Research Results
Scalable Extensible Toolkit for Dimensionaliy Reduction
This Scalable Extensible Toolkit for Dimensionality Reduction (SETDiR) is a parallel software framework for applying various Linear and Non-Linear dimensionality reduction (DR) techniques on a given set of high-dimensional data. Its current areas of application include (but are not limited to):
Material Science Data: property-structure-process relationships
Uncertainty Analysis: Generation of stochastic reduced order models.
SETDiR has a user-friendly interface which allows users to run these DR techniques with various different options in a very easy manner and also makes the pre and post processing of the data easier.
The current version of SETDiR is 1.7.04, is released in January, 2010. The software is currently a serial version which works on both Windows and Linux machines while the distributed and shared memory versions are currently under testing.
Scalable Graph Algorithms for Large Nano-scale Data
Atom Probe Tomography is a technique of extracting location and chemical identity information of individual atoms from a crystal specimen by applying very high voltage and disintegrating it into individual atoms. Each such experiment produces very rich information encoding the structural properties of the specimen. However, the challenge here is that the data-set is really large (usually of the order of a million). This necessitates the development of scalable algorithms which can analyze the data in order to extract that rich information
Images above represent the Scandium Precipitate topologies obtained by applying graph-theoretic algorithms to analyze the reconstruction data of Al-Mg-Sc alloy produced using Atom Probe Tomography. Note that scales of the images are of the order of nanometers
POWER2D : Parallel Eigensolver for 2d block-distributed Square Symmetric Dense Matrix
Click on the image for a better resolution.
Topology Estimation using Manifold Learning Techniques
This project compares the output from several different manifold learning techniques like Principal Component Analysis, Isomap and Hessian Locally Linear Embedding to quantify and extract the topological features like non-convexity, non-linearity of manifolds using a discrete representation of manifolds. I am currently working on mathematical proofs for a few proposed lemmas in this framework.