MATGEN: A REALISTIC SPARSE MATRIX GENERATOR USING SIGNAL PROCESSING AND IMAGE PROCESSING METHODS

Abstract

The limited size of publicly available sparse matrix datasets creates a significant challenge for benchmarking, testing, and validating algorithms in scientific computing, artificial intelligence and other data-intensive applications. Existing approaches such as random matrix generators or general data augmentation methods often fail to produce structurally realistic matrices. To address this gap, we present MatGen which a tool for generating realistic variations of a given sparse matrix using signal processing and image processing techniques. MatGen takes a real sparse matrix as input and produces structurally consistent matrices at different sizes, introducing controlled variation while preserving key sparsity patterns. We evaluate the effectiveness of MatGen by analyzing structural features and visual similarities between original and generated matrices. Experimental results show that MatGen can produce realistic, scalable sparse matrices suitable for a wide range of applications including benchmarking computational methods, and sparse data techniques.

Keywords

• Sparse matrices
• matrix generator
• matrix scaling
• data augmentation
• signal processing
• image processing

References

1. I. Rish, G. Grabarnik, Sparse modeling: theory, algorithms, and applications, CRC press, 2014.
2. T. M. A. U. Gunathilaka, P. D. Manage, J. Zhang, Y. Li, W. Kelly, Addressing sparse data challenges in recommendation systems: A systematic review of rating estimation using sparse rating data and profile enrichment techniques, Intelligent Systems with Applications (2025) 200474.
3. T. A. Davis, Y. Hu, The university of florida sparse matrix collection, ACM Transactions on Mathematical Software (TOMS) 38 (1) (2011) 1–25.
4. W. Hu, M. Fey, M. Zitnik, Y. Dong, H. Ren, B. Liu, M. Catasta, J. Leskovec, Open graph benchmark: Datasets for machine learning on graphs, Advances in neural information processing systems 33 (2020) 22118–22133.
5. R. Drikvandi, O. Lawal, Sparse principal component analysis for natural language processing, Annals of data science 10 (1) (2023) 25–41.
6. N. Liu, Y. Lei, R. Liu, Y. Yang, T. Wei, J. Gao, Sparse time–frequency analysis of seismic data: Sparse representation to unrolled optimization, IEEE Transactions on Geoscience and Remote Sensing 61 (2023) 1–10.
7. F. S. Torun, M. Manguoglu, C. Aykanat, Parallel minimum norm solution of sparse block diagonal column overlapped underdetermined systems, ACM Trans. Math. Softw. 43 (4) (Jan. 2017). doi:10.1145/3004280.
8. I. Duff, P. Leleux, D. Ruiz, F. S. Torun, Row replicated block cimmino, SIAM Journal on Scientific Computing 45 (4) (2023) C207–C232. doi:10.1137/22M1487710.

9. F. S. Torun, M. Manguoglu, C. Aykanat, Enhancing block cimmino for sparse linear systems with dense columns via schur complement, SIAM Journal on Scientific Computing 45 (2) (2023) C49–C72. [ T. Hoefler, D. Alistarh, T. Ben-Nun, N. Dryden, A. Peste, Sparsity in deep learning: Pruning and growth for efficient inference and training in neural networks, Journal of Machine Learning Research 22 (241) (2021) 1–124.
10. W. Li, X. Song, Y. Tu, Graphdrl: Gnn-based deep reinforcement learning for interactive recommendation with sparse data, Expert Systems with Applications (2025) 126832.
11. N. K. Unnikrishnan, J. Gould, K. K. Parhi, Scv-gnn: Sparse compressed vector-based graph neural network aggregation, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 42 (12) (2023) 4803–4816.
12. D. Chakrabarti, Y. Zhan, C. Faloutsos, R-mat: A recursive model for graph mining, SIAM International Conference on Data MiningAccessed from foundational works on graph mining (2004).
13. E. Abbe, Community detection and stochastic block models: Recent developments, Journal of Machine Learning Re- search 18 (177) (2017) 1–86.
14. A. Farhadi, A. Taheri, Application of genai in synthetic data generation in the healthcare system, in: Application of Generative AI in Healthcare Systems, Springer, 2025, pp. 67–89.
15. G. Huang, G. Dai, Y. Wang, H. Yang, Ge-spmm: General-purpose sparse matrix-matrix multiplication on gpus for graph neural networks, in: SC20: International Conference for High Performance Computing, Networking, Storage and Analysis, IEEE, 2020, pp. 1–12.
16. Z. Chen, Z. Qu, Y. Quan, L. Liu, Y. Ding, Y. Xie, Dynamic n: M fine-grained structured sparse attention mechanism, in: Proceedings of the 28th ACM SIGPLAN Annual Symposium on Principles and Practice of Parallel Programming, 2023, pp. 369–379.
17. R. Keys, Cubic convolution interpolation for digital image processing, IEEE transactions on acoustics, speech, and signal processing 29 (6) (2003) 1153–1160.
18. P. The´venaz, T. Blu, M. Unser, Image interpolation and resampling, Handbook of medical imaging, processing and analysis 1 (1) (2000) 393–420.
19. P. J. BURT, E. H. ADELSON, The laplacian pyramid as a compact image code, IEEE TRANSACTIONS ON COMMU- NICATIONS 3 (4) (1983).
20. C. E. Duchon, Lanczos filtering in one and two dimensions, Journal of Applied Meteorology (1962-1982) (1979) 1016– 1022.
21. W. L. Briggs, V. E. Henson, The DFT: an owner’s manual for the discrete Fourier transform, SIAM, 1995.
22. G. Strang, The discrete cosine transform, SIAM review 41 (1) (1999) 135–147.