| Classification---i.e. categorizing data instances into pre-defined categories---is an interesting and challenging task. Many real world problems involve classification, in domains such as medical informatics, image analysis, and text tagging. We consider the challenge of learning a classifier from data. This is especially challenging when data instances are correlated.This dissertation presents extensions to CRFs to address the following three challenging issues: (1) Modeling spatial correlations more effectively by using a variant of support vector machines for the random field potential, leading to Support Vector Random Fields (SVRFs). (2) Using both unlabelled and labelled data in a supervised learning framework, leading to Semi-Supervised Discriminative Random Fields (SSDRFs) that produce more accurate model parameters. (3) Modeling spatial correlations more efficiently, leading to both Decoupled Conditional Random Fields (DCRFs) that decouple learning of the two potentials of a random field, and Pseudo Conditional Random Fields (PCRFs) that explicitly model spatial correlation only in inference .Our empirical evaluations on complex tasks (such as segmenting brain tumors) show these systems perform statistically significantly better than existing methods and promise wide practical applications.Here, we focus on learning an image segmenter---e.g. a system that classifies each pixel of a magnetic resonance (MR) image of a brain as either tumor or non-tumor. Here the labels of neighboring pixels are correlated. By contrast, discriminative approaches that assume the data instances are independent and identically distributed (i.i.d.), such as Logistic Regression (LR) and Support Vector Machines (SVM), take a single pixel as an input to a fitted decision function and make a decision for that individual pixel that ignores the continuity of labels of neighboring pixels. To be effective here, it is important to also consider the spatial correlations of labels: that is, neighboring pixels tend to have same labels. This has led to the now-standard random field approach (eg, Conditional Random Fields, CRFs), which involves learning and using two potential functions: one for estimating relevant characteristics of the individual pixel, and the other that deals with interactions between adjacent pixels. |
