Topology-based kernels with application to inference problems in Alzheimer's disease

Area of Science:

• Neuroimaging
• Statistical Learning
• Computational Anatomy

Background:

• Alzheimer's disease (AD) research increasingly uses statistical learning for imaging data analysis.
• Support vector machines (SVM) and kernel methods are common but require predefined kernel matrices.
• Measuring similarity between complex neuroimaging data, like cortical thickness, is challenging for existing methods.

Purpose of the Study:

• To introduce novel techniques for computing similarity matrices from topologically-based attributed neuroimaging data.
• To enable the use of clinically relevant measures like cortical thickness in statistical inference frameworks.
• To address limitations in current kernel-based methods for neuroimaging analysis.

Main Methods:

• Developed new methods to compute similarity matrices for topologically-based attributed data.
• Leveraged topological feature persistence to characterize signals like cortical thickness.
• Constructed kernel matrices based on these topological characterizations.

Main Results:

• Demonstrated good performance on statistical inference tasks using Alzheimer's Disease Neuroimaging Initiative (ADNI) data (n=356).
• Achieved results without feature selection, dimensionality reduction, or parameter tuning.
• Successfully computed similarity matrices for cortical thickness data, proving the method's utility.

Conclusions:

• The novel techniques effectively compute similarity matrices for complex neuroimaging data.
• These methods enhance the application of statistical learning in Alzheimer's disease research.
• The approach offers a robust way to leverage cortical thickness for improved inference.