# Improved Sparse Coding Algorithm with Device-Free Localization Technique for Intrusion Detection and Monitoring

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- This paper proposes a block-group regularizer to extend the theory of the previous sparse-representation-based frameworks for DFL.
- We propose an improved sparse coding algorithm to achieve the robust DFL. Especially, through a modification on the objective function, we exploit the effective optimization process with the proximal operator for localizing target.
- For evaluating the localization performance and robustness of the proposed method, we establish the testbeds of indoor DFL system. Our experimental results show that the proposed method is more effective than the state-of-the-art sparse coding algorithms for DFL, especially in noisy cases.

## 2. Related Work

## 3. Problem Formulation

#### 3.1. Preliminary on System Model

#### 3.2. Sparse Representation Model of DFL

#### 3.2.1. Data Collection and Process of Background Elimination

#### 3.2.2. Dataset Construction

**Offline stage**for constructing sensing matrix (dictionary). Assume that the monitoring area is discretized into C grids as shown in Figure 2, and each grid is regarded as one location i.e., one class. Therefore, all the potential locations are divided into C classes in this DFL problem. For each class $c=1,2,\cdots ,C$, we perform experiments of $l=1,\cdots ,L$ trials with an object at this grid. For each trial, through data collection and background elimination, we can get an variation matrix data, $\Delta {\mathit{R}}_{cl}\in {\mathbb{R}}^{N\times N}$. Then, we convert the variation matrix $\Delta {\mathit{R}}_{cl}$ to a variation vector ${\mathit{d}}_{cl}$ by merging all the columns into the vector. Finally, stacking all the variation vectors together, we can obtain the sensing matrix with location information for all grids and trials as $\mathit{D}=[{\mathit{d}}_{11},{\mathit{d}}_{12},\cdots {\mathit{d}}_{1L},\cdots ,{\mathit{d}}_{c1},\cdots ,{\mathit{d}}_{cL},\cdots ,{\mathit{d}}_{C1},\cdots ,{\mathit{d}}_{CL}]$. This sensing matrix $\mathit{D}$ is normally termed as

**dictionary**, with a size of $m\times n$. For $m={N}^{2},n=CL$.

**Online stage**for processing the test signal. In the online test step, the same procedure is taken for processing the observation signal. Then, we can obtain the vector of observation signal as $\mathit{y}$ when M targets separately locate at several certain grids, where M must be smaller than the number of total grids. If M = 1, it is a single-target localization task; If M > 1, it is a multi-target localization problem.

#### 3.2.3. Sparse Representation of Testing Signal

## 4. Approach

#### 4.1. Proposed Solver

#### 4.1.1. Sparse Coding

#### 4.1.2. Objective Function

#### 4.2. Localization Algorithm with Improved Sparse Coding

#### 4.2.1. Fundamental Sparse Coding Algorithms via Proximal Operator

#### 4.2.2. Improved Sparse Coding Algorithm via Proximal Operator

#### 4.2.3. Target Localization Based on the Improved Sparse Solution

Algorithm 1 improved Sparse Coding with Proximal Operator (ISCPO). |

Require:$\mathit{y}\in {\mathbb{R}}^{m}$, $\mathit{D}\in {\mathbb{R}}^{m\times n},\phantom{\rule{4pt}{0ex}}\mu $, $\lambda ,\phantom{\rule{4pt}{0ex}}{\mathit{\alpha}}_{0}=\mathit{0}$Ensure:$\phi $ or {${\phi}_{1}$, …, ${\phi}_{S}$}1: for $k=0\phantom{\rule{4pt}{0ex}}\mathrm{to}\phantom{\rule{4pt}{0ex}}\mathrm{maxiteration}$ do2: $\mathit{b}\leftarrow {\mathit{\alpha}}^{\left(k\right)}+\frac{1}{\mu}{\mathit{D}}^{T}(\mathit{y}-\mathit{D}{\mathit{\alpha}}^{\left(k\right)})$ 3: ${\mathit{\alpha}}^{(k+1)}\leftarrow {\mathrm{prox}}_{{\parallel \xb7\parallel}_{2,1}}\left(\mathit{b}\right)$ 4: Until convergence or reach the maxiteration number. 5: end for6: ${\mathit{\alpha}}^{\ast}\leftarrow {\mathit{\alpha}}^{(k+1)}$ 7: if Single-target localization then8: Target is located at the $\phi $-th grid according to (16) 9: $\mathrm{Return}\phantom{\rule{4pt}{0ex}}\phi $ 10: end if |

## 5. Performance Evaluation

^{®}Core™ i7 CPU.

#### 5.1. Configuration of Experiment

#### 5.1.1. Hardware

#### 5.1.2. Data Pre-Process of Background Elimination

#### 5.1.3. Compared Approaches

#### 5.1.4. Other Settings and Metrics

- Assume that ${C}_{\mathrm{total}}$ is the total number of testing samples and ${C}_{\mathrm{correct}}$ is the number of samples that are correctly located. Then the localization accuracy is defined by$$\begin{array}{cc}\hfill \mathrm{Accuracy}& =\frac{{C}_{\mathrm{correct}}}{{C}_{\mathrm{total}}}\hfill \end{array}$$

#### 5.2. Experimental Result of Indoor Localization

#### 5.2.1. Experimental Setup of Indoor DFL System

#### 5.2.2. Localization Performance of the Proposed Approach and the Comparisons for Indoor DFL

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Kolias, C.; Kambourakis, G.; Stavrou, A.; Gritzalis, S. Intrusion detection in 802.11 networks: Empirical evaluation of threats and a public dataset. IEEE Commun. Surv. Tutor.
**2016**, 18, 184–208. [Google Scholar] [CrossRef] - Kolias, C.; Kambourakis, G.; Maragoudakis, M. Swarm intelligence in intrusion detection: A survey. Comput. Secur.
**2011**, 30, 625–642. [Google Scholar] [CrossRef] - Kaltiokallio, O.; Yigitler, H.; Jantti, R. A three-state received signal strength model for device-free localization. IEEE Trans. Veh. Technol.
**2017**, 66, 9226–9240. [Google Scholar] [CrossRef] - Meng, W.; Tischhauser, E.W.; Wang, Q.; Wang, Y.; Han, J. When intrusion detection meets blockchain technology: A review. IEEE Access
**2018**, 6, 10179–10188. [Google Scholar] [CrossRef] - Meng, W. Intrusion detection in the era of IoT: Building trust via traffic filtering and sampling. Computer
**2018**, 51, 36–43. [Google Scholar] [CrossRef] - Zhao, L.; Huang, H.; Ding, S.; Li, X. An Accurate and Efficient Device-Free Localization Approach Based on Gaussian Bernoulli Restricted Boltzmann Machine. In Proceedings of the 2018 IEEE International Conference on Systems, Man, and Cybernetics (SMC), Miyazaki, Japan, 7–10 October 2018; pp. 2323–2328. [Google Scholar]
- Bisio, I.; Delfino, A.; Lavagetto, F.; Sciarrone, A. Enabling IoT for in-home rehabilitation: Accelerometer signals classification methods for activity and movement recognition. IEEE Internet Things J.
**2017**, 4, 135–146. [Google Scholar] [CrossRef] - Verma, P.; Sood, S.K. Fog Assisted-IoT Enabled Patient Health Monitoring in Smart Homes. IEEE Internet Things J.
**2018**, 5, 1789–1796. [Google Scholar] [CrossRef] - Zhao, H.; Ding, S.; Li, X.; Huang, H. Deep Neural Network Structured Sparse Coding for Online Processing. IEEE Access
**2018**, 6, 74778–74791. [Google Scholar] [CrossRef] - Huang, H.; Zhao, H.; Li, X.; Ding, S.; Zhao, L.; Li, Z. An Accurate and Efficient Device-Free Localization Approach Based on Sparse Coding in Subspace. IEEE Access
**2018**, 6, 61782–61799. [Google Scholar] [CrossRef] - Han, Y.; Feng, X.C.; Baciu, G.; Wang, W.W. Nonconvex sparse regularizer based speckle noise removal. Pattern Recognit.
**2013**, 46, 989–1001. [Google Scholar] [CrossRef] - Micchelli, C.A.; Morales, J.M.; Pontil, M. Regularizers for structured sparsity. Adv. Comput. Math.
**2013**, 38, 455–489. [Google Scholar] [CrossRef] - Li, Z.; Ding, S.; Li, Y.; Yang, Z.; Xie, S.; Chen, W. Manifold optimization-based analysis dictionary learning with an l
_{1/2}-norm regularizer. Neural Netw.**2018**, 98, 212–222. [Google Scholar] [CrossRef] - Li, X.; Ding, S.; Li, Z.; Tan, B. Device-free localization via dictionary learning with difference of convex programming. IEEE Sens. J.
**2017**, 17, 5599–5608. [Google Scholar] [CrossRef] - Wang, H.; Leung, C.S.; So, H.C.; Liang, J.; Feng, R.; Han, Z. Robust MIMO Radar Target Localization based on Lagrange Programming Neural Network. arXiv
**2018**, arXiv:1805.12300. [Google Scholar] - Wang, J.; Gao, Q.; Wang, H.; Cheng, P.; Xin, K. Device-free localization with multidimensional wireless link information. IEEE Trans. Veh. Technol.
**2015**, 64, 356–366. [Google Scholar] [CrossRef] - Wang, D.; Guo, X.; Zou, Y. Accurate and robust device-free localization approach via sparse representation in presence of noise and outliers. In Proceedings of the IEEE International Conference on Digital Signal Processing (DSP), Beijing, China, 16–18 October 2016; pp. 199–203. [Google Scholar]
- Kolias, C.; Kolias, V.; Kambourakis, G. TermID: A distributed swarm intelligence-based approach for wireless intrusion detection. Int. J. Inf. Secur.
**2017**, 16, 401–416. [Google Scholar] [CrossRef] - Zhang, B.; Cheng, X.; Zhang, N.; Cui, Y.; Li, Y.; Liang, Q. Sparse target counting and localization in sensor networks based on compressive sensing. In Proceedings of the INFOCOM, 2011 Proceedings IEEE, Shanghai, China, 10–15 April 2011; pp. 2255–2263. [Google Scholar]
- Wang, J.; Gao, Q.; Wang, H.; Yu, Y.; Jin, M. Time-of-flight-based radio tomography for device free localization. IEEE Trans. Wirel. Commun.
**2013**, 12, 2355–2365. [Google Scholar] [CrossRef] - Li, Z. Efficient Learning Algorithms for Overcomplete Dictionaries for Sparse Representation of Signal. Ph.D. Thesis, The University of Aizu, Aizu-Wakamatsu, Japan, 2015. [Google Scholar]
- Feng, C.; Au, W.S.A.; Valaee, S.; Tan, Z. Received-signal-strength-based indoor positioning using compressive sensing. IEEE Trans. Mob. Comput.
**2012**, 11, 1983–1993. [Google Scholar] [CrossRef] - Zhao, L.; Huang, H.; Li, X.; Ding, S.; Zhao, H.; Han, Z. An Accurate and Robust Approach of Device-Free Localization with Convolutional Autoencoder. IEEE Internet Things J.
**2019**. [Google Scholar] [CrossRef] - Wright, J.; Yang, A.Y.; Ganesh, A.; Sastry, S.S.; Ma, Y. Robust face recognition via sparse representation. IEEE Trans. Pattern Anal. Mach. Intell.
**2009**, 31, 210–227. [Google Scholar] [CrossRef] - Zhu, X.; Li, X.; Zhang, S.; Ju, C.; Wu, X. Robust joint graph sparse coding for unsupervised spectral feature selection. IEEE Trans. Neural Netw. Learn. Syst.
**2017**, 28, 1263–1275. [Google Scholar] [CrossRef] [PubMed] - Figueiredo, M.A.; Bioucas-Dias, J.M.; Nowak, R.D. Majorization–minimization algorithms for wavelet-based image restoration. IEEE Trans. Image Process.
**2007**, 16, 2980–2991. [Google Scholar] [CrossRef] - Selesnick, I.W. Sparse Signal Restoration. Available online: http://cnx.org/content/m32168/latest (accessed on 28 April 2019).
- Wilson, J.; Patwari, N. Radio tomographic imaging with wireless networks. IEEE Trans. Mob. Comput.
**2010**, 9, 621–632. [Google Scholar] [CrossRef] - Wang, J.; Zhang, X.; Gao, Q.; Yue, H.; Wang, H. Device-Free Wireless Localization and Activity Recognition: A Deep Learning Approach. IEEE Trans. Veh. Technol.
**2017**, 66, 6258–6267. [Google Scholar] [CrossRef]

**Figure 1.**Internet-of-Things (IoT) fundamental blocks with Device-free localization (DFL) system for intrusion detection and monitoring.

**Figure 2.**Illustration for the framework of the proposed device-free localization approach. Here, we show an example of single-target localization. The proposed approach is also applicable to locating multi-targets.

**Figure 3.**Process of background elimination. Here, we take the single-target as an example, but the process is also suitable for the multiple targets. (

**a**) RSS measurement in a vacant monitoring area; (

**b**) RSS measurement and background elimination with a target in monitoring area.

**Figure 5.**Example of data pre-processing by background elimination. Here, the example is randomly selected in which the target is at the 10-th grid. Note that, the variation of (

**b**) is obtained by the signal of (

**a**) subtracting the signal of (

**R**

^{vacant}).

**Figure 6.**Scenarios and experimental setups of indoor DFL system. (

**a**) Scenario of living room; (

**b**) Scenario of corridor.

**Figure 7.**Localization results of the proposed approach and comparisons. (

**a**,

**b**) are for the scenario of living room; (

**c**,

**d**) are for the scenario of corridor.

Compared Terms | Regularizer | Formula | Sparse Pattern |
---|---|---|---|

The previous works [10,16,17] | ${l}_{1}$ norm | ${\parallel \mathit{\alpha}\parallel}_{1}={\Sigma}_{i=1}^{n}{\left|{\alpha}_{i}\right|}^{1}$ | Element-wise |

The proposed approach | ${l}_{2,1}$ norm | ${\parallel \mathit{\alpha}\parallel}_{2,1}={\Sigma}_{i=1}^{g}\sqrt{{\alpha}_{i1}^{2}+\dots +{\alpha}_{ic}^{2}}$ | Joint elements (improved sparsity) |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Huang, H.; Han, Z.; Ding, S.; Su, C.; Zhao, L.
Improved Sparse Coding Algorithm with Device-Free Localization Technique for Intrusion Detection and Monitoring. *Symmetry* **2019**, *11*, 637.
https://doi.org/10.3390/sym11050637

**AMA Style**

Huang H, Han Z, Ding S, Su C, Zhao L.
Improved Sparse Coding Algorithm with Device-Free Localization Technique for Intrusion Detection and Monitoring. *Symmetry*. 2019; 11(5):637.
https://doi.org/10.3390/sym11050637

**Chicago/Turabian Style**

Huang, Huakun, Zhaoyang Han, Shuxue Ding, Chunhua Su, and Lingjun Zhao.
2019. "Improved Sparse Coding Algorithm with Device-Free Localization Technique for Intrusion Detection and Monitoring" *Symmetry* 11, no. 5: 637.
https://doi.org/10.3390/sym11050637