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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
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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!!!!
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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
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Principal Component AnalysisRobust
Not robust to gross errors
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Robust Principal Component Analysis on Graphs
How & why?
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Robust Principal Component Analysis on Graphs:How?
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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
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Solution using ADMM
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Results
• Clustering in low-dimensional space• Static background
separation from dynamic foreground
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Results: Clustering
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Results: Principal Components for 3 classes of ORL dataset
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Results: Background Separation from Videos
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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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