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

OPML: A One-Pass Closed-Form Solution for Online Metric Learning

To achieve a low computational cost when performing online metric learning for large-scale data, we present a one-pass closed-form solution namely OPML in this paper. Typically, the proposed OPML first adopts a one-pass triplet construction strategy, which aims to use only a very small number of triplets to approximate the representation ability of whole original triplets obtained by batch-manner methods. Then, OPML employs a closed-form solution to update the metric for new coming samples, which leads to a low space (i.e., $O(d)$) and time (i.e., $O(d^2)$) complexity, where $d$ is the feature dimensionality. In addition, an extension of OPML (namely COPML) is further proposed to enhance the robustness when in real case the first several samples come from the same class (i.e., cold start problem). In the experiments, we have systematically evaluated our methods (OPML and COPML) on three typical tasks, including UCI data classification, face verification, and abnormal event detection in videos, which aims to fully evaluate the proposed methods on different sample number, different feature dimensionalities and different feature extraction ways (i.e., hand-crafted and deeply-learned). The results show that OPML and COPML can obtain the promising performance with a very low computational cost. Also, the effectiveness of COPML under the cold start setting is experimentally verified.Comment: 12 page

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

Forced Oscillation Source Location via Multivariate Time Series Classification

Precisely locating low-frequency oscillation sources is the prerequisite of suppressing sustained oscillation, which is an essential guarantee for the secure and stable operation of power grids. Using synchrophasor measurements, a machine learning method is proposed to locate the source of forced oscillation in power systems. Rotor angle and active power of each power plant are utilized to construct multivariate time series (MTS). Applying Mahalanobis distance metric and dynamic time warping, the distance between MTS with different phases or lengths can be appropriately measured. The obtained distance metric, representing characteristics during the transient phase of forced oscillation under different disturbance sources, is used for offline classifier training and online matching to locate the disturbance source. Simulation results using the four-machine two-area system and IEEE 39-bus system indicate that the proposed location method can identify the power system forced oscillation source online with high accuracy.Comment: 5 pages, 3 figures. Accepted by 2018 IEEE/PES Transmission and Distribution Conferenc

A Data-Driven Fault Detection Framework Using Mahalanobis Distance Based Dynamic Time Warping

Fault detection module is one of the most important components in modern industrial systems. In this paper, we propose a novel fault detection framework which makes use of both normal and faulty measurement signals at the same time. In this framework, the multivariate time series (MTS) pieces which are extracted from measurement signals in a time interval are used as the training and testing samples, and a K-nearest neighbour rule of MTS pieces is applied for fault detection. Moreover, a Mahalanobis distance based dynamic time warping method is used to measure the divergence among MTS pieces, and a one-class metric learning algorithm is proposed to learn the appropriate Mahalanobis distance. Experimental results on the Tennessee Eastman process demonstrate that the proposed method has improved fault detection performance compared with classical approaches on certain kinds of faults.10.13039/501100001809-National Natural Science Foundation of China (Grant Number: 51705453, 51879233 and 61911530251); 10.13039/501100004731-Zhejiang Provincial Natural Science Foundation of China (Grant Number: LHY20E090001); 10.13039/501100011491-Zhoushan Municipal Commission of Science and Technology (Grant Number: 2019C81036); 10.13039/501100012226-Fundamental Research Funds for the Central Universities