Implicitly Constrained Semi-Supervised Least Squares Classification

We introduce a novel semi-supervised version of the least squares classifier. This implicitly constrained least squares (ICLS) classifier minimizes the squared loss on the labeled data among the set of parameters implied by all possible labelings of the unlabeled data. Unlike other discriminative semi-supervised methods, our approach does not introduce explicit additional assumptions into the objective function, but leverages implicit assumptions already present in the choice of the supervised least squares classifier. We show this approach can be formulated as a quadratic programming problem and its solution can be found using a simple gradient descent procedure. We prove that, in a certain way, our method never leads to performance worse than the supervised classifier. Experimental results corroborate this theoretical result in the multidimensional case on benchmark datasets, also in terms of the error rate.Comment: 12 pages, 2 figures, 1 table. The Fourteenth International Symposium on Intelligent Data Analysis (2015), Saint-Etienne, Franc

Implicitly Constrained Semi-Supervised Linear Discriminant Analysis

Semi-supervised learning is an important and active topic of research in pattern recognition. For classification using linear discriminant analysis specifically, several semi-supervised variants have been proposed. Using any one of these methods is not guaranteed to outperform the supervised classifier which does not take the additional unlabeled data into account. In this work we compare traditional Expectation Maximization type approaches for semi-supervised linear discriminant analysis with approaches based on intrinsic constraints and propose a new principled approach for semi-supervised linear discriminant analysis, using so-called implicit constraints. We explore the relationships between these methods and consider the question if and in what sense we can expect improvement in performance over the supervised procedure. The constraint based approaches are more robust to misspecification of the model, and may outperform alternatives that make more assumptions on the data, in terms of the log-likelihood of unseen objects.Comment: 6 pages, 3 figures and 3 tables. International Conference on Pattern Recognition (ICPR) 2014, Stockholm, Swede

Manifold Constrained Low-Rank Decomposition

Low-rank decomposition (LRD) is a state-of-the-art method for visual data reconstruction and modelling. However, it is a very challenging problem when the image data contains significant occlusion, noise, illumination variation, and misalignment from rotation or viewpoint changes. We leverage the specific structure of data in order to improve the performance of LRD when the data are not ideal. To this end, we propose a new framework that embeds manifold priors into LRD. To implement the framework, we design an alternating direction method of multipliers (ADMM) method which efficiently integrates the manifold constraints during the optimization process. The proposed approach is successfully used to calculate low-rank models from face images, hand-written digits and planar surface images. The results show a consistent increase of performance when compared to the state-of-the-art over a wide range of realistic image misalignments and corruptions

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

Generative Adversarial Networks (GANs): Challenges, Solutions, and Future Directions

Generative Adversarial Networks (GANs) is a novel class of deep generative models which has recently gained significant attention. GANs learns complex and high-dimensional distributions implicitly over images, audio, and data. However, there exists major challenges in training of GANs, i.e., mode collapse, non-convergence and instability, due to inappropriate design of network architecture, use of objective function and selection of optimization algorithm. Recently, to address these challenges, several solutions for better design and optimization of GANs have been investigated based on techniques of re-engineered network architectures, new objective functions and alternative optimization algorithms. To the best of our knowledge, there is no existing survey that has particularly focused on broad and systematic developments of these solutions. In this study, we perform a comprehensive survey of the advancements in GANs design and optimization solutions proposed to handle GANs challenges. We first identify key research issues within each design and optimization technique and then propose a new taxonomy to structure solutions by key research issues. In accordance with the taxonomy, we provide a detailed discussion on different GANs variants proposed within each solution and their relationships. Finally, based on the insights gained, we present the promising research directions in this rapidly growing field.Comment: 42 pages, Figure 13, Table