Causal Fourier Analysis on Directed Acyclic Graphs and Posets

Seifert, Bastian; Wendler, Chris; Püschel, Markus

doi:10.1109/tsp.2023.3324988

Cited by 7 publications

(4 citation statements)

References 44 publications

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“…The DAG is a special type of a directed graph, whose main characteristic is that it is free of cycles. DAGs are commonly used to model causal relationships, dependencies, and flows in various systems [9]. In this context, DAGs are used to model and analyze dynamic systems where information (or signal) flows from one vertex to another, causing a cascade of effects.…”

Section: Introductionmentioning

confidence: 99%

“…In this context, DAGs are used to model and analyze dynamic systems where information (or signal) flows from one vertex to another, causing a cascade of effects. This is particularly relevant in the fields such as epidemiology, finance, neuroscience, and machine learning, where understanding causal relationships between variables or events can lead to better predictions and interventions [9,13,15].…”

Section: Introductionmentioning

confidence: 99%

“…One particular type of graph that is of great significance in various areas is the Directed Acyclic Graph (DAG) [9][10][11][12][13][14]. The DAG is a special type of a directed graph, whose main characteristic is that it is free of cycles.…”

Section: Introductionmentioning

confidence: 99%

“…Spectral analysis and processing based on the standard Graph Fourier Transform (GFT) are challenging for signals on DAGs, since all eigenvalues of the adjacency matrix are equal to zero, rendering the frequency components of the analyzed signal indistinguishable [9]. The majority of endeavors aimed at introducing an appropriate candidate for the GFT concentrate on altering the Fourier basis for Jordan Normal Form (JNF) computation, which can significantly influence the graph signal processing methods [16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Fourier Analysis of Signals on Directed Acyclic Graphs (DAG) Using Graph Zero-Padding

Stankovic,

Daković,

Bardi

et al. 2024

Preprint

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Directed acyclic graphs (DAGs) are used for modeling causal relationships, dependencies, and flows in various systems. However, spectral analysis becomes impractical in this setting because the eigendecomposition of the adjacency matrix yields all eigenvalues equal to zero. This inherent property of DAGs results in an inability to differentiate between frequency components of signals on such graphs. This problem can be addressed by alternating the Fourier basis or adding edges in a DAG. However, these approaches change the physics of the considered problem. To address this limitation, we propose a graph zero-padding approach. This approach involves augmenting the original DAG with additional vertices that are connected to the existing structure. The added vertices are characterized by signal values set to zero. The proposed technique enables the spectral evaluation of system outputs on DAGs (in almost all cases), that is the computation of vertex-domain convolution without the adverse effects of aliasing due to changes in a graph structure, with the ultimate goal of preserving the output of the system on a graph as if the changes in the graph structure were not performed.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%