## 2 ML Methodologies
### Unsupervised Learning
#### 2.2.2 Association Rules  
Association rules mining is a powerful and popular unsupervised data mining technique that aims to uncover meaningful associations, relationships, and dependencies within vast collections of data items. This method operates on data that are typically organized in the form of transactions, which can be generated through an external process or extracted from relational databases and data warehouses [139]. By examining these transactions, association rules mining endeavors to discover valuable patterns and connections that may be hidden within the data, providing valuable insights and facilitating decision-making processes in various domains. This approach is particularly useful in tasks such as market basket analysis, customer segmentation, recommendation systems, and fraud detection, where identifying significant associations between different items can lead to enhanced understanding, improved efficiency, and better decision outcomes [140]. Table 12 provides a concise summary of association rules algorithms. These algorithms are fundamental tools  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Metric. ** & **Ref. ** & **Description** & **Ref. ** \\ \hline Calinski–Harabasz & [123] & The CH index measures the quality of a clustering algorithm by evaluating the distance between cluster centroids and the global centroid (numerator), and the distances between centroids within each cluster (denominator). A higher CH index indicates a valid optimal partition with well-separated clusters. & Water quality monitoring  
in the realm of data mining and analytics, empowering the revelation of captivating and occasionally surprising connections within vast datasets. Table 13, connects various water management methods with association rules approaches, practical applications, and supporting references for validation. \begin{table}
\begin{tabular}{p{56.9 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Category** & **Algorithm** & **Description** & **Applications** & **Ref.** \\ \hline Data mining and water resources management & Apriori & Discovers frequent itemsets in water quality data for association rule mining. & Pattern discovery in water quality data, anomaly detection. & [149] \\ \hline Data mining and hydrological analysis & FP-Growth & Efficiently mines frequent patterns in hydrological time series data. & Hydrological pattern discovery, streamflow analysis. & [150] \\ \hline Water quality analysis and pattern mining & Eclat & Identifies frequent itemsets in water quality datasets, aiding in pollution source identification. & Water quality assessment, pollution source tracking. & [151] \\ \hline Data mining and water quality monitoring & CAR-SPAN & Discovers closed frequent patterns in sensor data to monitor water quality changes. & Sensor network data analysis, water quality monitoring. & [152] \\ \hline Hydrological pattern recognition & FPMax & Extends FP-Growth for maximal frequent pattern mining in hydrological datasets. & Hydrological pattern recognition, rainfall analysis. & [153] \\ \hline Data mining and environmental assessment & RuleGrowth & Mines association rules to identify relationships between environmental variables. & Environmental impact assessment, ecological modeling. & [154] \\ \hline Hydrological data analysis and pattern mining & R-Mine & Discovers recurring patterns in hydrological time series data. & Hydrological forecasting, drought prediction. & [155] \\ \hline Data mining and water resource allocation & Tertius & Supports decision making in water allocation by mining patterns in water usage data. & Water resource allocation optimization, demand management. & [156] \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Association rules algorithms. \begin{table}
\begin{tabular}{p{56.9 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Algorithm** & **Ref. ** & **Description** \\ \hline Apriori & [141] & Apriori is a classic algorithm for mining frequent itemsets and generating association rules.