ABSTRACT
Graph signal sampling and reconstruction techniques effectively reduce data dimensions while preserving the information and structure contained in networks. The distortion-free reduction of data dimensions not only aids in reducing the computational complexity of data but also facilitates the extraction of network features and attributes. This reduction in data dimensions provides convenience for the better analysis and processing of complex network data, ultimately enhancing the efficiency of complex network analysis tasks. Currently, the field of graph signal processing primarily consists of two fundamental frameworks: graph signal processing based on the graph Laplacian matrix and graph signal processing based on the graph's adjacency matrix . Although these two frameworks make full use of the topological structure of graph models, they do not consider the relationships between node information within networks, nor do they integrate individual node information with network structural information. Furthermore, they fail to approach the problem of sampling and reconstruction from the perspective of overall network information. This paper takes the network's intrinsic topological structure and the causal relationships between nodes as its starting point. The goal is to reduce network size and increase the effective information of individual nodes to make the entire network contain richer, valuable information. Combining the graph signal research method based on the graph Laplacian matrix, this paper introduces a graph signal sampling and reconstruction algorithm based on causal emergence. The algorithm initially employs a causal emergence algorithm based on spectral methods to obtain the sampled network and subsequently utilizes classical representation learning algorithms to acquire node representations of the sampled network. This approach enables us to obtain graph signal representations that are richer than those of the original network. Subsequently, we apply a reconstruction framework to reconstruct the obtained graph signals. Finally, the experimental results conducted on three real networks demonstrate that the proposed algorithm outperforms existing theories of graph signal sampling and reconstruction. This research contributes valuable insights and methods to the further development of the field of graph signal processing.
- Fan R K C. Spectral graph theory[M].Published for the Conference Board of the mathematical science by the American Mathematical Society,1997.Google Scholar
- Cvetkovic D, Rowlinson P, Simic S. An introduction to the theory of graph spectra[J]. Comparative & General Pharmacology,2009,2(6):217-224.Google Scholar
- Proakis J G, Manolakis D G. Digital signal processing: principles, algorithms, and applications [J].2006,23(4):392-394.Google Scholar
- Shuman D I, Narang S K, Frossard P, The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains. IEEE Signal Processing Magazine, 2013, 30(3):83–98.Google ScholarCross Ref
- Liu D, Brace C L. Big Data Analysis with Signal Processing on Graphs: Representation and processing of massive data sets with irregular structure[J].IEEE Signal Processing Magazine,2014,31(5):80-90.Google Scholar
- Brennan Klein and Erik Hoel. “The emergence of informative higher scales in complex networks”. In: Complexity (in press). url: https://arxiv.org/abs/1907.03902.Google Scholar
- Sandryhaila A, Moura J M F. Discrete Signal Processing on Graphs [J].IEEE Transactions on Signal Processing,2013,61(7):1644-1656Google Scholar
- Sandryhaila A, Moura J. Big Data Analysis with Signal Processing on Graphs: Representation and processing of massive data sets with irregular structure. IEEE Signal Processing Magazine,2014, 31(5):80–90.Google Scholar
- Sandryhaila A, Moura J M. Discrete signal processing on graphs: Frequency analysis. Signal Processing, IEEE Transactions on, 2014, 62(12):3042–3054.Google ScholarDigital Library
- Sardellitti S, Barbarossa S, Lorenzo P D. On the graph Fourier transform for directed graphs[J]. IEEE Journal of Selected Topics in Signal Processing, 2017, 11(6):796-811.Google ScholarCross Ref
- Magoarou L L, Gribonval R, Tremblay N. Approximate fast graph Fourier transforms via multilayer sparse approximations [J]. IEEE Transactions on Signal and Information Processing over Networks, 2018, 4(2): 407-420.Google ScholarCross Ref
- Tanaka Y, Eldar Y C . Generalized sampling on graphs with subspace and smoothness priors[J]. IEEE Transactions on Signal Processing, 2020,68:2272-2286.Google ScholarCross Ref
- Hammond D K, Vandergheynst P, Gribonval R. Wavelets on graphs via spectral graph theory[J]. Applied and Computational Harmonic Analysis, 2011, 30(2):129-150.Google ScholarCross Ref
- Pesenson I. Sampling in Paley-Wiener spaces on combinatorial graphs. Transactions of the American Mathematical Society, 2008, 360(10):5603–5627.Google ScholarCross Ref
- I. Pesenson, “Sampling in Paley-Wiener spaces on combinatorial graphs,” Trans. Amer. Math. Soc, vol. 360,no.10,pp.5603–5627, 2008.Google ScholarCross Ref
- OuM, CuiP,Pei J, Asymmetric transitivity preserving graph embedding[C]//Proceedings of the 22nd ACM SIGKDD international conference on Knowledge discovery and data mining2016: 1105-1114Google Scholar
- Erik P. Hoel. When the map is better than the territory.[J], Entropy, 2017, 19(5)Google Scholar
- Griebenow R, Klein B, Hoel E Finding the right scale of a network: Efficient identification of causal emergence through spectral clustering[J]. 2019.Google Scholar
- Finding the right scale of network:Efficient identification of causal emergence in preferential attachment networks through spectral clusting.Google Scholar
- Prabhakar Telagarapu, Gulivindala Suresh, J. Venkata Suman, and N. V. Lalitha, "Prabhakar Telagarapu, Gulivindala Suresh, J. Venkata Suman, and N. V. Lalitha," International Journal of Computer Theory and Engineering vol. 4, no. 1, pp. 81-84, 2012.Google Scholar
- Song Tiangang, Lyu Zhou, Ding Xinyang, and Wan Yi, "3D Surface Reconstruction Based on Kinect Sensor," International Journal of Computer Theory and Engineering vol. 5, no. 3, pp. 567-573, 2013.Google ScholarCross Ref
- Naveed Ahmed and Imran Junejo, "Using Multiple RGB-D Cameras for 3D Video Acquisition and Spatio-Temporally Coherent 3D Animation Reconstruction," International Journal of Computer Theory and Engineering vol. 6, no. 6, pp. 447-450, 2014.Google ScholarCross Ref
- Vicky Sintunata and Terumasa Aoki, "Color Segmentation Based Depth Adjustment for 3D Model Reconstruction from a Single Input Image," International Journal of Computer Theory and Engineering vol. 8, no. 2, pp. 171-176, 2016.Google ScholarCross Ref
Index Terms
- Research on Graph Signal Sampling and Reconstruction Method Based on Causal Emergence
Recommendations
Local-Set-Based Graph Signal Reconstruction
Signal processing on graph is attracting more and more attentions. For a graph signal in the low-frequency subspace, the missing data associated with unsampled vertices can be reconstructed through the sampled data by exploiting the smoothness of the ...
Generalized sampling of graph signals with the prior information based on graph fractional Fourier transform
AbstractThe graph fractional Fourier transform (GFRFT) has been applied to graph signal processing and has become an important tool in graph signal processing. However, most of the graph signals are usually non-bandlimited in the GFRFT domain. How to ...
Highlights- we develop a generalized sampling framework for graph signals based on the GFRFT.
- It allows arbitrary input of the graph signal with or without bandlimited in the GFRFT domain.
- When the space and smoothness are unknown, the ...
Graph-signal Reconstruction and Blind Deconvolution for Structured Inputs
Highlights- This paper provides a comprehensive view of several sampling, reconstruction, and recovery problems for signals defined on irregular domains that can be ...
AbstractKey to successfully deal with complex contemporary datasets is the development of tractable models that account for the irregular structure of the information at hand. This paper provides a comprehensive and unifying view of several ...
Comments