Sampling from Determinantal Point Processes for Scalable Manifold Learning.
Journal:
Information processing in medical imaging : proceedings of the ... conference
Published Date:
Jan 1, 2015
Abstract
High computational costs of manifold learning prohibit its application for large datasets. A common strategy to overcome this problem is to perform dimensionality reduction on selected landmarks and to successively embed the entire dataset with the Nyström method. The two main challenges that arise are: (i) the landmarks selected in non-Euclidean geometries must result in a low reconstruction error, (ii) the graph constructed from sparsely sampled landmarks must approximate the manifold well. We propose to sample the landmarks from determinantal distributions on non-Euclidean spaces. Since current determinantal sampling algorithms have the same complexity as those for manifold learning, we present an efficient approximation with linear complexity. Further, we recover the local geometry after the sparsification by assigning each landmark a local covariance matrix, estimated from the original point set. The resulting neighborhood selection .based on the Bhattacharyya distance improves the embedding of sparsely sampled manifolds. Our experiments show a significant performance improvement compared to state-of-the-art landmark selection techniques on synthetic and medical data.
Authors
Keywords
Algorithms
Artificial Intelligence
Computer Simulation
Data Interpretation, Statistical
Head and Neck Neoplasms
Humans
Imaging, Three-Dimensional
Models, Statistical
Pattern Recognition, Automated
Radiographic Image Enhancement
Radiographic Image Interpretation, Computer-Assisted
Reproducibility of Results
Sample Size
Sensitivity and Specificity
Signal Processing, Computer-Assisted
Tomography, X-Ray Computed