Detecting Localized Categorical Attributes on Graphs

Chen, Siheng; Yang, Yaoqing; Zong, Shi; Singh, Aarti; Kovačević, Jelena

doi:10.1109/tsp.2017.2666772

Cited by 11 publications

(12 citation statements)

References 68 publications

(128 reference statements)

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“…By default, we set σ = 0.2, b = 0.2. For binary graph signals, we consider adding Bernoulli noise [23]; that is, we randomly select a subset of vertices and flip the associated binary values.…”

Section: Methodsmentioning

confidence: 99%

Graph Signal Denoising Via Unrolling Networks

Chen

Eldar

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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We propose an interpretable graph neural network framework to denoise single or multiple noisy graph signals. The proposed graph unrolling networks expand algorithm unrolling to the graph domain and provide an interpretation of the architecture design from a signal processing perspective. We unroll an iterative denoising algorithm by mapping each iteration into a single network layer where the feed-forward process is equivalent to iteratively denoising graph signals. We train the graph unrolling networks through unsupervised learning, where the input noisy graph signals are used to supervise the networks. By leveraging the learning ability of neural networks, we adaptively capture appropriate priors from input noisy graph signals, instead of manually choosing signal priors. To validate the proposed methods, we conduct extensive experiments on both real-world datasets and simulated datasets, and demonstrate that our methods have smaller denoising errors than conventional denoising algorithms and state-of-the-art graph neural networks. For denoising a single smooth graph signal, the normalized mean square error of the proposed networks is around 40% and 60% lower than that of graph Laplacian denoising and graph wavelets, respectively.

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Section: Methodsmentioning

confidence: 99%

Graph Signal Denoising Via Unrolling Networks

Chen

Eldar

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…While this is similar to localizing an activated piece, it is either computationally inefficient or hindered by strong assumptions. For example, in [39], the authors analyze the theoretical performance of detecting paths, blobs and spatial temporal sets by exhaustive search, resulting in a costly algorithm, while in [42], [43], the authors aim to detect a node set with a specific cut number, resulting in a computationally efficient algorithm, but limited by strong assumptions.…”

Section: Signal Localization On Graphsmentioning

confidence: 99%

“…We can adaptively update the edge weights by using graph signal coefficients and solve (4) by using efficient graph-cut solvers. Inspired by [42], [43], we add the number of edges connecting activated and inactivated nodes to the objective function to induce a connected component. Let ∆ ∈ R M ×N be the graph incidence matrix of G [54].…”

Section: Signal Localization On Graphsmentioning

confidence: 99%

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Localization, Decomposition, and Dictionary Learning of Piecewise-Constant Signals on Graphs

Chen,

Yang,

Moura

et al. 2016

Preprint

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Motivated by the need to extract meaning from large amounts of complex data that can be best modeled by graphs, we consider three critical problems on graphs: localization, decomposition, and dictionary learning of piecewise-constant signals. These graph-based problems are related to many real-world applications, such as localizing virus attacks in cyber-physical systems, localizing stimulus in brain connectivity networks, and mining traffic events in city street networks, where the key issue is to separate localized activated patterns and background noise; in other words, we aim to find the supports of localized activated patterns. Counterparts of these problems in classical signal/image processing, such as impulse detection, foreground detection, and wavelet construction, have been intensely studied over the past few decades. We use piecewise-constant graph signals to model localized patterns, where each piece indicates a localized pattern that exhibits homogeneous internal behavior and the number of pieces indicates the number of localized patterns. For such signals, we show that decomposition and dictionary learning are natural extensions of localization, the goal of which is not only to efficiently approximate graph signals, but also to accurately find supports of localized patterns. For each of the three problems, i.e., localization, decomposition, and dictionary learning, we propose a specific graph signal model, an optimization problem, and a computationally efficient solver. The proposed solvers directly find the supports of arbitrary localized activated patterns without tuning any thresholds, which is a notorious challenge in many localization problems. We then conduct an extensive empirical study to validate the proposed methods on both simulated and real data including the analysis of a large volume of spatio-temporal Manhattan urban data. From taxi-pickup activities and using our methods, we are able to detect both everyday as well as special events and distinguish weekdays from weekends. Our findings validate the effectiveness of the approach and suggest that graph signal processing tools may aid in urban planning and traffic forecasting.

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“…A closely related line of work considers the problem of detecting signals in irregular domains [34]- [39]. In particular, [40], [41] consider optimal random walk detection on a graph which is closely related to the problem of path localization.…”

Section: Introductionmentioning

confidence: 99%

Fast path localization on graphs via multiscale Viterbi decoding

Yang

Chen

Maddah-Ali

et al. 2017

2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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We consider a problem of localizing a path-signal that evolves over time on a graph. A path-signal can be viewed as the trajectory of a moving agent on a graph in several consecutive time points. Combining dynamic programming and graph partitioning, we propose a path-localization algorithm with significantly reduced computational complexity. We analyze the localization error for the proposed approach both in the Hamming distance and the destination's distance between the path estimate and the true path using numerical bounds. Unlike usual theoretical bounds that only apply to restricted graph models, the obtained numerical bounds apply to all graphs and all nonoverlapping graph-partitioning schemes. In random geometric graphs, we are able to derive a closed-form expression for the localization error bound, and a tradeoff between localization error and the computational complexity. Finally, we compare the proposed technique with the maximum likelihood estimate under the path constraint in terms of computational complexity and localization error, and show significant speedup (100×) with comparable localization error (4×) on a graph from real data. Variants of the proposed technique can be applied to tracking, road congestion monitoring, and brain signal processing.

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Detecting Localized Categorical Attributes on Graphs

Cited by 11 publications

References 68 publications

Graph Signal Denoising Via Unrolling Networks

Graph Signal Denoising Via Unrolling Networks

Localization, Decomposition, and Dictionary Learning of Piecewise-Constant Signals on Graphs

Fast path localization on graphs via multiscale Viterbi decoding

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