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Register a new userLearning parametric dictionaries for graph signals
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Dorina Thanou
Publication date
2014
fields
Informatics Engineering
and research's language is
English
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In sparse signal representation, the choice of a dictionary often involves a tradeoff between two desirable properties -- the ability to adapt to specific signal data and a fast implementation of the dictionary. To sparsely represent signals residing on weighted graphs, an additional design challenge is to incorporate the intrinsic geometric structure of the irregular data domain into the atoms of the dictionary. In this work, we propose a parametric dictionary learning algorithm to design data-adapted, structured dictionaries that sparsely represent graph signals. In particular, we model graph signals as combinations of overlapping local patterns. We impose the constraint that each dictionary is a concatenation of subdictionaries, with each subdictionary being a polynomial of the graph Laplacian matrix, representing a single pattern translated to different areas of the graph. The learning algorithm adapts the patterns to a training set of graph signals. Experimental results on both synthetic and real datasets demonstrate that the dictionaries learned by the proposed algorithm are competitive with and often better than unstructured dictionaries learned by state-of-the-art numerical learning algorithms in terms of sparse approximation of graph signals. In contrast to the unstructured dictionaries, however, the dictionaries learned by the proposed algorithm feature localized atoms and can be implemented in a computationally efficient manner in signal processing tasks such as compression, denoising, and classification.
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How can we find the right graph for semi-supervised learning? In real world applications, the choice of which edges to use for computation is the first step in any graph learning process. Interestingly, there are often many types of similarity available to choose as the edges between nodes, and the choice of edges can drastically affect the performance of downstream semi-supervised learning systems. However, despite the importance of graph design, most of the literature assumes that the graph is static. In this work, we present Grale, a scalable method we have developed to address the problem of graph design for graphs with billions of nodes. Grale operates by fusing together different measures of(potentially weak) similarity to create a graph which exhibits high task-specific homophily between its nodes. Grale is designed for running on large datasets. We have deployed Grale in more than 20 different industrial settings at Google, including datasets which have tens of billions of nodes, and hundreds of trillions of potential edges to score. By employing locality sensitive hashing techniques,we greatly reduce the number of pairs that need to be scored, allowing us to learn a task specific model and build the associated nearest neighbor graph for such datasets in hours, rather than the days or even weeks that might be required otherwise. We illustrate this through a case study where we examine the application of Grale to an abuse classification problem on YouTube with hundreds of million of items. In this application, we find that Grale detects a large number of malicious actors on top of hard-coded rules and content classifiers, increasing the total recall by 89% over those approaches alone.
Graphon is a nonparametric model that generates graphs with arbitrary sizes and can be induced from graphs easily. Based on this model, we propose a novel algorithmic framework called textit{graphon autoencoder} to build an interpretable and scalable graph generative model. This framework treats observed graphs as induced graphons in functional space and derives their latent representations by an encoder that aggregates Chebshev graphon filters. A linear graphon factorization model works as a decoder, leveraging the latent representations to reconstruct the induced graphons (and the corresponding observed graphs). We develop an efficient learning algorithm to learn the encoder and the decoder, minimizing the Wasserstein distance between the model and data distributions. This algorithm takes the KL divergence of the graph distributions conditioned on different graphons as the underlying distance and leads to a reward-augmented maximum likelihood estimation. The graphon autoencoder provides a new paradigm to represent and generate graphs, which has good generalizability and transferability.
We study the problem of semi-supervised learning on graphs, for which graph neural networks (GNNs) have been extensively explored. However, most existing GNNs inherently suffer from the limitations of over-smoothing, non-robustness, and weak-generalization when labeled nodes are scarce. In this paper, we propose a simple yet effective framework---GRAPH RANDOM NEURAL NETWORKS (GRAND)---to address these issues. In GRAND, we first design a random propagation strategy to perform graph data augmentation. Then we leverage consistency regularization to optimize the prediction consistency of unlabeled nodes across different data augmentations. Extensive experiments on graph benchmark datasets suggest that GRAND significantly outperforms state-of-the-art GNN baselines on semi-supervised node classification. Finally, we show that GRAND mitigates the issues of over-smoothing and non-robustness, exhibiting better generalization behavior than existing GNNs. The source code of GRAND is publicly available at https://github.com/Grand20/grand.
Attributed networks nowadays are ubiquitous in a myriad of high-impact applications, such as social network analysis, financial fraud detection, and drug discovery. As a central analytical task on attributed networks, node classification has received much attention in the research community. In real-world attributed networks, a large portion of node classes only contain limited labeled instances, rendering a long-tail node class distribution. Existing node classification algorithms are unequipped to handle the textit{few-shot} node classes. As a remedy, few-shot learning has attracted a surge of attention in the research community. Yet, few-shot node classification remains a challenging problem as we need to address the following questions: (i) How to extract meta-knowledge from an attributed network for few-shot node classification? (ii) How to identify the informativeness of each labeled instance for building a robust and effective model? To answer these questions, in this paper, we propose a graph meta-learning framework -- Graph Prototypical Networks (GPN). By constructing a pool of semi-supervised node classification tasks to mimic the real test environment, GPN is able to perform textit{meta-learning} on an attributed network and derive a highly generalizable model for handling the target classification task. Extensive experiments demonstrate the superior capability of GPN in few-shot node classification.
This paper introduces a novel graph signal processing framework for building graph-based models from classes of filtered signals. In our framework, graph-based modeling is formulated as a graph system identification problem, where the goal is to learn a weighted graph (a graph Laplacian matrix) and a graph-based filter (a function of graph Laplacian matrices). In order to solve the proposed problem, an algorithm is developed to jointly identify a graph and a graph-based filter (GBF) from multiple signal/data observations. Our algorithm is valid under the assumption that GBFs are one-to-one functions. The proposed approach can be applied to learn diffusion (heat) kernels, which are popular in various fields for modeling diffusion processes. In addition, for specific choices of graph-based filters, the proposed problem reduces to a graph Laplacian estimation problem. Our experimental results demonstrate that the proposed algorithm outperforms the current state-of-the-art methods. We also implement our framework on a real climate dataset for modeling of temperature signals.
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