: fixed typos and new method

Learning joint feature adaptation for zero-shot recognition

Zero-shot recognition (ZSR) aims to recognize target-domain data instances of unseen classes based on the models learned from associated pairs of seen-class source and target domain data. One of the key challenges in ZSR is the relative scarcity of source-domain features (e.g. one feature vector per class), which do not fully account for wide variability in target-domain instances. In this paper we propose a novel framework of learning data-dependent feature transforms for scoring similarity between an arbitrary pair of source and target data instances to account for the wide variability in target domain. Our proposed approach is based on optimizing over a parameterized family of local feature displacements that maximize the source-target adaptive similarity functions. Accordingly we propose formulating zero-shot learning (ZSL) using latent structural SVMs to learn our similarity functions from training data. As demonstration we design a specific algorithm under the proposed framework involving bilinear similarity functions and regularized least squares as penalties for feature displacement. We test our approach on several benchmark datasets for ZSR and show significant improvement over the state-of-the-art. For instance, on aP&Y dataset we can achieve 80.89% in terms of recognition accuracy, outperforming the state-of-the-art by 11.15%

Learning joint feature adaptation for zero-shot recognition

Zero-shot recognition (ZSR) aims to recognize target-domain data instances of unseen classes based on the models learned from associated pairs of seen-class source and target domain data. One of the key challenges in ZSR is the relative scarcity of source-domain features (e.g. one feature vector per class), which do not fully account for wide variability in target-domain instances. In this paper we propose a novel framework of learning data-dependent feature transforms for scoring similarity between an arbitrary pair of source and target data instances to account for the wide variability in target domain. Our proposed approach is based on optimizing over a parameterized family of local feature displacements that maximize the source-target adaptive similarity functions. Accordingly we propose formulating zero-shot learning (ZSL) using latent structural SVMs to learn our similarity functions from training data. As demonstration we design a specific algorithm under the proposed framework involving bilinear similarity functions and regularized least squares as penalties for feature displacement. We test our approach on several benchmark datasets for ZSR and show significant improvement over the state-of-the-art. For instance, on aP&Y dataset we can achieve 80.89% in terms of recognition accuracy, outperforming the state-of-the-art by 11.15%

Labeling the Features Not the Samples: Efficient Video Classification with Minimal Supervision

Feature selection is essential for effective visual recognition. We propose an efficient joint classifier learning and feature selection method that discovers sparse, compact representations of input features from a vast sea of candidates, with an almost unsupervised formulation. Our method requires only the following knowledge, which we call the \emph{feature sign}---whether or not a particular feature has on average stronger values over positive samples than over negatives. We show how this can be estimated using as few as a single labeled training sample per class. Then, using these feature signs, we extend an initial supervised learning problem into an (almost) unsupervised clustering formulation that can incorporate new data without requiring ground truth labels. Our method works both as a feature selection mechanism and as a fully competitive classifier. It has important properties, low computational cost and excellent accuracy, especially in difficult cases of very limited training data. We experiment on large-scale recognition in video and show superior speed and performance to established feature selection approaches such as AdaBoost, Lasso, greedy forward-backward selection, and powerful classifiers such as SVM.Comment: arXiv admin note: text overlap with arXiv:1411.771

Task-Driven Dictionary Learning

Modeling data with linear combinations of a few elements from a learned dictionary has been the focus of much recent research in machine learning, neuroscience and signal processing. For signals such as natural images that admit such sparse representations, it is now well established that these models are well suited to restoration tasks. In this context, learning the dictionary amounts to solving a large-scale matrix factorization problem, which can be done efficiently with classical optimization tools. The same approach has also been used for learning features from data for other purposes, e.g., image classification, but tuning the dictionary in a supervised way for these tasks has proven to be more difficult. In this paper, we present a general formulation for supervised dictionary learning adapted to a wide variety of tasks, and present an efficient algorithm for solving the corresponding optimization problem. Experiments on handwritten digit classification, digital art identification, nonlinear inverse image problems, and compressed sensing demonstrate that our approach is effective in large-scale settings, and is well suited to supervised and semi-supervised classification, as well as regression tasks for data that admit sparse representations.Comment: final draft post-refereein

Distributed Low-rank Subspace Segmentation

Vision problems ranging from image clustering to motion segmentation to semi-supervised learning can naturally be framed as subspace segmentation problems, in which one aims to recover multiple low-dimensional subspaces from noisy and corrupted input data. Low-Rank Representation (LRR), a convex formulation of the subspace segmentation problem, is provably and empirically accurate on small problems but does not scale to the massive sizes of modern vision datasets. Moreover, past work aimed at scaling up low-rank matrix factorization is not applicable to LRR given its non-decomposable constraints. In this work, we propose a novel divide-and-conquer algorithm for large-scale subspace segmentation that can cope with LRR's non-decomposable constraints and maintains LRR's strong recovery guarantees. This has immediate implications for the scalability of subspace segmentation, which we demonstrate on a benchmark face recognition dataset and in simulations. We then introduce novel applications of LRR-based subspace segmentation to large-scale semi-supervised learning for multimedia event detection, concept detection, and image tagging. In each case, we obtain state-of-the-art results and order-of-magnitude speed ups