Rational Kernels: Theory and Algorithms
The Journal of Machine Learning Research
Shortest-Path Kernels on Graphs
ICDM '05 Proceedings of the Fifth IEEE International Conference on Data Mining
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
Graph kernels between point clouds
Proceedings of the 25th international conference on Machine learning
The Journal of Machine Learning Research
LIBSVM: A library for support vector machines
ACM Transactions on Intelligent Systems and Technology (TIST)
Optimal graph based segmentation using flow lines with application to airway wall segmentation
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Dissimilarity-based classification of anatomical tree structures
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Weisfeiler-Lehman Graph Kernels
The Journal of Machine Learning Research
The Journal of Machine Learning Research
Means in spaces of tree-like shapes
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
Complexity of computing distances between geometric trees
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
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Methodological contributions: This paper introduces a family of kernels for analyzing (anatomical) trees endowed with vector valued measurements made along the tree. While state-of-the-art graph and tree kernels use combinatorial tree/graph structure with discrete node and edge labels, the kernels presented in this paper can include geometric information such as branch shape, branch radius or other vector valued properties. In addition to being flexible in their ability to model different types of attributes, the presented kernels are computationally efficient and some of them can easily be computed for large datasets (N ~10.000) of trees with 30−600 branches. Combining the kernels with standard machine learning tools enables us to analyze the relation between disease and anatomical tree structure and geometry. Experimental results: The kernels are used to compare airway trees segmented from low-dose CT, endowed with branch shape descriptors and airway wall area percentage measurements made along the tree. Using kernelized hypothesis testing we show that the geometric airway trees are significantly differently distributed in patients with Chronic Obstructive Pulmonary Disease (COPD) than in healthy individuals. The geometric tree kernels also give a significant increase in the classification accuracy of COPD from geometric tree structure endowed with airway wall thickness measurements in comparison with state-of-the-art methods, giving further insight into the relationship between airway wall thickness and COPD. Software: Software for computing kernels and statistical tests is available at http://image.diku.dk/aasa/software.php.