Large-Scale Manifold Learning Using an Adaptive Sparse Neighbor Selection Approach for Brain Tumor Progression Prediction

Abstract

Manifold learning performs dimensionality reduction by identifying low-dimensional structures (manifolds) embedded in a high-dim- ensional space. Many algorithms involve an eigenvector or singular value decomposition (SVD) procedure on a similarity matrix of size n ×n, where n denotes the number of data samples, making them not scalable to big data. A method to overcome large data set size is to create a manifold with a subset of the original data while embedding the rest into the manifold skeleton. An adequate number of neighbors varies and depends on the geometry of the manifold. Points that contain too few neighbors may not be able to encompass the intrinsic manifold geometry. Conversely, too many neighbors will cause a short circuit in the manifold. To overcome these problems, we introduce a novel adaptive neighbor selection approach using ℓ₁ optimization. We show that this neighborhood selection can be useful in creating a more robust manifold in regards to MRI brain tumor data.