# Crowd Sensing-Enabling Security Service Recommendation for Social Fog Computing Systems

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

- We design an advanced social networking architecture for fog computing called social fog computing to control and organize fog computing system efficiently as well as securely;
- We propose a novel crowd sensing-enabling security service recommendation method for a social fog computing architecture. The computation model and parameters of security service discovery as recommendation are designed for social fog computing systems.

## 2. Preliminaries

#### 2.1. Fog Computing

#### 2.2. Chance Discovery Theory

#### 2.3. Crowd Sensing

## 3. Proposed Social Fog Computing Systems

#### 3.1. Design Motivation of Social Fog Systems

#### 3.2. Innovations from Fog to Social Fog

#### 3.3. Social Fog Architecture

## 4. Proposed Security Service Recommendation Mechanism

#### 4.1. Architecture of the Security Service Recommendation of Social Fog

#### 4.2. Security Services Assessment

_{i}(t) denotes the transition probability matrix of the finite homogeneous continuous-time Markov chain. Let CH

_{j}(t) = CH(SP(t) = j), where CH is the transition probability matrix of the finite homogeneous continuous-time Markov chain, and SP is the state space. The transition probability matrix of the finite homogeneous continuous time Markov chain in j-th time slot is the transition probability matrix of the corresponding state space. Assume that infinitesimal generated matrix is denoted as GM = [g

_{ij}], then:

_{T}can take the place of GM in Equation (7). $Re{s}_{T}$ is the reserve of state j in time slot T. Next, assume $Re{s}_{T}(\infty )$ can be obtained by:

_{ab}denotes the time when the system enters the absorbing state totally, which can be computed by:

#### 4.3. Security Service Discovery Scheme

#### 4.3.1. KeyGraph Establishment

_{1}, fs

_{2}, …,fs

_{j}, …, fs

_{m}. To map the relations of the services, each service fs

_{j}is regarded as a KeyGraph, which is denoted as KG

_{j}. To consider continuity of the time, assume that a service time includes m time slots, the service process during time t

_{j}to t

_{j}

_{+1}is described based on the graph KG

_{j}presents. In KG

_{j}, an interoperability relation between two services is mapped to an edge, and a service of the social networking advanced fog computing system is mapped to a vertex of KG

_{j}. For each edge of KG

_{j}, the edge of the graph has the attributions in terms of the weight value and direction, where the number of the frequencies of the interoperability is mapped to the direction and the direction is from sender to receiver. The principle of the security service discovery follows.

#### 4.3.2. KeyGraph Connection Value

_{i}and AC

_{j}denote two vertices in KG*. Association (AC

_{i}, AC

_{j}) denotes the association between AC

_{i}and AC

_{j}, which can be computed by:

_{i}to AC

_{j}, which can be mapped to the service fs

_{m}. Based on the association value, the assessment for the tightness between AC

_{i}and AC

_{j}can be performed. In KeyGraph KG*, according to the association value between the pairs of vertices, they are sorted and identified. In other words, the tightness and relation of a pair of vertices can be assessed. A connected sub-graph called a cluster is used to denote a full procedure of security service discovery.

#### 4.3.3. Tightness Calculation

_{y}is denoted as Lev (X

_{y}).

_{m}. Moreover, the nodes with higher security level will be added if they are not present in the KeyGraph. Most importantly, the infrequent and security service nodes with importance can be found, which is regarded as a candidate chance.

#### 4.3.4. Security Service Discovery

#### 4.4. Security Service Recommendation Based on Particle Swarm Optimization (PSO)

**Step 1:**Initialization: Set the learning factor ler

_{1}, ler

_{2}, and maximal evolution algebra al

_{max}, when evolution algebra al = 1. Assume that m service particles are generated randomly in space R, which are denoted as p

_{1}, p

_{2}, …, p

_{m}, and the service swarm matrix sw(t). Next, the displacement variations are generated randomly for each service particle, which are denoted as c

_{1}, c

_{2}, …, c

_{m}forming a displacement variation matrix C(t).

**Step 2:**The service swarm is evaluated, and the adaptive value ADA(P

_{i}) is computed.

**Step 3:**The adaptive value ADA(P

_{i}) of the current service particle is compared with its history optimization value HisBe; if ADA(P

_{i}) is better than HisBe, HisBe is set as the current value of ADA(P

_{i}), and the location of HisBe is set as the current location.

**Step 4:**The current adaptive value ADA(P

_{i}) is compared with the optimal value of the service swarm, which is denoted as SwaBe. If ADA(P

_{i}) is better than SwaBe, SwaBe is set as the current value of ADA(P

_{i}), where the order number of SwaBe is the order number of the current service particle.

**Step 5:**The new service swarm, denoted as P(t + 1), can be generated based on the updates of the velocity and location of the service particle. The location matrix of the i-th service particle is denoted as Li = (l

_{i}

_{1}, l

_{i}

_{2}, …, l

_{id}). Assume that the best location searched by the i-th service particle is LOC

_{i}= (trac

_{i}

_{1}, trac

_{i}

_{2}, …, trac

_{id}), which is the location that the i-th service particle passed with the best adaptive value. LOC

_{g}= (trac

_{g}

_{1}, trac

_{g}

_{2}, …, trac

_{gd}) is used to denote the best location where all the service particles passed so far. The best adaptive value can be computed based on the objective function of the object problem. In the t-th step of the computation, assume the security assessment factor and service track of the i-th service particle in the j-dimensionality space are loc

_{ij}(t) and v

_{ij}(t), respectively:

_{1}, a

_{2}is the variation coefficients of the security assessment factor. Assume the a

_{1}is an adjustment factor used to adapt the security assessment factor of the service particle based on its own optimal solution. Additionally, let a

_{2}be an adjustment factor used to adjust the security assessment factor of the service particle adapting to the global optimal solution.

_{i}) is compared with the optimal value of the service swarm SwaBe. If ADA(P

_{i}) is better than SwaBe, SwaBe is set as the current value of ADA(P

_{i}), where the order number of SwaBe is the order number of current service particle.

**Step 6:**The evaluation value is checked to judge whether it achieves a given accuracy. If the evaluation value achieves given accuracy, the circulation is finished. Otherwise, set t = t + 1 and jump to

**Step 2**.

_{N}are the mean value and standard deviation of N, respectively.

_{i}are the mean value and standard deviation of the i-th independent variable, respectively.

^{n}and N

^{n}are introduced. The construction method is as follows: Assume that the p-th sample occurs β

_{f}times in the original data matrices M

^{n}and N

^{n}. In fact, when the data volume increases, the dimensionality number and the computation complexity of the data are very high. To decrease the computation complexity, we introduce the new matrices M

^{nn}and N

^{nn}, which can be computed as follows:

^{1}, p

^{2}, …, p

^{n}]

^{T}. Partial least-squares (PLS) regression is a multivariate analysis method, which was proposed by Wold and lbano for some import regression problems, such as multicollinearity. PLS regression performs the integrations and selections, then extracts the aggregative variable with the best explanations for the systems. At the same time, PLS regression can delete the multicollinearity information and the information without explanation meanings, thus, it can resolve the problem of multicollinearity among the variables. Therefore, the model with good imitative effect, robustness, and prediction capabilities can be obtained. PLS regression can be used to analyze the mass data with the multicollinearity among the variables. Moreover it can deal with the situation in which the samples less than predication variates. Based on the above advantages of PLS regression, we introduce this regression to improve the crowd sensing-based security service recommendation.

^{n}, N

^{n}is the same as that of M

^{nn}, N

^{nn}. Thus the computation of sample weights between M and N can translate into the computation of the PLS regression between M

^{nn}and N

^{nn}. It is necessary to obtain service particles p = [p

^{1}, p

^{2}, …, p

^{3}]

^{T}and get the best predication precision, which is a global optimization problem. To resolve aforementioned problem, the objective function is set as:

_{i}. The process of the security service recommendation for social fog is shown in Figure 3.

**Step 1:**Standardization is performed for the initial security service data based on Equations (17) and (18).

**Step 2:**Initial security service sample weight p with x-dimension is generated, which means x initial particles are generated for the crowd sensing algorithm. At the same time, all parameters of the crowd sensing algorithm are initialized.

**Step 3:**M

^{nn}and N

^{nn}are computed based on p. For each particle, PLS regression is performed on M

^{nn}and N

^{nn}. Then the weights are obtained for each predication method.

**Step 4:**The value of objective function is computed based Equation (21), which act as the adaptive degree for each service particle.

**Step 5:**For each particle, the adaptive value is compared with the best security service it applied. If the adaptive value is better, it is set as the current best security service.

**Step 6:**For each service particle, the adaptive value is compared with the best security service of all the uses applied. If the adaptive degree is better, it is set as the current global best security service, which is recommended to the users.

**Step 7:**Each particle is updated based on Equations (15) and (16) then jump to Step 3 again.

## 5. Evaluation

#### 5.1. Simulation Settings

#### 5.2. Simulation Results and Analysis

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Wu, J.; Su, Z.; Wang, S.; Li, J. Crowd Sensing-Enabling Security Service Recommendation for Social Fog Computing Systems. *Sensors* **2017**, *17*, 1744.
https://doi.org/10.3390/s17081744

**AMA Style**

Wu J, Su Z, Wang S, Li J. Crowd Sensing-Enabling Security Service Recommendation for Social Fog Computing Systems. *Sensors*. 2017; 17(8):1744.
https://doi.org/10.3390/s17081744

**Chicago/Turabian Style**

Wu, Jun, Zhou Su, Shen Wang, and Jianhua Li. 2017. "Crowd Sensing-Enabling Security Service Recommendation for Social Fog Computing Systems" *Sensors* 17, no. 8: 1744.
https://doi.org/10.3390/s17081744