| 1. |
- Venkitaraman, Arun, et al.
(author)
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KERNEL REGRESSION FOR GRAPH SIGNAL PREDICTION IN PRESENCE OF SPARSE NOISE
- 2019
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In: 2019 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP). - : IEEE. - 9781479981311 ; , s. 5426-5430
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Conference paper (peer-reviewed)abstract
- In presence of sparse noise we propose kernel regression for predicting output vectors which are smooth over a given graph. Sparse noise models the training outputs being corrupted either with missing samples or large perturbations. The presence of sparse noise is handled using appropriate use of l(1)-norm along-with use of l(2)-norm in a convex cost function. For optimization of the cost function, we propose an iteratively reweighted least-squares (IRLS) approach that is suitable for kernel substitution or kernel trick due to availability of a closed form solution. Simulations using real-world temperature data show efficacy of our proposed method, mainly for limited-size training datasets.
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| 2. |
- Venkitaraman, Arun, et al.
(author)
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Learning Sparse Graphs for Prediction of Multivariate Data Processes
- 2019
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In: IEEE Signal Processing Letters. - : IEEE. - 1070-9908 .- 1558-2361. ; 26:3, s. 495-499
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Journal article (peer-reviewed)abstract
- We address the problem of prediction of multivariate data process using an underlying graph model. We develop a method that learns a sparse partial correlation graph in a tuning-free and computationally efficient manner. Specifically, the graph structure is learned recursively without the need for cross validation or parameter tuning by building upon a hyperparameter-free framework. Our approach does not require the graph to be undirected and also accommodates varying noise levels across different nodes. Experiments using real-world datasets show that the proposed method offers significant performance gains in prediction, in comparison with the graphs frequently associated with these datasets.
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| 3. |
- Venkitaraman, Arun, et al.
(author)
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On Hilbert transform, analytic signal, and modulation analysis for signals over graphs
- 2019
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In: Signal Processing. - : Elsevier. - 0165-1684 .- 1872-7557. ; 156, s. 106-115
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Journal article (peer-reviewed)abstract
- We propose Hilbert transform and analytic signal construction for signals over graphs. This is motivated by the popularity of Hilbert transform, analytic signal, and modulation analysis in conventional signal processing, and the observation that complementary insight is often obtained by viewing conventional signals in the graph setting. Our definitions of Hilbert transform and analytic signal use a conjugate symmetry-like property exhibited by the graph Fourier transform (GFT), resulting in a 'one-sided' spectrum for the graph analytic signal. The resulting graph Hilbert transform is shown to possess many interesting mathematical properties and also exhibit the ability to highlight anomalies/discontinuities in the graph signal and the nodes across which signal discontinuities occur. Using the graph analytic signal, we further define amplitude, phase, and frequency modulations for a graph signal. We illustrate the proposed concepts by showing applications to synthesized and real-world signals. For example, we show that the graph Hilbert transform can indicate presence of anomalies and that graph analytic signal, and associated amplitude and frequency modulations reveal complementary information in speech signals.
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| 4. |
- Venkitaraman, Arun, et al.
(author)
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Predicting Graph Signals Using Kernel Regression Where the Input Signal is Agnostic to a Graph
- 2019
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In: IEEE TRANSACTIONS ON SIGNAL AND INFORMATION PROCESSING OVER NETWORKS. - : IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. - 2373-776X. ; 5:4, s. 698-710
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Journal article (peer-reviewed)abstract
- We propose a kernel regression method to predict a target signal lying over a graph when an input observation is given. The input and the output could be two different physical quantities. In particular, the input may not be a graph signal at all or it could be agnostic to an underlying graph. We use a training dataset to learn the proposed regression model by formulating it as a convex optimization problem, where we use a graph-Laplacian based regularization to enforce that the predicted target is a graph signal. Once the model is learnt, it can be directly used on a large number of test data points one-by-one independently to predict the corresponding targets. Our approach employs kernels between the various input observations, and as a result the kernels are not restricted to be functions of the graph adjacency/Laplacian matrix. We show that the proposed kernel regression exhibits a smoothing effect, while simultaneously achieving noise-reduction and graph-smoothness. We then extend our method to the case when the underlying graph may not be known apriori, by simultaneously learning an underlying graph and the regression coefficients. Using extensive experiments, we show that our method provides a good prediction performance in adverse conditions, particularly when the training data is limited in size and is noisy. In graph signal reconstruction experiments, our method is shown to provide a good performance even for a highly under-determined subsampling.
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