ThetA -- fast and robust clustering via a distance parameter

Clustering is a fundamental problem in machine learning where distance-based approaches have dominated the field for many decades. This set of problems is often tackled by partitioning the data into K clusters where the number of clusters is chosen apriori. While significant progress has been made on these lines over the years, it is well established that as the number of clusters or dimensions increase, current approaches dwell in local minima resulting in suboptimal solutions. In this work, we propose a new set of distance threshold methods called Theta-based Algorithms (ThetA). Via experimental comparisons and complexity analyses we show that our proposed approach outperforms existing approaches in: a) clustering accuracy and b) time complexity. Additionally, we show that for a large class of problems, learning the optimal threshold is straightforward in comparison to learning K. Moreover, we show how ThetA can infer the sparsity of datasets in higher dimensions.

Fitting IVIM with Variable Projection and Simplicial Optimization

Fitting multi-exponential models to Diffusion MRI (dMRI) data has always been challenging due to various underlying complexities. In this work, we introduce a novel and robust fitting framework for the standard two-compartment IVIM microstructural model. This framework provides a significant improvement over the existing methods and helps estimate the associated diffusion and perfusion parameters of IVIM in an automatic manner. As a part of this work we provide capabilities to switch between more advanced global optimization methods such as simplicial homology (SH) and differential evolution (DE). Our experiments show that the results obtained from this simultaneous fitting procedure disentangle the model parameters in a reduced subspace. The proposed framework extends the seminal work originated in the MIX framework, with improved procedures for multi-stage fitting. This framework has been made available as an open-source Python implementation and disseminated to the community through the DIPY project.