Logo PTI Logo FedCSIS

Position and Communication Papers of the 16th Conference on Computer Science and Intelligence Systems

Annals of Computer Science and Information Systems, Volume 26

An impact of tensor-based data compression methods on deep neural network accuracy


DOI: http://dx.doi.org/10.15439/2021F127

Citation: Position and Communication Papers of the 16th Conference on Computer Science and Intelligence Systems, M. Ganzha, L. Maciaszek, M. Paprzycki, D. Ślęzak (eds). ACSIS, Vol. 26, pages 311 ()

Full text

Abstract. In this article, an in-depth analysis of the influence of the tensor-based lossy data compression on the performance of the various deep neural architectures is presented. We show that the Tucker and the Tensor Train decomposition methods allow for very high compression ratios, while maintaining enough information in the compressed data to achieve only a negligible drop in the accuracy. The measurements were performed on the popular architectures: AlexNet, ResNet, VGG, and MNASNet. Further augmentation of the tensor decompositions with the ZFP floating-point compression algorithm allows for finding optimal parameters and even higher compressions ratio at the same recognition accuracy.


  1. Cococcioni, M., et al. Novel arithmetics in deep neural networks signal processing for autonomous driving: Challenges and opportunities. In IEEE Signal Processing Magazine, 2020, 38.1: 97-110. http://dx.doi.org/10.1109/MSP.2020.2988436
  2. Cyganek, B. Object Detection and Recognition in Digital Images: Theory and Practice; John Wiley & Sons: New York, NY, USA, 2013. http://dx.doi.org/10.1002/9781118618387
  3. Kolda, T.; Bader, B. Tensor Decompositions and Applications. SIAM Rev. 51.3 2009, 51, 455–500. http://dx.doi.org/10.1137/07070111X
  4. Cyganek, B., Thumbnail Tensor—A Method for Multidimensional Data Streams Clustering with an Efficient Tensor Subspace Model in the Scale-Space, Sensors, 19(19), 4088, 2019, http://dx.doi.org/10.3390/s19194088
  5. LI, J., LIU, Z., Multispectral transforms using convolution neural networks for remote sensing multispectral image compression. In Remote Sensing 11.7: 759, 2019. http://dx.doi.org/10.3390/rs11070759
  6. CHOI, Y., EL-KHAMY, M., LEE, J., Universal deep neural network compression. In IEEE Journal of Selected Topics in Signal Processing, 14.4, 2020, pp. 715-726. http://dx.doi.org/10.1109/JSTSP.2020.2975903
  7. Przyborowski M., et al. Toward Machine Learning on Granulated Data – a Case of Compact Autoencoder-based Representations of Satellite Images. In 2018 IEEE International Conference on Big Data (Big Data), 2018, pp. 2657-2662, http://dx.doi.org/10.1109/BigData.2018.8622562.
  8. Wang, N; Yeung, D. Y., Learning a deep compact image representation for visual tracking. In Advances in neural information processing systems, 2013
  9. Lindstrom, P., Fixed-Rate Compressed Floating-Point Arrays. In IEEE Transactions on Visualization and Computer Graphics 20(12) 2014, pp. 2674-2683, http://dx.doi.org/10.1109/TVCG.2014.2346458
  10. Ziv, J., Lempel, A., Compression of individual sequences via variable-rate coding. In IEEE transactions on Information Theory, 1978, 24.5: 530-536. http://dx.doi.org/10.1109/TIT.1978.1055934
  11. Cyganek, B., A Framework for Data Representation, Processing, and Dimensionality Reduction with the Best-Rank Tensor Decomposition. Proceedings of the ITI 2012 34th International Conference Information Technology Interfaces, June 25-28, 2012, Cavtat, Croatia, pp. 325-330, http://dx.doi.org/10.2498/iti.2012.0466, 2012.
  12. De Lathauwer, L.; De Moor, B.; Vandewalle, J. On the best rank-1 and rank-(R1, R2,..., Rn) approximation of higher-order tensors. Siam J. Matrix Anal. Appl. 2000, 21, 1324–1342. http://dx.doi.org/10.1137/S0895479898346995
  13. Ballé, J., Laparra, V., Simoncelli, E. P., End-to-end optimized image compression. In arXiv preprint https://arxiv.org/abs/1611.01704, 2016.
  14. Zhang, L., et al. Compression of hyperspectral remote sensing images by tensor approach. In Neurocomputing, 147, 2015, pp. 358-363. http://dx.doi.org/10.1016/j.neucom.2014.06.052
  15. Aidini, A., Tsagkatakis, G., Tsakalides, P., Compression of high-dimensional multispectral image time series using tensor decomposition learning. In: 2019 27th European Signal Processing Conference (EUSIPCO). IEEE, 2019. p. 1-5. http://dx.doi.org/10.23919/EUSIPCO.2019.8902838
  16. Watkins, Y. Z., Sayeh, M. R., Image data compression and noisy channel error correction using deep neural network. In Procedia Computer Science, 95, 2016, pp. 145-152. http://dx.doi.org/10.1016/j.procs.2016.09.305
  17. Friedland, G., et al. On the Impact of Perceptual Compression on Deep Learning. In 2020 IEEE Conference on Multimedia Information Processing and Retrieval (MIPR). IEEE, 2020, p. 219-224. http://dx.doi.org/10.1109/MIPR49039.2020.00052
  18. Dejean-Servières, M., et al. Study of the impact of standard image compression techniques on performance of image classification with a convolutional neural network. 2017. PhD Thesis. INSA Rennes; Univ Rennes; IETR; Institut Pascal.
  19. Ullrich, K., Meeds, E., Welling, M., Soft weight-sharing for neural network compression. In arXiv preprint https://arxiv.org/abs/1702.04008, 2017.
  20. JIN, S. et al. DeepSZ: A novel framework to compress deep neural networks by using error-bounded lossy compression. In Proceedings of the 28th International Symposium on High-Performance Parallel and Distributed Computing, 2019 p. 159-170. http://dx.doi.org/10.1145/3307681.3326608
  21. Deng, Lei, et al. Model compression and hardware acceleration for neural networks: A comprehensive survey. In Proceedings of the IEEE, 2020, 108.4: 485-532. http://dx.doi.org/10.1109/JPROC.2020.2976475
  22. Muti, D.; Bourennane, S. Multidimensional filtering based on a tensor approach. Signal Process. 2005, 85, 2338–2353. http://dx.doi.org/10.1016/j.sigpro.2004.11.029
  23. Cyganek, B.; Smołka, B. Real-time framework for tensor-based image enhancement for object classification. Proc. SPIE 2016, 9897, 98970Q. http://dx.doi.org/10.1117/12.2227797
  24. Cyganek, B.; Krawczyk, B.; Wozniak, M. Multidimensional Data Classification with Chordal Distance Based Kernel and Support Vector Machines. Eng. Appl. Artif. Intell. 2015, 46, 10–22. http://dx.doi.org/10.1016/j.engappai.2015.08.001
  25. Cyganek, B.; Wozniak, M. Tensor-Based Shot Boundary Detection in Video Streams. New Gener. Comput. 2017, 35, 311–340. http://dx.doi.org/10.1007/s00354-017-0024-0
  26. Marot, J.; Fossati, C.; Bourennane, S. Fast subspace-based tensor data filtering. In Proceedings of the 2009 16th IEEE International Conference on Image Processing (ICIP), Cairo, Egypt, 7–10 November 2009; pp. 3869–3872. http://dx.doi.org/10.1109/ICIP.2009.5414048
  27. Khoromskij, B. N., Khoromskaia, V., Multigrid accelerated tensor approximation of function related multidimensional arrays. In SIAM J. Sci. Comput., 31, 2009, pp. 3002–3026. http://dx.doi.org/10.1137/080730408
  28. Oseledets, I. V., Savostianov, D. V., Tyrtyshnikov, E. E., Tucker dimensionality reduction of three-dimensional arrays in linear time. In SIAM J. Matrix Anal. Appl., 30, 2008, pp. 939–956. http://dx.doi.org/10.1137/060655894
  29. Lee, N., Cichocki, A., Fundamental tensor operations for large-scale data analysis using tensor network formats. In Multidimensional Syst. Signal Process., vol. 29, no. 3, 2017, pp. 921–960 http://dx.doi.org/10.1007/s11045-017-0481-0
  30. Hubener, R., Nebendahl, V., Dur, W., Concatenated tensor network states. In New J. Phys., 12, 2010, 025004. http://dx.doi.org/10.1088/1367-2630/12/2/025004
  31. Van Loan, C. F., Tensor network computations in quantum chemistry Technical report, available online at www.cs.cornell.edu/cv/OtherPdf/ZeuthenCVL.pdf, 2008.
  32. Oseledets, I., Tensor-Train Decomposition. In SIAM J. Scientific Computing. 33., 2011, pp. 2295-2317. http://dx.doi.org/10.1137/090752286.
  33. Lindstrom, P., Fixed-Rate Compressed Floating-Point Arrays. In IEEE Transactions on Visualization and Computer Graphics vol. 20; 2014, http://dx.doi.org/10.1109/TVCG.2014.2346458.
  34. Lemley, J., Deep Learning for Consumer Devices and Services: Pushing the limits for machine learning, artificial intelligence, and computer vision. In IEEE Consumer Electronics Magazine vol. 6, Iss. 2; 2017 http://dx.doi.org/10.1109/MCE.2016.2640698
  35. Krizhevsky, A., Sutskever, I., Hinton, G. E., ImageNet classification with deep convolutional neural networks. In Communications of the ACM. 60 (6) pp. 84–90. http://dx.doi.org/10.1145/3065386
  36. Simonyan, K., Zisserman, A. Very deep convolutional networks for large-scale image recognition. In arXiv preprint https://arxiv.org/abs/1409.1556. 2014
  37. He, Kaiming, et al. Deep Residual Learning for Image Recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition 2016, pp. 770-778 http://dx.doi.org/10.1109/CVPR.2016.90
  38. Krizhevsky, A., et al., ImageNet classification with deep convolutional neural networks. In Proc. 25th Int. Conf. Neural Inf. Process. Syst. (NIPS), vol. 1., Red Hook, NY, USA: Curran Associates, 2012, pp. 1097–1105. http://dx.doi.org/10.1145/3065386
  39. Simonyan K. and Zisserman A., Very deep convolutional networks for large-scale image recognition. In Proc. 3rd Int. Conf. Learn. Represent. (ICLR), San Diego, CA, USA, Y. Bengio and Y. LeCun, Eds., 2015, pp. 1–14.
  40. Xie S., et al., Aggregated residual transformations for deep neural networks.In Proc. IEEE Conf. Comput. Vis. Pattern Recognit. (CVPR), 2017, pp. 5987–5995. http://dx.doi.org/10.1109/CVPR.2017.634
  41. Szegedy, S. et al., Inception-v4, inception-resnet and the impact of residual connections on learning. In Proc. 31st AAAI Conf. Artif. Intell., San Francisco, CA, USA, S. P. Singh and S. Markovitch, Eds., 2017, pp. 4278–4284.
  42. Tan, M., et al. Mnasnet: Platform-aware neural architecture search for mobile. In Proceedings of the IEEE/CVF Conference on Com- puter Vision and Pattern Recognition 2019, pp. 2820-2828 doi: 10.1109/CVPR.2019.00293
  43. Kossaifi, J.; Panagakis, Y.; Kumar, A.; Pantic, M. TensorLy: Tensor Learning in Python. arXiv preprint 2018, https://arxiv.org/abs/1610.09555.
  44. Howard, J., imagenette dataset, https://github.com/fastai/imagenette/
  45. Oseledets, I. V., Tensor-train decomposition. In SIAM J. Sci. Comput., vol. 33, no. 5, 2011, pp. 2295–2317 http://dx.doi.org/10.1137/090752286