Nonconvex Approaches in Data Science
|主 题||Nonconvex Approaches in Data Science|
|报告人||Yifei Lou（The University of Texas Dallas）|
|时 间||2018年12月10日下午， 14：00--15：00|
Although ``big data'' is ubiquitous in data science, one often faces challenges of ``small data,''as the amount of data that can be taken or transmitted is limited by technical or economic constraints.
To retrieve useful information from the insufficient amount of data, additional assumptions on the signal of interest are required, e.g. sparsity (having only a few non-zero elements). Conventional methods favor incoherent systems, in which any two measurements are as little correlated as possible. In reality, however,many problems are coherent. I will present two nonconvex approaches: one is the difference of the $L_1$ and $L_2$ norms and the other is the ratio of the two. The difference model $L_1$-$L_2$ works particularly well for the coherent case, while $L_1/L_2$ is a scale-invariant metric that works better when underlying signals have large fluctuations in non-zero values. Various numerical experiments have demonstrated advantages of the proposed methods over the state-of-the-art. Applications, ranging from MRI reconstruction to super-resolution and low-rank approximation, will be discussed.