DATA ANALYTICS USING LINEAR AND MULTILINEAR ALGEBRA

Using novel principles for dimesnionality reduction from theory of linear and multilinear algebra, we consider several data analytic problems that involve multidimensional data, i.e. each datum is a multidimensional array (often referred to as a tensor). We show that one can successfully exploit additional algebraic structure imposed on the low dimensional linear and multilinear subspaces for better performance. Examples of such structures are invariance of the subspace to action of a group, approximation of a subspace as a tensor product of subspaces.

Research Funding: NSF:CCF:1319653, Mitsubishi Electric Research Lab (MERL) Research Gift, NSF REU

**Applications: **

**(A) Optimal Sampling and Recovery: ****5-D ****Seismic (pre-stack) data completion from missing traces, ****3-D dynamic MRI data sampling and recovery under operational constraints on sampling (collaboration with Brigham and Womens Hospital)**

**(B) Adaptive sampling of Indoor RF fingerprint data for localization (collaboration with AT&T research and Purdue University)**

**(C) Unsupervised Clustering of 2-D data: Face images under varying pose and illumination, Clustering under missing data**

GEOPHYSICS

**Hydraulic Fracture Monitoring:**** **We developed fast and robust algorithms for localization of micro-siesmic events in presence of heavy noise and interference. Using the geometry of wave propagation in an isotropic media we modeled the *joint estimation of the siesmic moment tensor and the amplitude pattern as a sparse recovery of a 3-D array, where each slice is rank-1*.

**Statistical Signal Processing for Geophysics: **This project is a part of industrial collaboration with Schlumberger Technology Corporation on statistical estimation and detection problems that arise in geophysical prospecting for oil and gas production and exploration, primarily related to acoustic measurements.

Research Funding: (1) Data compression for Ultrasonic Borehole Imaging, Schlumberger SKK Center, Japan. Total Funding: $50k

(2) Machine Learning for Geophysics, Schlumberger Doll Research, Cambridge, MA, USA. Total Funding: $50k

**Related Patents**

1. S. Aeron, S. Bose and H.P. Valero, Automatic dispersion extraction of multiple time overlapped acoustic signals, 2012, Patent # **US 8,339,897 B2**

2. S. Bose, H.P. Valero and S. Aeron, Dispersion Extraction for Acoustic Data using Time FrequencyAnalysis, 2009, Patent # **US ****7,649,805 B2**

3. S. Aeron, S. Bose and H.P. Valero, Semblance enhancement for robust slowness estimation in monopole logging while drilling (LWD), filed 2012 [technology currently implemented in real LWD systems]

THREAT IDENTIFICATION AT A DISTANCE

In collaboration with a start-up EOS/Pendar technologies we are building signal and image processing systems for reliable real time identification of threats from FTIR imaging at a distance. The system will integarte the novel hardware FTIR system developed by EOS Pendar using Quantum Cascade Lasers.

Research funding: DHS

COMPUTATIONAL BIOLOGY

Analysis of metabolic networks in collaboration with Prof. Soha Hassoun and Ehsan Ullah.

This project is related to efficient computation of Elementary Flux Modes (EFM) for a given metabolic network for an organism such as a bacerium responsible for producing ethanol. An example is shown below for a subsection of a tricarboxylic acid cycle (TCA). EFMs are balanced pathways such that any other reaction can be expressed as a positive linear combination of these pathways. This is useful for synthetic biology applications.

The problem is initmately connected to an open problem in polyhedral combinatorics, namely that of efficiently enumerating the vertices of a given pointed polyhedral cone.