Predicting Graph Signals Using Kernel Regression Where the Input Signal is Agnostic to a Graph
| Autor: | Arun Venkitaraman, Peter Händel, Saikat Chatterjee |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Signal processing
Computer Networks and Communications Computer science Signal reconstruction 020206 networking & telecommunications 02 engineering and technology Signal Processing Convex optimization 0202 electrical engineering electronic engineering information engineering Graph (abstract data type) Kernel regression Adjacency list 020201 artificial intelligence & image processing Laplacian matrix Algorithm Smoothing Information Systems |
| Zdroj: | IEEE Transactions on Signal and Information Processing over Networks. 5:698-710 |
| ISSN: | 2373-7778 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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