Weekly Seminar – 3/31/2017 – Low Rank and Sparse Signal Processing #3

Davood Hajinezhad from Dr. Hong’s research group will be giving the talk tomorrow. The title is “Nonconvex Low Rank Matrix Factorization via Inexact First Order Oracle”. The details are as follows:
Date: March 31st, Friday
Time: 3:00 – 4:00 pm
Venue: 2222 Coover hall
Davood’s abstract: We study the low rank matrix factorization problem via nonconvex optimization. Compared with the convex relaxation approach, nonconvex optimization exhibits superior empirical performance for large scale low rank matrix estimation. However, the understanding of its theoretical guarantees is limited. To bridge this gap, we exploit the notion of inexact first order oracle, which naturally appears in low rank matrix factorization problems such as matrix sensing and completion. Particularly, our analysis shows that a broad class of nonconvex optimization algorithms, including alternating minimization and gradient-type methods, can be treated as solving two sequences of convex optimization algorithms using inexact first order oracle. Thus we can show that these algorithms converge geometrically to the global optima and recover the true low rank matrices under suitable conditions. Numerical results are provided to support our theory.


Weekly Seminar – 3/24/2017 – Low Rank and Sparse Signal Processing #2

The weekly seminar series resumes after the spring break with a talk on Graph Signal Processing by Rahul Singh from Dr. Dogandzic’s research group. The details are as follows:
Date: March 24th, Friday
Time: 3:00 – 4:00 pm
Venue: 2222 Coover hall
Rahul’s abstract:  Graph Signal Processing (GSP) is concerned with modeling, representation, and processing of signals defined on irregular structures, known as graphs. In this setting, we deal with graph signals which are collection of data values lying on the vertices of arbitrary graphs. Graph signals can be defined as temperatures within a geographical area, traffic capacities at hubs in a transportation network, or human behaviors in a social network. In the talk, we will discuss the existing graph signal processing tools and concepts such as graph Fourier transform, spectral graph wavelets. Following references are good starting point for graph signal processing.

1. David I Shuman et al. “The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains”. In: Signal Processing Magazine, IEEE 30.3 (2013), pp. 83–98.

2. A. Sandryhaila and J.M.F. Moura. “Discrete Signal Processing on Graphs: Frequency Analysis”. In: Signal Processing, IEEE Transactions on 62.12 (2014), pp. 3042–3054.

3. David I Shuman, Benjamin Ricaud, and Pierre Vandergheynst. “Vertex-frequency analysis on graphs”. In: Applied and Computational Harmonic Analysis 40.2 (2016), pp. 260–291.

Slides: GSP

Weekly Seminar – 3/3/2017 – Low Rank and Sparse Signal Processing #1

Songtao Lu from Dr. Wang’s research group will start the series of talks on low rank and sparse signal processing in our weekly meetings. The details are as follows:
Date: March 3rd, Friday
Time: 3:00 – 4:00 PM
Venue: 2222 Coover hall
Songtao‘s Abstract: I would like to mainly talk about low rank matrix factorization with applications to machine learning on this Friday, including spectral clustering, nonnegative matrix factorization. If time is enough, I plan to introduce some new relevant works about deep neural networks for dimensionality reduction.
Selected references:
Slides: LMF