Title: Tensors for Statistics
Advances in medical imaging technology as well as telecommunication data-collection have ushered in massive datasets that make multidimensional data more commonplace. The muliti-linear structure of these datasets (e.g. individuals x traits x time) gives impetus for statistical techniques that preserve the dimensionality while still tying into the familiar framework of statistical inference and learning.
While flattening of the the data and then applying traditional matrix-based methods is the common heuristic, methods that do not reduce the structural integrity of the data often outperform in both model parsimony and predictive performance. Hence it is important to extend the data-mining framework to utilize datasets that inherently have multi-level structures.
The tensor framework have been actively used and investigated in chemometrics, image sensing, facial recognition, psychometrics, data mining, and applied mathematics. In fact, many of the techniques that have been developed in lieu of a formal tensor setup are later show to be special cases of models based on the tensor structure, which further strengthens the claim that tensors are the natural extension to accommodate the multi-linearity of today's Big Data.
My talk will mostly be an overview of tensor analysis used for data mining and facial recognition. Along the way I will cover the most prevalent methods of compression and regression models, including a state-of-the-art tensor SVD that show intricate connections with the Fast-Fourier-Transform. I will also discuss current software available for tensor computations, as well as my own R package designed specifically for this task. Finally, I will discuss the possibilities of parallel computation for many of these models.