# Innovation in Company Labor Productivity Management: Data Science Methods Application
## 3 Experimental Results
### Clustering and Classification of Companies' Employers
The third cluster includes 26% of all respondents consist of mainly men with secondary education and two children, they rate their health not very high, they have irregular meals and often have seasonal diseases along with chronic diseases. The fourth cluster is about unmarried women with higher education, who do not have children and bad habits, and they characterize their health as quite satisfactory. To select the most effective methods for the employers' clustering and then classification by the health quality in order to increase labor productivity, we compare the effectiveness of different statistical and machine learning methods and then choose one with the maximum quality value [59; 60; 61; 62; 63; 64]. For this we solve two subproblems:  
* Clustering an employers to form homogeneous groups with similar labor productivity profiles. For this we test two clustering methods--\(k\)-means method and neural network method based on self-organizing Kohonen maps (SOM);
* Classification an employers to identify the performance profile of the new employee, or to determine the cluster to which he is more likely to belong. At this stage we use the following methods: decision trees and support vector machines. Results of the first subproblem decision. In the clustering problem the number of clusters is not known in advance and the personnel sample is rather heterogeneous. Therefore, to obtain adequate division into clusters, we use another machine learning method--Automated Neural Networks (ANN) based on SOM. Then we compare the effectiveness of two methods for obtaining personnel clusters--\(k\)-means method and ANN method. To obtain the number of clusters we use the Self-organizing Kohonen map--a neural network with unsupervised learning. We divide the initial data set into three subsets--the first is a training sample in the amount of 70% of the total sample, which is used to train the neural network and adjust its weights. The second subsample is a test one, is about 15% of the total sample, it is used to check the training and retraining. The third subsample, the validation sample, is used to assess the neural network accuracy on a \"new data\". First, the topological dimension of the network is set to 25 neurons (the matrix has a dimension of five rows and five columns). As simulation result, it was shown that four clusters can be clearly distinguished, since it was precisely four neurons that described most of the initial data. The clustering results obtained on the basis of the ANN method is shown in Table 6.  
The clustering results are similar to the result of cluster analysis based on \(k\)-means. For a more reasonable choice one of the clustering methods and obtaining homogeneous personnel groups we conduct an analysis of used methods robustness. For this, an additional quantitative variable was introduced into the data set, reflecting the number of days spent by an employee on sick. Further, taking into account this new factor, new clustering \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Variable**} & \multicolumn{4}{c}{**Average Value of the Variable in the Cluster**} \\  & **1** & **2** & **3** & **4** \\ \hline age & 34.2 & 34.1 & 41.0 & 41.7 \\ gender & 1 & 0 & 1 & 1 \\ mar & 1 & 1 & 1 & 0 \\ edu & 1 & 1 & 1 & 1 \\ child & 1 & 1 & 2 & 2 \\ chron\_dis & 0 & 0 & 1 & 0 \\ bad\_health & 0 & 1 & 1 & 1 \\ health\_self-ass & 0 & 1 & 1 & 0 \\ nurt & 0 & 1 & 1 & 0 \\ bad\_hab & 0 & 1 & 1 & 1 \\ labor\_pert & 294.12 & 287.35 & 224.46 & 265.26 \\ cluster size & 170 & 142 & 241 & 149 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Clusters’ centers (ANN-method). is formed. Clustering based on \(k\)-means showed higher stability of groups in terms of their identical composition before and after the introduction of a new factor than the ANN clustering. Therefore, for clustering it is most expedient to use the \(k\)-means method. Results of the second subproblem decision. Two classification models are compared.