iPGA: incremental principal geodesic analysis with applications to movement disorder classification.

Area of Science:

• Medical image analysis
• Computational statistics
• Differential geometry

Background:

• Principal Geodesic Analysis (PGA) is used for analyzing manifold-valued data like diffusion tensors.
• Batch PGA is computationally intensive for high-dimensional data.
• There is a need for efficient algorithms for analyzing large diffusion tensor fields.

Purpose of the Study:

• To introduce a novel incremental Principal Geodesic Analysis (iPGA) algorithm.
• To demonstrate computational and memory efficiency of iPGA compared to batch PGA.
• To apply iPGA for Parkinson's Disease and Essential Tremor classification using HARDI brain scans.

Main Methods:

• Developed an incremental algorithm to update Karcher mean and principal sub-manifolds.
• Implemented iPGA for diffusion tensor fields.
• Utilized iPGA-derived representations in a neural network (NN) classifier.

Main Results:

• iPGA offers substantial computational and memory savings over batch PGA.
• The algorithm effectively handles newly introduced data without recomputation.
• iPGA-based NN classifier accurately discriminated between controls, Parkinson's Disease, and Essential Tremor patients.

Conclusions:

• iPGA provides an efficient alternative to batch PGA for manifold-valued data analysis.
• The algorithm is suitable for large-scale datasets, such as diffusion tensor fields.
• iPGA facilitates advanced neuroimaging analysis and disease classification.