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

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Domain Adaptive Computational Models for Computer Vision

abstract: The widespread adoption of computer vision models is often constrained by the issue of domain mismatch. Models that are trained with data belonging to one distribution, perform poorly when tested with data from a different distribution. Variations in vision based data can be attributed to the following reasons, viz., differences in image quality (resolution, brightness, occlusion and color), changes in camera perspective, dissimilar backgrounds and an inherent diversity of the samples themselves. Machine learning techniques like transfer learning are employed to adapt computational models across distributions. Domain adaptation is a special case of transfer learning, where knowledge from a source domain is transferred to a target domain in the form of learned models and efficient feature representations. The dissertation outlines novel domain adaptation approaches across different feature spaces; (i) a linear Support Vector Machine model for domain alignment; (ii) a nonlinear kernel based approach that embeds domain-aligned data for enhanced classification; (iii) a hierarchical model implemented using deep learning, that estimates domain-aligned hash values for the source and target data, and (iv) a proposal for a feature selection technique to reduce cross-domain disparity. These adaptation procedures are tested and validated across a range of computer vision applications like object classification, facial expression recognition, digit recognition, and activity recognition. The dissertation also provides a unique perspective of domain adaptation literature from the point-of-view of linear, nonlinear and hierarchical feature spaces. The dissertation concludes with a discussion on the future directions for research that highlight the role of domain adaptation in an era of rapid advancements in artificial intelligence.Dissertation/ThesisDoctoral Dissertation Computer Science 201

Learning from the mistakes of others: matching errors in cross dataset learning

Can we learn about object classes in images by looking at a collection of relevant 3D models? Or if we want to learn about human (inter-)actions in images, can we benefit from videos or abstract illustrations that show these actions? A common aspect of these settings is the availability of additional or privileged data that can be exploited at training time and that will not be available and not of interest at test time. We seek to generalize the learning with privileged information (LUPI) framework, which requires additional information to be defined per image, to the setting where additional information is a data collection about the task of interest. Our framework minimizes the distribution mismatch between errors made in images and in privileged data. The proposed method is tested on four publicly available datasets: Image+ClipArt, Image+3Dobject, and Image+Video. Experimental results reveal that our new LUPI paradigm naturally addresses the cross-dataset learning

Kernel methods in machine learning

We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS) of functions defined on the data domain, expanded in terms of a kernel. Working in linear spaces of function has the benefit of facilitating the construction and analysis of learning algorithms while at the same time allowing large classes of functions. The latter include nonlinear functions as well as functions defined on nonvectorial data. We cover a wide range of methods, ranging from binary classifiers to sophisticated methods for estimation with structured data.Comment: Published in at http://dx.doi.org/10.1214/009053607000000677 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Regression on fixed-rank positive semidefinite matrices: a Riemannian approach

The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The mathematical developments rely on the theory of gradient descent algorithms adapted to the Riemannian geometry that underlies the set of fixed-rank positive semidefinite matrices. In contrast with previous contributions in the literature, no restrictions are imposed on the range space of the learned matrix. The resulting algorithms maintain a linear complexity in the problem size and enjoy important invariance properties. We apply the proposed algorithms to the problem of learning a distance function parameterized by a positive semidefinite matrix. Good performance is observed on classical benchmarks