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Sparsity regularization and graph-based representation in medical imaging

Abstract : Medical images have been widely used in modern medicine to depict the anatomy or function for both clinical purposes and for studying normal anatomy. Analyzing medical images efficiently and with high accuracy is a crucial step. The high-dimensionality and the non-linear nature of medical imaging data makes their analysis a difficult and challenging problem. In this thesis, we address the medical image analysis from the viewpoint of statistical learning theory and we concentrate especially on the use of regularization methods and graph representation and comparison. First, we approach the problem of graph representation and comparison for analyzing medical images. Graphs are a commonly used technique to represent data with inherited structure. Exploiting these data, requires the ability to efficiently compare and represent graphs. Unfortunately, standard solutions to these problems are either NP-hard, hard to parametrize and adapt to the problem at hand or not expressive enough. Graph kernels, which have been introduced in the machine learning community the last decade, are a promising solution to the aforementioned problems. Despite the significant progress in the design and improvement of graph kernels in the past few years, existing graph kernels focus on either unlabeled or discretely labeled graphs, while efficient and expressive representation and comparison of graphs with complex labels, such as real numbers and high-dimensional vectors, remains an open research problem. We introduce a novel method, the pyramid quantized Weisfeiler-Lehman graph representation to tackle the graph comparison and representation problem for continuous vector labeled graphs. Our algorithm considers statistics of subtree patterns based on the Weisfeiler-Lehman algorithm and uses a pyramid quantization strategy to determine a logarithmic number of discrete labellings. As a result, we approximate a graph representation with continuous or vector valued labels as a sequence of graphs discrete labels with increasing granularity. We evaluate our proposed algorithm on two different tasks with real datasets, on a fMRI analysis task and on the generic problem of 3D shape classification. Second, we examine different regularization methods for analyzing medical images, and more specifically MRI data. Regularization methods are a powerful tool for improving the predicted performance and avoid overfitting by introducing additional information to an ill-posed problem, such as the analysis of medical images. Towards this direction, we introduce a novel regularization method, the k-support regularized Support Vector Machine. This algorithm extends the l1 regularized SVM to a mixed norm of both l1 and l2 norms. This enables the use of a correlated sparsity regularization with the power of the SVM framework. We evaluate our novel algorithm in a euromuscular disease classification task using MRI-based markers. We furthermore explore the importance of diffusion tensor imaging for the discrimination between neuromuscular conditions. Overall, as graphs are fundamental mathematical objects and regularization methods are widely used to control ill-pose problems, both the pyramid quantized Weisfeiler-Lehman graph representation and the k-support regularized SVM are potentially applicable to a wide range of applications domains in computer vision, analysis of medical images and data mining.
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https://theses.hal.science/tel-00960163
Contributor : Katerina Gkirtzou Connect in order to contact the contributor
Submitted on : Monday, March 17, 2014 - 4:42:50 PM
Last modification on : Thursday, July 9, 2020 - 4:06:04 PM
Long-term archiving on: : Tuesday, June 17, 2014 - 12:46:32 PM

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  • HAL Id : tel-00960163, version 1

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Katerina Gkirtzou. Sparsity regularization and graph-based representation in medical imaging. Machine Learning [cs.LG]. Ecole Centrale Paris, 2013. English. ⟨NNT : ⟩. ⟨tel-00960163v1⟩

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