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

TagBook: A Semantic Video Representation without Supervision for Event Detection

We consider the problem of event detection in video for scenarios where only few, or even zero examples are available for training. For this challenging setting, the prevailing solutions in the literature rely on a semantic video representation obtained from thousands of pre-trained concept detectors. Different from existing work, we propose a new semantic video representation that is based on freely available social tagged videos only, without the need for training any intermediate concept detectors. We introduce a simple algorithm that propagates tags from a video's nearest neighbors, similar in spirit to the ones used for image retrieval, but redesign it for video event detection by including video source set refinement and varying the video tag assignment. We call our approach TagBook and study its construction, descriptiveness and detection performance on the TRECVID 2013 and 2014 multimedia event detection datasets and the Columbia Consumer Video dataset. Despite its simple nature, the proposed TagBook video representation is remarkably effective for few-example and zero-example event detection, even outperforming very recent state-of-the-art alternatives building on supervised representations.Comment: accepted for publication as a regular paper in the IEEE Transactions on Multimedi

Exploring the mirror TBA

We apply the contour deformation trick to the Thermodynamic Bethe Ansatz equations for the AdS_5 \times S^5 mirror model, and obtain the integral equations determining the energy of two-particle excited states dual to N=4 SYM operators from the sl(2) sector. We show that each state/operator is described by its own set of TBA equations. Moreover, we provide evidence that for each state there are infinitely-many critical values of 't Hooft coupling constant \lambda, and the excited states integral equations have to be modified each time one crosses one of those. In particular, estimation based on the large L asymptotic solution gives \lambda \approx 774 for the first critical value corresponding to the Konishi operator. Our results indicate that the related calculations and conclusions of Gromov, Kazakov and Vieira should be interpreted with caution. The phenomenon we discuss might potentially explain the mismatch between their recent computation of the scaling dimension of the Konishi operator and the one done by Roiban and Tseytlin by using the string theory sigma model.Comment: 69 pages, v2: new "hybrid" equations for YQ-functions, figures and tables are added. Analyticity of Y-system is discussed, v3: published versio