# Majority Voting Based Multi-Task Clustering of Air Quality Monitoring Network in Turkey
## 4 Multi-task Clustering
In Step 3, cluster labels are assigned to clusters according to their weight values, assigning \(L_{1}\) to the cluster which has the lowest mean value, and then increasing the label values until giving \(L_{k}\) to the highest one. The last step is the place where joint decision from different tasks is taken by applying a majority voting mechanism. As a result, all data points are placed into the most suitable clusters and final cluster labels are assigned from joint decision. ``` Inputs: Dataset \(D=\{o_{1},o_{2},\ldots,o_{n}\}\) Task space \(T=\{t_{1},t_{2},\ldots,t_{r}\}\)\(CA\): a clustering algorithm Cluster label set \(L=\{L_{1},L_{2},\ldots,L_{k}\}\)\(n\): the number of instances \(k\): the number of clusters \(r\): the number of tasks Process:// Step 1: Clustering according to task \(t_{i}\)
1. for\(i=1\) to \(r\)
2. \(C_{t_{i}}\)\(=CA(D,t_{i})\)
3. \(C_{add}(C_{t_{i}})\)
4. Output:\(C=\{C_{t_{1}},C_{t_{2}},\ldots,C_{t_{r}}\}\)// cluster assignments in terms of different tasks \(C_{t_{i}}=\{c_{1},c_{2},\ldots,c_{k}\}\)// \(k\) different clusters under the task \(t_{i}\)// Step 2: Determine average intra-cluster weights
5. for each\(C_{t_{i}}\) in \(C\)
6. for\(i=1\) to \(k\)
7. for each\(o\) in \(c_{k}\)
8. \(m_{i}=\text{sum}/|c_{k}|\)
9. Output:\(\mu_{i}=\text{[}m_{1},\,m_{2},\,\ldots,\,m_{k}\text{]}\)// \(k\) different average intra-clusters weights under the task \(t_{i}\)// Step 3: Label each cluster \(c_{i}\) in \(C_{t_{i}}\) for all tasks according to \(\mu_{i}\) values
10. for each\(c_{i}\) in \(C_{t_{i}}\)
11. for\(i=1\) to \(k\)
12. \(L_{c_{i}}=L_{index(m)}\)// an appropriate cluster label from \(L\) in terms of the index of \(m_{i}\)// Step 4: Obtaining joint decision
13. for\(i=1\) to \(n\)
14. for\(j=1\) to \(r\)
15. \(L(o_{i})=arg\underset{L_{i}\in L}{\max}\sum\limits_{L_{j}(o_{i})}1\)// final cluster assignment of \(o_{i}\) where each \(L_{t_{j}}\) is the cluster label of \(o_{i}\) in task \(t_{j}\) and \(j\in\{1,2,\ldots,r\}\)

\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Ins. ID** & \(\mathbf{C_{t_{1}}}\) & \(\mathbf{C_{t_{2}}}\) & \(\mathbf{C_{t_{3}}}\) & **MV-MTC** & **Ins. ID** & \(\mathbf{C_{t_{1}}}\) & \(\mathbf{C_{t_{2}}}\) & \(\mathbf{C_{t_{3}}}\) & **MV-MTC** \\ \hline
1 & \(L_{1}\) & \(L_{2}\) & \(L_{2}\) & \(L_{2}\) & 7 & \(L_{1}\) & \(L_{2}\) & \(L_{1}\) & \(L_{1}\) \\
2 & \(L_{2}\) & \(L_{1}\) & \(L_{1}\) & \(L_{1}\) & 8 & \(L_{1}\) & \(L_{3}\) & \(L_{1}\) & \(L_{1}\)

## 5 Dataset Description and Used Platforms

There are seven geographical regions, namely as Eastern Anatolia, Central Anatolia, Southeastern Anatolia, Blacksea, Mediterranean, Aegean, and Marmara, in Turkey and numerous air quality monitoring stations (AQMS) at each region. This study was conducted on 49 AQMSs from 32 provinces which are from different regions. The features of each station are listed in Tables 6 and 7 by showing the name of AQMS, in which city it is located, the corresponding county of the city, longitude and latitude information, network type (urban/rural/industrial), and which air pollutants are regularly measured in there. The National Air Quality Monitoring Network of Turkey includes 330 Air Quality Monitoring Stations. The air quality of all provinces in the country is monitored. To facilitate public access to information on air quality, the monitoring results are published online at the website of [[http://laboratuvar.cevre.gov.tr](http://laboratuvar.cevre.gov.tr)]([http://laboratuvar.cevre.gov.tr](http://laboratuvar.cevre.gov.tr)) [54]. In all of the air pollution measurement stations, SO\({}_{2}\) and PM\({}_{10}\) parameters are measured; in addition, NO, NO\({}_{2}\), NO\({}_{\rm x}\), CO and O\({}_{3}\) are measured automatically in many of them. In this study, all of the AQMSs were investigated and 49 out of 330 stations were selected because the aforementioned air pollutants (PM\({}_{10}\), SO\({}_{2}\), NO\({}_{2}\), NO and O\({}_{3}\)) are regularly measured in these stations together.