journal article·2019-06-13Open access

Beyond Stochastic Gradient Descent for Matrix Completion Based Indoor Localization

Wafa Njima, Rafik Zayani, Iness Ahriz, Michel Terre, Ridha Bouallegue

Applied Sciences· Volume 9· Issue 12

Abstract

In this paper, we propose a high accuracy fingerprint-based localization scheme for the Internet of Things (IoT). The proposed scheme employs mathematical concepts based on sparse representation and matrix completion theories. Specifically, the proposed indoor localization scheme is formulated as a simple optimization problem which enables efficient and reliable algorithm implementations. Many approaches, like Nesterov accelerated gradient (Nesterov), Adaptative Moment Estimation (Adam), Adadelta, Root Mean Square Propagation (RMSProp) and Adaptative gradient (Adagrad), have been implemented and compared in terms of localization accuracy and complexity. Simulation results demonstrate that Adam outperforms all other algorithms in terms of localization accuracy and computational complexity.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Indoor and Outdoor Localization Technologies · Sparse and Compressive Sensing Techniques · Underwater Vehicles and Communication Systems

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

University of Carthage, Higher School of Communication of Tunis, LR-11/TIC-03 Innov’COM Laboratory, 2083 Ariana, Tunisia

Conservatoire National des Arts et Métiers, CEDRIC/ LAETITIA Laboratory, 75003 Paris, France

References (45)

Show source-provided references
1. The internet of things: A survey10.1016/j.comnet.2010.05.010 ↗
2. Hennebert, C., Denis, B., Le Gall, F., Copigneaux, B., Clari, F., Sottile, F., Mauro, F., Smadja, P., Pascali, S., and Preuveneers, D. (2018, July 05). uBiquitous, secUre inTernet-of-things with Location and contEx-awaReness. BUTLER project D 2, 1–134. Available online: www.iot-butler.eu.
3. Dil, B., Dulman, S., and Havinga, P. (2006, January 13–15). Range-based localization in mobile sensor networks. Proceedings of the European Workshop on Wireless Sensor Networks, Zurich, Switzerland.10.1007/11669463_14 ↗
4. Range free localization techniques in wireless sensor networks: A review10.1016/j.procs.2015.07.357 ↗
5. Distributed and adaptive location identification system for mobile devices10.1186/s13634-018-0583-3 ↗
6. Kaplan, E., and Hegarty, C. (2005). Understanding GPS: Principles and Applications, Artech House.
7. Gu, Y., Chen, M., Ren, F., and Li, J. (2016, January 3–6). HED: Handling environmental dynamics in indoor WiFi fingerprint localization. Proceedings of the IEEE Wireless Communications and Networking Conference (WCNC), Doha, Qatar.10.1109/WCNC.2016.7565019 ↗
8. Multifloor Wi-Fi localization system with floor identification10.1155/2015/131523 ↗
9. Cheng, J., Song, Z., Ye, Q., and Du, H. (2016, January 23–27). MIL: A mobile indoor localization scheme based on matrix completion. Proceedings of the IEEE International Conference on Communications (ICC), Kuala Lumpur, Malaysia.10.1109/ICC.2016.7510871 ↗
10. Quality of trilateration: Confidence-based iterative localization10.1109/TPDS.2009.90 ↗
11. Norrdine, A. (2012, January 13–15). An algebraic solution to the multilateration problem. Proceedings of the 15th International Conference on Indoor Positioning and Indoor Navigation, Sydney, Australia.
12. Najib Yasmeen, N.A., Daud, N., Abd Aziz, A., and Razali, R. (2016). 3-Dimensional wireless sensor network localization: A review. AIP Conf. Proc., 080029.
13. Kumar, P., Reddy, L., and Varma, S. (2009, January 15–19). Distance measurement and error estimation scheme for RSSI based localization in Wireless Sensor Networks. Proceedings of the 5th IEEE Conference on Wireless Communication and Sensor Networks (WCSN), Allahabad, India.10.1109/WCSN.2009.5434802 ↗
14. Nguyen, T.L., and Shin, Y. (2016). Matrix completion optimization for localization in wireless sensor networks for intelligent IoT. Sensors, 16.10.3390/s16050722 ↗
15. Nguyen, L., Kim, S., and Shim, B. (February, January 31). Localization in Internet of Things network: Matrix completion approach. Proceedings of the Information Theory and Applications Workshop (ITA), San Diego, CA, USA.
16. Nguyen, L., and Shim, B. (2016, January 27–29). Localization of Internet of Things network via Euclidean distance matrix completion. Proceedings of the IEEE/CIC International Conference on Communications in China (ICCC), Chengdu, China.10.1109/ICCChina.2016.7636902 ↗
17. ADMM-Based Sensor Network Localization Using Low-Rank Approximation10.1109/JSEN.2018.2866686 ↗
18. Solving Euclidean distance matrix completion problems via semidefinite programming10.1023/A:1008655427845 ↗
19. Newton algorithms for Riemannian distance related problems on connected locally symmetric manifolds10.1109/JSTSP.2013.2261799 ↗
20. A singular value thresholding algorithm for matrix completion10.1137/080738970 ↗
21. Chen, M., Ganesh, A., Lin, Z., Ma, Y., Wright, J., and Wu, L. (2009). Fast convex optimization algorithms for exact recovery of a corrupted low-rank matrix. Coordinated Science Laboratory Report no. UILU-ENG-09-2214, Coordinated Science Laboratory, University of Illinois at Urbana-Champaign.
22. Lin, Z., Chen, M., and Ma, Y. (2010). The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices. arXiv.
23. Liu, C., Shan, H., and Wang, B. (2018). Wireless Sensor Network Localization via Matrix Completion Based on Bregman Divergence. Sensors, 18.10.3390/s18092974 ↗
24. Noise-tolerant wireless sensor networks localization via multinorms regularized matrix completion10.1109/TVT.2017.2771805 ↗
25. Grant, M., Boyd, S., and Ye, Y. (2008). CVX: Matlab Software for Disciplined Convex Programming, CVX Research, Inc.
26. Accurate localization of multiple sources using semidefinite programming based on incomplete range matrix10.1109/JSEN.2016.2558184 ↗
27. Joint localization of multiple sources from incomplete noisy Euclidean distance matrix in wireless networks10.1016/j.comcom.2018.03.007 ↗
28. Chen, J., and Mitra, U. (2019). Unimodality-Constrained Matrix Factorization for Non-Parametric Source Localization. IEEE Trans. Signal Process., 67.10.1109/TSP.2019.2904026 ↗
29. Nguyen, L.T., Kim, J., Kim, S., and Shim, B. (2019). Localization of IoT Networks Via Low-Rank Matrix Completion. IEEE Trans. Commun.10.1109/TCOMM.2019.2915226 ↗
30. Zhang, H., Liu, Y., and Lei, H. (2019). Localization from Incomplete Euclidean Distance Matrix: Performance Analysis for the SVD-MDS Approach. IEEE Trans. Signal Proces., 67.10.1109/TSP.2019.2904022 ↗
31. Multidimensional scaling of similarity10.1007/BF02289530 ↗
32. Path-loss and shadowing (large-scale fading)
33. Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization10.1137/070697835 ↗
34. Exact matrix completion via convex optimization10.1007/s10208-009-9045-5 ↗
35. Adaptive subgradient methods for online learning and stochastic optimization
36. Sebastian, R. (2016). An overview of gradient descent optimization algorithms. arXiv.
37. Sutskever, I., Martens, J., Dahl, G., and Hinton, G. (2013, January 16–21). On the importance of initialization and momentum in deep learning. Proceedings of the International Conference on Machine Learning, Atlanta, GA, USA.
38. Wang, Y., Kim, S.-P., and Principe, J.C. (August, January 31). Comparison of TDNN training algorithms in brain machine interfaces. Proceedings of the IEEE International Joint Conference on Neural Networks (IJCNN’05), Montreal, QC, Canada.
39. Neural networks for machine learning lecture 6a overview of mini-batch gradient descent
40. Kingma, D.P., and Ba, J. (2014). Adam: A method for stochastic optimization. arXiv.
41. STCDG: An efficient data gathering algorithm based on matrix completion for wireless sensor networks10.1109/TWC.2012.121412.120148 ↗
42. Recover corrupted data in sensor networks: A matrix completion solution10.1109/TMC.2016.2595569 ↗
43. Gaussian elimination is not optimal10.1007/BF02165411 ↗
44. Benoit, A. (2009). Algorithmique I-Cours et Travaux Dirigés L3, Ecole Normale Supérieure de Lyon.
45. On the Newton method for the matrix p th root10.1137/050624790 ↗