A hybrid approach based on k-means and SVM algorithms in selection of appropriate risk assessment methods for sectors

Dataset

In the study, a literature review was conducted in Scopus and Web of Science (WoS) databases to determine both the risk assessment criterion set and risk assessment methods. In this context, 223 articles were found in the WoS database and 461 articles were found in the Scopus database by using the keywords “Risk assessment methods”, “occupational health and safety”, “risk analysis”, “risk assessment criteria”. A total of 23 articles with a high level of relevance to risk assessment methods and 44 articles with a high level of relevance to risk assessment criteria were selected. As a result of the literature review, 17 technical criteria shown in Fig. 1 were determined by 9 experts with a Class A occupational safety certificate and at least 10 years of field experience.

In ‘Selection of Attributes’, the 10 most effective features used in practice, obtained using the chi-square feature selection method for 17 technical criteria, and the MATLAB program section of the values of these features are presented in Table 1. Of the total 260 data, 80% was used for training machine learning models and the remaining 20% was used for testing.

When we look at risk assessment methodologies, that is, methodologies and standards, all over the world within the scope of ISO 31010 Risk Management Standard for the selection of risk assessment methods, it can be seen that there are more than 150 methods. As a result of the literature review in practice, the 10 most frequently used risk assessment methods in studies were determined by the expert team.

The study was based on the list of sectors determined and approved by the Vocational Qualifications Authority of the Republic of Turkey according to the sectoral qualifications included in the European Qualifications Framework consultation document adopted by the European Parliament and Council on 23 April 2008 (Vocational Qualifications Authority, 2024).

K-means algorithm

MacQueen developed the k-means algorithm in 1967 (MacQueen, 1967). This widely used unsupervised learning method assigns each data point to only one cluster, making it a precise clustering algorithm. The method is based on the concept that the central point represents the cluster (Han & Kamber, 2006) and aims to find globular clusters of equal size (Fayyad et al., 1996).

The k-means clustering method is commonly evaluated using the sum of squared errors (SSE). The clustering result with the lowest SSE value is considered the best. To calculate SSE, sum the squares of the distances of the objects to the center points of the cluster using Eq. (1) (Pang-Ning Tan, Steinbach & Kumar, 2006). (1)${\displaystyle \mathrm{SSE}=\sum _{\mathrm{i}=1}^k\sum _{\mathrm{x}\in {\mathrm{C}}_{\mathrm{i}}}{\text{dist}}^2\left({\mathrm{m}}_{\mathrm{i}},\mathrm{x}\right)}$

The objective of this criterion is to generate k clusters that are both dense and well-separated. Clustering is done by minimizing the number of nodes, n, the sum of the distances between each sensor (xi, yi) and the cluster centroid (Xμi, Yμi). The distance usually used is the quadratic or Euclidean distance.

In Fig. 2, when each data point is a d-dimensional real vector represented by a set of observations (x1, x2,…,xn), K-means clustering aims to divide the n observations (k ≤ n) into clusters. The sum of squares within the cluster (minimum mean square error) within the grouped clusters (S = {S1, S2, …, Sk}) is minimized in the following Eq. (4) (Atzori, Iera & G. Morabito, 2010) . (2)${\displaystyle X=\frac{1}{n}\sum _{i=1}^n{x}_{i}Y=\frac{1}{n}\sum _{i=1}^n{y}_i}$ (3)${\displaystyle Cost=J=\frac{1}{n}\sum _{i=1}^n\left({\left(x_i-X_{\mu \mathrm{i}}\right)}^2+{\left(y_i-Y_{\mu \mathrm{i}}\right)}^2\right)}$ (4)${\displaystyle argmin\mathrm{s}\sum _{i=1}^k\sum _{x\in s_i}{\left|\left|x-{\mu }_i\right|\right|}^2.}$

In clustering, the cost function of any centroid configuration is measured by calculating the average sum of squares of the differences between the coordinates of each data point and the nearest centroid. The aim of the algorithm is to minimize the mean square error function. The mathematical representation of clustering is shown in Fig. 3.

S: represents objects whose elements are represented by vectors, xj: represents the data set. Table 2 presents the pseudocode structure showing the mathematical interpretation of the k-means clustering algorithm.

In the study, the k-means method was used to divide the data set into subsets. The reason for this is to ensure that the SVM classification algorithm is applied not to a single and large cluster, but to all subsets with different characteristics. Thus, instead of requiring a single threshold value for the entire cluster, a flexible structure is provided by applying it to subsets with different characteristics.

Support vector machine algorithm

Support vector machines (SVM) is a supervised machine learning algorithm with strong foundations based on Vapnik–Chervonenkis theory. SVM; Although it is similar to neural networks and radial basis artificial neural networks, it generally outperforms these algorithms. SVMs are widely used in real-life classification applications. Compared to other methods, significant improvements have been made in ease of calculation, scalability and resistance to outliers. SVM performs well on classification and regression problems even when there is a small amount of training data and a large number of features.

SVM is divided into two as Linear SVM and Non-Linear SVM according to the linear separation of data.

Linear support vector machines

Where X and Y are subsets of R^d and d is the number of features, if there is a hyperplane that can separate the elements of X and Y into different sides, X and Y can be linearly separated from each other (Elizondo, 2006). There are two types of SVMs, Hard-Marijn and Soft-Marjin, which are used for linearly separable situations.

Hard-margin support vector machines.

Let the target variable be entered in two options such that the training data is {x_i,y_i}, i = 1,2, …, L, yi ∈ {−1,1}, x_i ∈ R^d. The formula of the hyperplane that can linearly separate the positive and negative training data from each other is as in Eq. (5). In this equation, w is the normal of the hyperplane, —b— / ||w|| is the perpendicular distance from the hyperplane to the origin, ||w|| is the Euclidean norm of w (Burges, 1998). (5)${\displaystyle w.x+b=0.}$

The purpose of SVMs is; The aim is to keep the hyperplane separating the data belonging to different classes as far away from the closest points of all classes to each other. SVM can actually be summarized as the selection of w and b. In this case, the data set can be defined as in Eq. (6) and summarized as in Eq. (7) (Kartal & Balaban, 2019). (6)${\displaystyle x_i.w+b\left\{\begin{array}{c}\hfill \ge +1,y_i=+1\hfill \\ \hfill \le -1,y_i=-1\hfill \end{array}\right\}}$

(7)${\displaystyle y_i\left(x_i.w+b\right)-1\ge 0for\forall \mathrm{i}.}$

The planes marked H₁ and H₂ in Fig. 4 are support planes. The closest different class members on these planes are support vectors. The dividing plane passes right through the middle of the support planes. d₁ and d₂ are the distances of the support planes to the separating plane, and these two distances are equal to each other. Additionally, the sum of these distances is the margin. This margin needs to be maximized so that the dividing plane is as far away from the support vectors as possible. The margin is represented as 1 / ||w|| based on vector geometry, and ||w|| must be minimized to maximize the margin.

Soft-margin support vector machines.

Soft-margin SVM is used when the training data cannot be classified without error. In order to perform the classification process with the least error, incorrectly classified data are removed from the training data set (Cortes & Vapnik, 1995). The Soft-Margin SVM structure showing the situations that can be classified as linear with a certain error is as shown in Fig. 5.

In soft-margin SVMs, a non-negative idle variable is defined to express Eq. (7). In this case, where ξi ≥ 0, Eq. (7) can be generalized as follows: (8)${\displaystyle y_i\left(x_i.w+b\right)-1+{\xi }_i\ge 0for\forall \mathrm{i}.}$

The choice of ξi requires considering many situations together, and the choices affect the margin. A parameter C is used to ensure the balance between ξi and margin. If C is chosen larger, there will be less misclassified data. But it also causes the wTw product to be large and the margin to be small. The primal problem, defined as in Eq. (7) for hard-margin, is expressed as in Eq. (9) for soft-margin. Afterwards, the processes of obtaining the dual form Eq. (10) and finding b and w proceed similarly to hard-margin support vector machines (Kartal & Balaban, 2019).

$y_i\left(x_i.w+b\right)-1+{\xi }_i\ge 0$ for ∀i including: (9)${\displaystyle min\frac{1}{2}|\left|w\right|{|}^2+C\sum _{i=1}^L{\xi }_i}$

${\sum }_{i=1}^L{a}_i{y}_i=0,0\le a_i\le C$ for ∀i including: (10)${\displaystyle L_D\equiv \sum _{I=1}^L{a}_i-\frac{1}{2}\left(\sum _{i,j=1}^L{a}_i{a}_j{y}_i{y}_j{x}_{i.}{x}_j\right).}$

Nonlinear support vector machine

Most real-life problems do not lend themselves to being separated by a linear hyperplane. In this case, SVMs map the input space to a higher dimensional space. Thus, a linear decision boundary can be created between classes, as seen in Fig. 6. For this, the observation vector x ∈ Rⁿ is transformed into the vector z ∈R^F in a higher order space. To map Rⁿ →R^F, the ∅ function is expressed as z = ∅(x). (11)${\displaystyle x\in R^n\to z\left(x\right)={\left[a_1,{\varnothing }_1\left(x\right),\dots ,a_n,{\varnothing }_n\left(x\right)\right]}^TϵR^F.}$

Since the mapping function that enables this size change in linearly inseparable cases is not known and it is difficult to perform operations in high dimensions, arrangements called kernel tricks are made. Thus, instead of the mapping function in the transformed space, kernel functions that directly use the data in the input space are included in the process. Although there are many kernel functions in the literature; The most frequently used ones are linear function, polynomial function, sigmoid function and radial basis functions. Vapnik stated that the performance of these kernel functions did not make a big difference experimentally. The important thing is to determine the parameters of the selected core function (Erasto, 2001).

Formulations of frequently used kernel functions are as follows: (12)${\displaystyle \text{Linear function}:\mathrm{K}\left({\mathrm{x}}_{\mathrm{i}},{\mathrm{x}}_{\mathrm{j}}\right)={\mathrm{x}}_{\mathrm{i}}^{\mathrm{T}}{\mathrm{x}}_{\mathrm{j}}}$ (13)${\displaystyle \text{Polynomial function}:\mathrm{K}\left({\mathrm{x}}_{\mathrm{i}},{\mathrm{x}}_{\mathrm{j}}\right)={\left({\mathrm{x}}_{\mathrm{i}},{\mathrm{x}}_{\mathrm{j}}\right)}^{\mathrm{d}}}$ (14)${\displaystyle \text{Sigmoid function}:\mathrm{K}\left({\mathrm{x}}_{\mathrm{i}},{\mathrm{x}}_{\mathrm{j}}\right)=tanh\left(\mathrm{k}{\mathrm{x}}_{\mathrm{i}},{\mathrm{x}}_{\mathrm{j}}-\delta \right)}$ (15)${\displaystyle \text{Radial basis function}:\mathrm{K}\left({\mathrm{x}}_{\mathrm{i}},{\mathrm{x}}_{\mathrm{j}}\right)=exp\left(-\gamma {\left|\left|{\mathrm{x}}_{\mathrm{i}}-{\mathrm{x}}_{\mathrm{j}}\right|\right|}^2\right),\gamma >0}$

The K(x_i.x_j) function is called the kernel function and gives the one-to-one product of the feature space maps of the actual data points. For this reason, all elements of the dataset should be used for training. Thus, a more accurate error rate is obtained compared to manual selections. But due to random selection, there may be very small differences in error rates. Table 3 gives the pseudo-code structure of the SVM classification algorithm.

Table 3:

SVM algorithm –pseudocode.

Data: Data set containing p* variables and binary results

Output: Ranking of variables by relevance

Find the optimal values for SVM model tuning parameters; Train the SVM model; p ←p*; while p ≥2 do SVMp ← SVM with optimised tuning parameters for the p variables and observations in Data; ωp←Calculate SVMp weight vector(ω_p1, …..ω_pp);  rank.criteria ←$\left({\omega }_{p1}^2,\dots .{\omega }_{pp}^2\right);$ minimum rank criterion ← variable with the lowest value in the rank criterion vector; Remove minimum ranking criteria from data; Rankp← min.rank.criteria; P ← p-1; end Rank1 ← variable in Data ⁄ ∈ (Rank2,…..Rankp∗); return (Rank1,…..Rankp∗)

DOI: 10.7717/peerjcs.2198/table-3

Risk assessment methods

Risk assessment is the process of estimating the magnitude of risks arising from hazards in any system and deciding whether these risks are acceptable, taking into account the adequacy of existing controls, and can be symbolized in Fig. 7.

When we look at risk assessment methodologies, that is, methodologies and standards, all over the world, we see that there are more than 150 methods (Özkılıç, 2007). The most important difference between risk assessment methods is the unique methods they use to find the risk value. The advantages and disadvantages of these methods compared to each other are given in detail in the sources. The basic risk assessment methods to be analyzed for the sectors within the scope of the study and the symbols used in the study are given in Table 4.

Risk assessment techniques can be divided into two main groups in terms of estimating risks, their probability of occurrence, and their possible effects. These are qualitative and quantitative approaches (Özkılıç, 2005). Depending on the conditions to be analyzed, semi-quantitative methods, in which both methods are used together, can also be used. In quantitative risk analysis, numerical methods are used to calculate the risk. Numerical values are used as data regarding the probability of the risk occurring and what its impact will be after it occurs (Özkılıç, 2005). These values are analyzed with mathematical and logical methods and risk scores are found. In qualitative risk analyses, instead of numerical values, descriptive expressions such as low, and high or definitions such as A, B, I, and II are used in calculating the risk (Özkılıç, 2005).

These methods are part of risk management, almost the core part. In the study, 10 different risk assessment methods determined by the expert team as a result of literature review were tested for all sectors.

Data preprocessing

Risk value segmentation in the preprocessing stage was based on the Fine-Kinney method risk scale. As seen in Fig. 9, as a preliminary process, risk dimensions were evaluated by dividing them into different value ranges (<20), (20<R<70), …., (>400). The purpose of using different segments is to determine the risk range that has the highest performance for the sectors and to ensure that the most accurate features are extracted.

The study was based on the list of sectors determined and approved by the Vocational Qualifications Authority of the Republic of Turkey, according to the sectoral qualifications included in the European Qualifications Framework consultation document adopted by the European Parliament and Council on 23 April 2008. The list of sectors determined by the Vocational Qualifications Authority and to be used within the scope of the study is presented in Table 4 (Vocational Qualifications Authority, 2024).

When we look at risk assessment methodologies, that is, methodologies and standards, all over the world within the scope of ISO 31010 Risk Management Standard for the selection of risk assessment methods, it can be seen that there are more than 150 methods. The 10 risk assessment methods most frequently used in the studies, determined by the expert team as a result of the literature review in the study, are presented in Table 5.

Selection of attributes

In practice, 17 criteria determined by the expert team as a result of the literature review were evaluated with the chi-square feature selection method and the most effective features were determined. The use of unimportant attributes that will not affect the result in the selection of the most appropriate risk assessment method increases the processing time and may also cause a decrease in performance (Chebrolu, Abraham & Thomas, 2005). The chi-square method, also known as the X² test, can be used to determine whether the variables are suitable for describing the dataset (Kavzoğlu, Şahin & Çölkesen, 2014).

There are two hypotheses in the chi-square test: H₀ and H₁. H₀ is the hypothesis that the variables in the data set are appropriate, and H₁ is the hypothesis that the variables in the data set are not suitable. If the calculated value is greater than the determined value, the H₁ hypothesis is accepted, and if it is smaller, the H₀ hypothesis is accepted. How the chi-square statistic is calculated is formulated in Eq. (16). (16)${\displaystyle {\mathrm{X}}^2=\sum _{\mathrm{i}=1}^{\mathrm{n}}\frac{{\left({\mathrm{o}}_{\mathrm{i}}-{\mathrm{e}}_{\mathrm{i}}\right)}^2}{{\mathrm{e}}_{\mathrm{i}}}}$

Table 5:

Risk assessment methods and symbols.

Classificationtags	Risk assessment methods
Δ	L Type Matrix Analysis
$○$	X Type Matrix Analysis
□	Fine-Kinney Method
◊	Failure Modes and Effects Analysis (FMEA)
	Preliminary Hazard Analysis (PHA)
▴	Fault Tree Analysis (FTA)
•	Hazard and Operability Analysis (HAZOP)
■	Event Tree Analysis (ETA)
⧫	What If
★	Job Security Analysis (JSA)

DOI: 10.7717/peerjcs.2198/table-5

In this equation, n represents the number of features in the data set, o_i represents the observed frequency value for the ith feature, and e_i represents the expected frequency value for the ith feature. The features obtained with the chi square algorithm within the scope of the study are given in Fig. 10.

The features obtained using the chi-square feature selection method for 17 technical criteria defined in the data set were found as Precautions, Risk Assessment, Risk Prevention, Intensity/Frequency, Detectability, Effect/Damage Result Scale, Labor Loss, Danger Frequency, Danger Situation and Risk Score.

Hybrid method

In the k-means method, which is the first step of the application, the analysis results made on the data set with k = {3, 4, 5, 6, 7} values were examined to select the most appropriate {k}. K-means code structure in Matlab application in Table 6:

>>[idx,ort,sumd,D] =kmeans(Dataset_Name, Cluster_Number);

When the results obtained with were examined, it was seen that the best result was obtained for k = 5 with an accuracy of 0.9763 and an error rate of 0.0153. Additionally, the Matlab program analysis images obtained for k = 5 are presented in Fig. 11.

In the second step of the application, the SVM classification algorithm is run for each of the five subsets formed by k-means application, and the risk assessment methods whose average is greater than the determined threshold value are classified as appropriate, while those less than the threshold value are classified as unsuitable. All subsets were run for threshold value = {0.80,0.85,0.90, 0.95} and the threshold value that gave the best results was selected. SVM code structure in Matlab application:

>>pt = cvpartition(Dataset_Name,“HoldOut”,0.2);

hdTrain = Data(training(pt),:);

hdTest = Data(test(pt),:);

>>svmModel = fitcsvm(hdTrain”,Dataset_Ad ı”);

>>tahmin = predict(svmModel,hdTest)

>>hata = loss(svmModel,hdTest);

The training data results of the SVM application for k = 5 obtained with are shown in Table 7, the test data results are shown in Table 8, and the ROC curves representing all threshold values are shown in Fig. 12.

When the ROC curves and accuracy metrics in the tables were examined, it was seen that the best classification result was obtained for the threshold value = 0.90 in the data set.

In the third step of the application, the experimental setup and results obtained by running the optimum number of clusters determined by the k-means clustering algorithm for k = 5 and the optimum threshold value obtained by running the SVM classification algorithm on all clusters for TV = 0.90 are presented in Fig. 13.

In the study, the detailed results of the experimental setup designed in Fig. 14 are as follows:

(a), the data set codes determined by the Vocational Qualifications Authority and representing the 26 sectors used within the scope of the study in a single and large cluster are shown.

(b), in the k-means clustering method, sectors are grouped for the optimum number of clusters k = 5, determined using the Euclidean distance algorithm. Thus, instead of the SVM classification algorithm affecting the entire cluster and being required for all of them, the infrastructure for applying it separately for each subset separated according to their characteristics is provided. For example, cluster C1; from Automotive (S4), Electrical and Electronics (S7), Wood Processing/Paper/Paper Products (S15), Textile/Ready-made Clothing/Paper Products (S22), Tourism and Accommodation (S25) and Transportation/Logistics/Communication (S26) sectors is formed.

(c), the most appropriate risk assessment methods were found for each subset and the sectors in this cluster with SVM. For example, for cluster C1; Fine–Kinney Method, X Type Matrix Analysis, Preliminary Hazard Analysis (PHA), Fault Tree Analysis (FTA), What if and Job Security Analysis (JSA) were found to be the most appropriate risk assessment methods.

(d), SVM was run for the threshold value {0.80,0.85,0.90, 0.95} for the C1 subset and the best threshold value was selected. The optimum threshold value for the C1 subset was found to be = 0.95. This process was repeated for each subset and the optimum threshold value for all clusters was found to be TV = 0.90, as seen in Table 7.

(e), k-means and SVM hybrid methods were run for the optimum threshold value determined for each cluster, and the most appropriate final risk assessment methods were determined. In this context, the final result for cluster C1; Fine Kiney Method, Fault Tree Analysis (FTA), What if and Failure Models and Effects Analysis (FMEA) were found.

Table 9 presents the performance results of the k-means algorithm, SVM algorithm and the proposed hybrid method (k-means and SVM) algorithm.

Comparative performance results of the proposed hybrid method with artificial neural networks (ANN), naive Bayes (NB), decision tree (DT), random forest (RF) and k-nearest neighbors (KNN) machine learning algorithm are presented in Table 10. Confusion matrix results are presented in Fig. 14. Additionally, R², mean absolute error (MAE), mean absolute percentage error (MAPE) prediction metrics and regression graphs are presented in Fig. 15.