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Register a new userTopology-Aware Joint Graph Filter and Edge Weight Identification for Network Processes
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Added by
Alberto Natali
Publication date
2020
fields
Electronic Engineering
and research's language is
English
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Data defined over a network have been successfully modelled by means of graph filters. However, although in many scenarios the connectivity of the network is known, e.g., smart grids, social networks, etc., the lack of well-defined interaction weights hinders the ability to model the observed networked data using graph filters. Therefore, in this paper, we focus on the joint identification of coefficients and graph weights defining the graph filter that best models the observed input/output network data. While these two problems have been mostly addressed separately, we here propose an iterative method that exploits the knowledge of the support of the graph for the joint identification of graph filter coefficients and edge weights. We further show that our iterative scheme guarantees a non-increasing cost at every iteration, ensuring a globally-convergent behavior. Numerical experiments confirm the applicability of our proposed approach.
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In this work, we explore the state-space formulation of network processes to recover the underlying structure of the network (local connections). To do so, we employ subspace techniques borrowed from system identification literature and extend them to the network topology inference problem. This approach provides a unified view of the traditional network control theory and signal processing on networks. In addition, it provides theoretical guarantees for the recovery of the topological structure of a deterministic linear dynamical system from input-output observations even though the input and state evolution networks can be different.
In this work, we explore the state-space formulation of a network process to recover, from partial observations, the underlying network topology that drives its dynamics. To do so, we employ subspace techniques borrowed from system identification literature and extend them to the network topology identification problem. This approach provides a unified view of the traditional network control theory and signal processing on graphs. In addition, it provides theoretical guarantees for the recovery of the topological structure of a deterministic continuous-time linear dynamical system from input-output observations even though the input and state interaction networks might be different. The derived mathematical analysis is accompanied by an algorithm for identifying, from data, a network topology consistent with the dynamics of the system and conforms to the prior information about the underlying structure. The proposed algorithm relies on alternating projections and is provably convergent. Numerical results corroborate the theoretical findings and the applicability of the proposed algorithm.
Several works based on Generative Adversarial Networks (GAN) have been recently proposed to predict a set of medical images from a single modality (e.g, FLAIR MRI from T1 MRI). However, such frameworks are primarily designed to operate on images, limiting their generalizability to non-Euclidean geometric data such as brain graphs. While a growing number of connectomic studies has demonstrated the promise of including brain graphs for diagnosing neurological disorders, no geometric deep learning work was designed for multiple target brain graphs prediction from a source brain graph. Despite the momentum the field of graph generation has gained in the last two years, existing works have two critical drawbacks. First, the bulk of such works aims to learn one model for each target domain to generate from a source domain. Thus, they have a limited scalability in jointly predicting multiple target domains. Second, they merely consider the global topological scale of a graph (i.e., graph connectivity structure) and overlook the local topology at the node scale of a graph (e.g., how central a node is in the graph). To meet these challenges, we introduce MultiGraphGAN architecture, which not only predicts multiple brain graphs from a single brain graph but also preserves the topological structure of each target graph to predict. Its three core contributions lie in: (i) designing a graph adversarial auto-encoder for jointly predicting brain graphs from a single one, (ii) handling the mode collapse problem of GAN by clustering the encoded source graphs and proposing a cluster-specific decoder, (iii) introducing a topological loss to force the reconstruction of topologically sound target brain graphs. Our MultiGraphGAN significantly outperformed its variants thereby showing its great potential in multi-view brain graph generation from a single graph.
Brain graphs (i.e, connectomes) constructed from medical scans such as magnetic resonance imaging (MRI) have become increasingly important tools to characterize the abnormal changes in the human brain. Due to the high acquisition cost and processing time of multimodal MRI, existing deep learning frameworks based on Generative Adversarial Network (GAN) focused on predicting the missing multimodal medical images from a few existing modalities. While brain graphs help better understand how a particular disorder can change the connectional facets of the brain, synthesizing a target brain multigraph (i.e, multiple brain graphs) from a single source brain graph is strikingly lacking. Additionally, existing graph generation works mainly learn one model for each target domain which limits their scalability in jointly predicting multiple target domains. Besides, while they consider the global topological scale of a graph (i.e., graph connectivity structure), they overlook the local topology at the node scale (e.g., how central a node is in the graph). To address these limitations, we introduce topology-aware graph GAN architecture (topoGAN), which jointly predicts multiple brain graphs from a single brain graph while preserving the topological structure of each target graph. Its three key innovations are: (i) designing a novel graph adversarial auto-encoder for predicting multiple brain graphs from a single one, (ii) clustering the encoded source graphs in order to handle the mode collapse issue of GAN and proposing a cluster-specific decoder, (iii) introducing a topological loss to force the prediction of topologically sound target brain graphs. The experimental results using five target domains demonstrated the outperformance of our method in brain multigraph prediction from a single graph in comparison with baseline approaches.
This paper presents a quarter Laplacian filter that can preserve corners and edges during image smoothing. Its support region is $2times2$, which is smaller than the $3times3$ support region of Laplacian filter. Thus, it is more local. Moreover, this filter can be implemented via the classical box filter, leading to high performance for real time applications. Finally, we show its edge preserving property in several image processing tasks, including image smoothing, texture enhancement, and low-light image enhancement. The proposed filter can be adopted in a wide range of image processing applications.
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