Search

Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance.

Machine learning is a popular method for mining and analyzing large collections of medical data. We focus on a particular problem from medical research, supervised multiple sclerosis (MS) lesion segmentation in structural magnetic resonance imaging (MRI). We examine the extent to which the choice of machine learning or classification algorithm and feature extraction function impacts the performance of lesion segmentation methods. As quantitative measures derived from structural MRI are important clinical tools for research into the pathophysiology and natural history of MS, the development of automated lesion segmentation methods is an active research field. Yet, little is known about what drives performance of these methods. We evaluate the performance of automated MS lesion segmentation methods, which consist of a supervised classification algorithm composed with a feature extraction function. These feature extraction functions act on the observed T1-weighted (T1-w), T2-weighted (T2-w) and fluid-attenuated inversion recovery (FLAIR) MRI voxel intensities. Each MRI study has a manual lesion segmentation that we use to train and validate the supervised classification algorithms. Our main finding is that the differences in predictive performance are due more to differences in the feature vectors, rather than the machine learning or classification algorithms. Features that incorporate information from neighboring voxels in the brain were found to increase performance substantially. For lesion segmentation, we conclude that it is better to use simple, interpretable, and fast algorithms, such as logistic regression, linear discriminant analysis, and quadratic discriminant analysis, and to develop the features to improve performance.