Fast Robust PCA on Graphs - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles IEEE Journal of Selected Topics in Signal Processing Year : 2016

Fast Robust PCA on Graphs


Mining useful clusters from high dimensional data has received significant attention of the computer vision and pattern recognition community in the recent years. Linear and non-linear dimensionality reduction has played an important role to overcome the curse of dimensionality. However, often such methods are accompanied with three different problems: high computational complexity (usually associated with the nuclear norm minimization), non-convexity (for matrix factorization methods) and susceptibility to gross corruptions in the data. In this paper we propose a principal component analysis (PCA) based solution that overcomes these three issues and approximates a low-rank recovery method for high dimensional datasets. We target the low-rank recovery by enforcing two types of graph smoothness assumptions, one on the data samples and the other on the features by designing a convex optimization problem. The resulting algorithm is fast, efficient and scalable for huge datasets with O(n log(n)) computational complexity in the number of data samples. It is also robust to gross corruptions in the dataset as well as to the model parameters. Clustering experiments on 7 benchmark datasets with different types of corruptions and background separation experiments on 3 video datasets show that our proposed model outperforms 10 state-of-the-art dimensionality reduction models. Our theoretical analysis proves that the proposed model is able to recover approximate low-rank representations with a bounded error for clusterable data.
Fichier principal
Vignette du fichier
main.pdf (5.04 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-01277624 , version 1 (22-02-2016)



Nauman Shahid, Nathanael Perraudin, Vassilis Kalofolias, Gilles Puy, Pierre Vandergheynst. Fast Robust PCA on Graphs. IEEE Journal of Selected Topics in Signal Processing, 2016, 10 (4), pp.740 - 756. ⟨10.1109/JSTSP.2016.2555239⟩. ⟨hal-01277624⟩
455 View
207 Download



Gmail Facebook X LinkedIn More