Analysis And Application Of Graph Based Semi Supervised Learning Methods
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Graph-Based Semi-Supervised Learning
Author: Amarnag Subramanya
language: en
Publisher: Springer Nature
Release Date: 2022-05-31
While labeled data is expensive to prepare, ever increasing amounts of unlabeled data is becoming widely available. In order to adapt to this phenomenon, several semi-supervised learning (SSL) algorithms, which learn from labeled as well as unlabeled data, have been developed. In a separate line of work, researchers have started to realize that graphs provide a natural way to represent data in a variety of domains. Graph-based SSL algorithms, which bring together these two lines of work, have been shown to outperform the state-of-the-art in many applications in speech processing, computer vision, natural language processing, and other areas of Artificial Intelligence. Recognizing this promising and emerging area of research, this synthesis lecture focuses on graph-based SSL algorithms (e.g., label propagation methods). Our hope is that after reading this book, the reader will walk away with the following: (1) an in-depth knowledge of the current state-of-the-art in graph-based SSL algorithms, and the ability to implement them; (2) the ability to decide on the suitability of graph-based SSL methods for a problem; and (3) familiarity with different applications where graph-based SSL methods have been successfully applied. Table of Contents: Introduction / Graph Construction / Learning and Inference / Scalability / Applications / Future Work / Bibliography / Authors' Biographies / Index
Introduction to Semi-Supervised Learning
Semi-supervised learning is a learning paradigm concerned with the study of how computers and natural systems such as humans learn in the presence of both labeled and unlabeled data. Traditionally, learning has been studied either in the unsupervised paradigm (e.g., clustering, outlier detection) where all the data are unlabeled, or in the supervised paradigm (e.g., classification, regression) where all the data are labeled. The goal of semi-supervised learning is to understand how combining labeled and unlabeled data may change the learning behavior, and design algorithms that take advantage of such a combination. Semi-supervised learning is of great interest in machine learning and data mining because it can use readily available unlabeled data to improve supervised learning tasks when the labeled data are scarce or expensive. Semi-supervised learning also shows potential as a quantitative tool to understand human category learning, where most of the input is self-evidently unlabeled. In this introductory book, we present some popular semi-supervised learning models, including self-training, mixture models, co-training and multiview learning, graph-based methods, and semi-supervised support vector machines. For each model, we discuss its basic mathematical formulation. The success of semi-supervised learning depends critically on some underlying assumptions. We emphasize the assumptions made by each model and give counterexamples when appropriate to demonstrate the limitations of the different models. In addition, we discuss semi-supervised learning for cognitive psychology. Finally, we give a computational learning theoretic perspective on semi-supervised learning, and we conclude the book with a brief discussion of open questions in the field. Table of Contents: Introduction to Statistical Machine Learning / Overview of Semi-Supervised Learning / Mixture Models and EM / Co-Training / Graph-Based Semi-Supervised Learning / Semi-Supervised Support Vector Machines / Human Semi-Supervised Learning / Theory and Outlook
Analysis and Application of Graph-Based Semi-Supervised Learning Methods
In recent years, the need for pattern recognition and data analysis has grown exponentially in various fields of scientific research. My research is centered around graph Laplacian based techniques for image processing and machine learning. Three papers pertaining to this theme will be presented in this thesis.The first work is an application of graph Laplacian regularization to the problem of convolutional sparse coding. The additional regularization improves the robustness of the sparse representation with respect to noise, and has empirically shown to improve the performance of denoising on several well-known images. Efficient algorithms for computing the eigen-decomposition of the graph Laplacian were also incorporated to the solver for fast implementations of the method.The second piece of work studies the convergence of the graph Allen-Cahn scheme. A technique inspired by the maximum principle for the heat equation is used to show stability of the convex-splitting numeric scheme. This coupled with techniques from convex optimization allows for a proof of convergence under an a-posteriori condition. The analysis is then generalized to handle spectral trunction, a common method to save computational cost, and also to the case of multi-class classification. In particular, the results for spectral trunction are drastically different from that of the original scheme in the worst case, but does not present itself in practical applications.The third piece of work combines two fields of research, uncertainty quantification, and semi-supervised learning on graphs. The work presents a unified Bayesian framework thatincorporates most previous methods for graph-based semi-supervised learning. A Bayesianframework allows for the computation of uncertainty for certain quantities under the pos-terior distribution. We show via solid numerical evidence that for a few carefully designedquantities, the expectations computed under the posterior yields meaningful notions of un-certainty for the classification problem. Efficient numerical methods were also devised tomake possible the evaluation of these quantities for large scale graphs.