Sponsored Research

Traditional data analysis and signal processing is based on squared residual errors and projections. This is motivated by statistical foundations (scaled sum of squares estimates variance) and ease in optimization methods (e.g., least-squares, SVD). However, learning metrics based on the sum of squares (L2-norm) benefits highly deviating / peripheral points (sensitivity against outliers). In this research direction, we explore theory and develop algorithms for data analysis and feature extraction based on the sum of absolute values (L1-norm) of data projections. While L1-norm minimization has been used for decades in signal processing and data science as a way to promote sparsity, in this research direction we do something different: we use L1-norm maximization as a means to promote balanced focus across all processed data points and, thus, achieve robustness against faulty data and adversarial contaminations.

Tensors are multi-way arrays that can generalize matrices to higher orders. Tensor modeling and processing are ubiquitous in modern data analysis and machine learning, as they capture inherent multi-linear structures within the data. For example, tensors are used for modeling multi-relational graphs, multi-spectral images/videos, wireless spectrum utilization maps, and even the parameters of neural networks. While matrix analysis has been thoroughly studied for a very long time, there is still much room (and need) for research in tensor analysis. Primarily funded by NSF and AFOSR, in this research direction we develop new methods for dynamic and robust analysis of tensor data.

Typically, the more the trainable parameters, the higher the network capacity and the higher its ability to represent more complex models. However, this is only attainable when there is a correspondingly high number of data to train on. Otherwise, a large network can overfit the limited training examples and fail to properly generalize to unseen data. In this work, we focus on adjusting the network capacity to the available data by tuning the tensor rank of its parameters. Then, we apply this idea to incremental learning (increase capacity as more data become available) and continual learning (learn new tasks, in new multi-linear subspaces of the network parameters).

In this research direction, we develop neural network architectures that are specifically designed for object detection and tracking in aerial imagery (can handle rotated objects, small scarce/objects, and limited training examples). In addition, we explore novel methods for in-the-network fusion that allow for the use of multi-modal aerial imagery for object detection. In a new thread of this project, we develop generic methods for mid-level network fusion applicable to a wide range of data modalities and problems.