UCLA

In this thesis, we present a myriad of applications of online matrix and tensor dictionarylearning algorithms to the analysis of time series and image data, as well as a theoretical analysis of our algorithm, Online CP-Dictionary Learning (OCPDL). First, we present a method which applies online nonnegative matrix factorization (ONMF), an algorithm which learns a sparse, nonnegative representation of streaming data, to perform joint dictionary learning on multivariate COVID-19 time-series data, followed by a certain “restrict and predict" algorithm to tackle the future time regression problem. Next, we apply ONMF to meteorological time series data, as well as to video data, and demonstrate the particular utility of online as opposed to online algorithms in dealing with said data. In the following section, we present our extension of ONMF, our OCPDL algorithm, as well as a proof of some convergence guarantees.