Deep learning, first proposed in 1989, still represents the most effective means for extracting specific information from large datasets. This approach exploits many nonlinear processing layers to develop representations of data at increasing levels of abstraction. Deep learning has demonstrated best-in-class performance in a range of applications, including image and speech recognition, and demonstrated promising results for tasks based on natural language understanding and translation. Crudely speaking, deep learning acquires ¡®knowledge¡¯ by tuning large numbers (¡Ý200) of fitting parameters during a supervised learning phase. These parameters are then used to extract information from previously ¡®unseen¡¯ data. Ultimately, deep learning is premised on using a large number of tuning parameters to develop nonlinear feature detectors capable of efficiently representing the intrinsic structure of the data at an abstract level.¡±

This project will examine two potentially powerful, but highly speculative alternative approaches to extract information from data. These approaches exploit the intrinsic properties of the data rather than an extensive set of tuning parameters. Both approaches are based on conjectures made by the PIs regarding possible extensions of techniques successfully applied in very different branches of mathematics. The first concerns the extraction of specific structural information from random sightings of objects; the second, forecasting the behavior of dynamical systems [6]. The ultimate goal of this project is to determine whether the aforementioned algebraic topological approaches or techniques developed for the forecasting of high-dimensional time-series or some variations thereof, can be exploited to create a new class of non-iterative unsupervised learning algorithms. The broader impact of the project is the training of young scientists at the hitherto unexplored intersection of abstract mathematics and machine learning, with possible applications in science, technology, and commerce.

Project Start
Project End
Budget Start
2015-09-01
Budget End
2018-08-31
Support Year
Fiscal Year
2015
Total Cost
$199,891
Indirect Cost
Name
University of Wisconsin Milwaukee
Department
Type
DUNS #
City
Milwaukee
State
WI
Country
United States
Zip Code
53201