Date: Friday, September 15, 2017
Location: 1084 East Hall (4:10 PM to 5:00 PM)
Title: Generalized CP Tensor Decompositions
Abstract: Given a tensor (i.e., a multidimensional array), a CP decomposition is formed by finding a lowrank tensor approximation. The CP decomposition is one of several extensions of decompositions for matrices (i.e., twodimensional arrays) to tensors and has many exciting applications in fields ranging from neuroscience to network science and signal processing. In this talk, we will see two example applications: a) finding latent structure (i.e., political parties) in senate voting data and b) distinguishing gasses in chemosensing data.
The CP decomposition, in particular, forms a lowrank tensor approximation that has good fit as measured by the total entrywise square difference. However, different fit/loss functions may be more appropriate in some cases and can provide new ways to look at the data. For example, the logistic loss is a natural choice for binary tensors. We propose a new generalized tensor decomposition method that allows users to select a generic loss function. To solve the resulting optimization problem, we use a stochastic gradient algorithm from machine learning to exploit the fact that approximate gradients can be computed efficiently from small samples of the entries.
Files:
Speaker: David Hong
Institution: University of Michigan
Event Organizer: Audra McMillan amcm@umich.edu
