Stationary Signal Processing on Graphs

Perraudin, Nathanaël; Vandergheynst, Pierre

doi:10.1109/tsp.2017.2690388

Cited by 222 publications

(295 citation statements)

References 52 publications

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“…In fact such types of experiments have become a standard practice in the PCA community [5], [14], [4], [6], [15]. We perform our clustering experiments on 3 benchmark databases: CMU PIE, ORL and COIL20 using two opensource toolboxes: the UNLocBoX [16] for the optimization part and the GSPBox [17] for the graph creation.…”

Section: Resultsmentioning

confidence: 99%

PCA using graph total variation

Shahid

Perraudin

Kalofolias

et al. 2016

2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Mining useful clusters from high dimensional data has received significant attention of the signal processing and machine learning 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 problems such as high computational complexity (usually associated with the nuclear norm minimization), non-convexity (for matrix factorization methods) or susceptibility to gross corruptions in the data. In this paper we propose a convex, robust, scalable and efficient Principal Component Analysis (PCA) based method to approximate the low-rank representation of high dimensional datasets via a two-way graph regularization scheme. Compared to the exact recovery methods, our method is approximate, in that it enforces a piecewise constant assumption on the samples using a graph total variation and a piecewise smoothness assumption on the features using a graph Tikhonov regularization. Futhermore, it retrieves the low-rank representation in a time that is linear in the number of data samples. Clustering experiments on 3 benchmark datasets with different types of corruptions show that our proposed model outperforms 7 state-ofthe-art dimensionality reduction models.

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Section: Resultsmentioning

confidence: 99%

PCA using graph total variation

Shahid

Perraudin

Kalofolias

et al. 2016

2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…1. 17 This work assumes that the graph power spectrum of a WSS graph signal can be written as a function of the graph frequency. These graph signals are also WSS according to our definition (the converse is not always true).…”

Section: A Global Definition For Graphsmentioning

confidence: 99%

“…Following our work on stationarity for graph signals, and inspired by the work of Perraudin and Vandergheynst, 17 we introduced recently a notion of local stationarity.…”

Section: A Local Definition For Graphsmentioning

confidence: 99%

Local stationarity of graph signals: insights and experiments

Girault

Narayanan

Ortega

2017

Wavelets and Sparsity XVII

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In this paper, we look at one of the most crucial ingredient to graph signal processing: the graph. By taking a step back on the conventional approach using Gaussian weights, we are able to obtain a better spectral representation of a stochastic graph signal. Our approach focuses on learning the weights of the graphs, thus enabling better richness in the structure by incorporating both the distance and the local structure into the weights. Our results show that the graph power spectrum we obtain is closer to what we expect, and stationarity is better preserved when going from a continuous signal to its sampled counterpart on the graph. We further validate the approach on a real weather dataset.

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“…Interestingly, for a class of random f ν there exists a function r(·) such that the LMMSE and KRR estimators yield the same estimate. These graph signals are deemed to be graph stationary in [19], [20], and their covariance matrix is diagonalizable by the eigenvectors of L.…”

Section: B Kernel Kriged Kalman Filtermentioning

confidence: 99%

Inference of spatiotemporal processes over graphs via kernel kriged Kalman filtering

Ioannidis

Romero

Giannakis

2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-Inference of space-time signals evolving over graphs emerges naturally in a number of network science related applications. A frequently encountered challenge pertains to reconstructing such dynamic processes given their values over a subset of vertices and time instants. The present paper develops a graph-aware kernel-based kriged Kalman filtering approach that leverages the spatio-temporal dynamics to allow for efficient online reconstruction, while also coping with dynamically evolving network topologies. Laplacian kernels are employed to perform kriging over the graph when spatial second-order statistics are unknown, as is often the case. Numerical tests with synthetic and real data illustrate the superior reconstruction performance of the proposed approach.

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Stationary Signal Processing on Graphs

Cited by 222 publications

References 52 publications

PCA using graph total variation

PCA using graph total variation

Local stationarity of graph signals: insights and experiments

Inference of spatiotemporal processes over graphs via kernel kriged Kalman filtering

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