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Robust Principal Component Analysis on Graphs Nauman Shahid Vassilis Kalofolias, Xavier Bresson, Michael Bronstein & Pierre Vandergheynst EPF Lausanne, Switzerland SPARS 2015, Cambridge UK

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Robust Principal Component Analysis on Graphs

Nauman ShahidVassilis Kalofolias, Xavier Bresson, Michael Bronstein &

Pierre VandergheynstEPF Lausanne, Switzerland

SPARS 2015, Cambridge UK
What is this talk about?

Sparsity?

True for most of the people in this auditorium

Unfortunately “sparsity” in this talk represents “gross errors”

This talk is about Principal Component Analysis / Low-rank representation: The most widely used tool for linear dimensionality reduction & clustering!

NO!

SPARSITY!!!!
Outline

Principal Component AnalysisRobust Principal Component Analysis

Robust Principal Component Analysis on GraphsHow and Why?

Solution using ADMM

Results:Clustering in low-dimensional spaceLow-rank recovery
Principal Component AnalysisRobust

Not robust to gross errors
Robust Principal Component Analysis on Graphs

How & why?
Robust Principal Component Analysis on Graphs:How?
Robust Principal Component Analysis on GraphsWhy?

Exploit local similarity information

Enhanced low-rank representation,smooth on the manifold

Better clusters in low-dimensional space

Two important applications of PCA!

IMPORTANT: Smooth low-rank, NOT only principal components

convexity
Solution using ADMM
Results

• Clustering in low-dimensional space• Static background separation from dynamic foreground
Results: Clustering
Results: Principal Components for 3 classes of ORL dataset
Results: Background Separation from Videos
Please have a look at thefull version of the paper on arXiv

Demo & code available at:https://lts2.epfl.ch/blog/nauman/recent-projects/

Fast version and its code will be available in 2 weeks.

Future Work: Theoretical investigation

https://lts2.epfl.ch/blog/nauman/recent-projects/

Robust Principal Component Analysis on GraphsWhat is this talk about?OutlinePrincipal Component AnalysisRobust Principal Component Analysis on GraphsRobust Principal Component Analysis on Graphs:How?Robust Principal Component Analysis on Graphs�Why?Solution using ADMMResultsResults: ClusteringResults: Principal Components for 3 classes of ORL datasetResults: Background Separation from VideosSlide Number 13

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