# Majority Voting Based Multi-Task Clustering of Air Quality Monitoring Network in Turkey
## 4 Multi-task Clustering
Since the data become roughly periodic after one-year period, only one year of (November 2017 to November 2018) data were used in the experiments. The pollutant concentrations are mean values of daily (24 h) measurements. The application was developed using Weka open source data mining library [55] on Visual Studio. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline ID & AQMS SAME & CITY & COUNTY & LOSMICIDE & LATTIDE & TYPE & THE MEASURED POLULTASTS \\ \hline
1 & Adara-Castina & Adams & Yunger & 35.26919 & 37.1884 & Rural & PMa, So, No, No, NO, NO, NO, NO \\
2 & Adara-Denggment & Adara & Yunger & 35.3691 & 35.86545 & Rural & PMa, So, No, NO, NO, NO \\
3 & Adara-Meteorich & Adam & Karatishi & 35.34047 & 37.0014 & Urban & PMa, So, NO, NO, NO \\
4 & Adara-Valita & Adara & Seyman & 35.32424 & 36.9991 & Urban & PMa, So, NO, NO, NO, NO \\
5 & Aggi & Meiser & 4.03967 & 37.7123 & Urban & PMa, So, NO, NO, NO, NO \\
6 & Aggi-Diegevazzi & Agri & Dougherty & 44.08555 & 39.5676 & Urban & PMa, So, NO, NO, NO, NO \\
7 & Aggi-Diegevazzi & Agri & Pruna & 42.85309 & 39.2654 & Urban & PMa, So, NO, NO, NO, NO \\
8 & Adara-Escourier & Adara & Koelcome & 32.8628 & 39.2652 & Urban & PMa, So, NO, NO, NO, NO, NO, NO \\
9 & Adara-Sabhiye & Adara & Camelay & 32.85949 & 39.9272 & Industrial & PMa, So, NO, NO, NO, NO, NO, NO, NO, NO, NO \\
10 & Abraham & Adarshan & Me



\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**ID** & **AQMS SAME** & **CITY** & **COUNTY** & **LONGTUDE** & **LATTIDE** & **TYPE** & **THE MEASURED POLUITANTS** \\ \hline
28 & [PERSON] 1 & Kanish & Merkeler & 32.6274 & 41.1920 & Industrial & PMa, SO, NO, NO, NO, NO, NO, CO \\
29 & [PERSON] 3 & [PERSON] & [PERSON] & 33.0194 & 40.0960 & Urban & PMa, SO, NO, NO, NO, NO, NO, CO \\
30 & [PERSON] 4 & [PERSON] & 1.2059 & 41.0855 &



## 6 Experimental Results

In this study, the proposed MTC method, MV-MTC, was compared with traditional clustering algorithms K-Means (KM), Expectation Maximization (EM), Hierarchical Clustering (HIER), Canopy and Farthest First (FFIRST). Each task was clustered by the selected algorithm and then their decision from consensus was obtained in MV-MTC framework. Performance evaluation was done via sum of squared error (SSE) calculation. Before constructing the model, data were normalized and missing data imputation was performed using the mean values. The number of clusters, \(k\), was selected as 10% of the number of instances in the dataset, therefore it was 5. Distance metric was chosen as Euclidean distance. To take the joint decision from each single clustering algorithm, each cluster was labeled according to the weights calculated as the average value of the instances of intra-cluster. According to this scheme, five cluster labels were determined as \"\(L_{1}\)\", \"\(L_{2}\)\", \"\(L_{3}\)\", \"\(L_{4}\)\" and \"\(L_{5}\)\". Table 8 displays the average normalized weight of each cluster in terms of different air pollutants and their corresponding cluster labels. As a result of the joint decision of different tasks, where evaluation of PM\({}_{10}\), SO\({}_{2}\), NO\({}_{2}\), NO and O\({}_{3}\) pollutants were assumed as a new task, final cluster assignments were done. To evaluate the performance of the applied methodology, values of sum of squared error were calculated. SSE is the sum of the squared differences between each observation and its group's mean. In Equation (4), \(o_{i}\) represents an instance of dataset \(D\), \(C_{j}\) represents the \(j\)th cluster, \(m_{j}\) is the centroid value of the specified cluster \(j\) where \(o_{i}\) is assigned and \(k\) is the number of cluster. Total SSE of a method is the sum of all separate SSE calculations coming from distinct clusters. \[\text{SSE }=\sum\
olimits^{k}\sum\
olimits_{j=1}^{k}\sum\
olimits_{o_{i}\in C _{j}}\left(o_{i}-m_{j}\right)^{2}, \tag{4}\]

Final assignments are obtained both by MV-MTC and single clustering algorithms. Clustering algorithms is applied on each single task, i.e., the model is formed just by taking one pollutant into consideration.