## 2 Background Fundamentals
### Randomized Low-Rank Approximations
In dependent methods, the result of one classifier has an impact on the next classifier's formation. Some of the examples are boosting algorithms [28, 29, 30]. On the other hand, the independent methods build each classifier separately from the subset of the data and combine its results [7, 8, 9, 31]. Various ensemble techniques have been proposed for the successful improvement of predictive accuracy [17, 18, 20]. The final predictive model requires a proper combination of several learners. The combination of these classifiers is divided into averaging and meta-learning. Simple ensemble techniques come under averaging methods, whereas advanced ensemble techniques include stacking, blending, bagging, and boosting methods. As our proposed model aims to improve predictive accuracy, the stacking ensemble approach will be discussed. #### 2.3.1 Stacking Ensemble Learning

Stacking is a powerful ensemble learning mechanism. The base learners are stacked in a parallel manner by combining with the meta learners to obtain better prediction accuracy. The general architecture of the stacking mechanism is given in Figure 4. It consists of two or more base learner models and meta-models combined to form a predictive model. The data are divided into folds and partitioned into training and testing data. The base learners are triggered with the predictions as first-level predictions on the training data. The meta-model helps to combine the predictions of the first level, and the prediction pattern is trained on other models to obtain the prediction accuracy. Figure 3: Similarity check against reduced information system and approximated information system. Figure 2: Heatmap of reduced information system and approximated information system. ## 3 Proposed Research Methodology on Groundwater Level Prediction

### Study Area Investigation and Data Pre-Processing

The paper aims to investigate the groundwater level in India. Groundwater level data were collected from all the districts of India from 2000 to 2021. As per the census of India, 593 districts were counted in the years 2001 to 2010, whereas 640 districts were counted from 2011 to 2020. The census of India reported 773 districts from the year 2021. Thus, the data collected are from 2000 to 2021 and have the objects of \(5930+6400+773=13\),103 records. For a better understanding of the data pattern, India was divided into four divisions, such as East and Northeast India, encompassing the states Arunachal Pradesh, Assam, Meghalaya, Nagaland, Manipur, Mizoram, Tripura, Sikkim, West Bengal, Jharkhand, Bihar; Northwest India includes the states Uttar Pradesh, Uttarakhand, Haryana, Chandigarh, Delhi, Punjab, Himachal Pradesh, Jammu, Kashmir, and Rajasthan. Central India includes the Nicobar Islands, Madhya Pradesh, Gujarat, Dadra, Nagar Haveli, Daman and Diu, Goa, Maharashtra, and Chhattisgarh, whereas South India includes Andhra Pradesh, Telangana, Tamil Nadu, Puducherry, Karnataka, Kerala, Lakshadweep, Andaman, and the Nicobar Islands, as represented in Figure 5. The groundwater sampling was carried out from representative borewells in various districts of every state of India through web resources [32]. With consultation with the domain expert, the variables that have a significant impact on GWL are listed in Table 5. As per the expert advice, the data were collected on three main factors, such as geological, topological, and hydrological properties, as given in Figure 6. The collected data underwent pre-processing to check their consistency. Out of 13,103 objects, 387 records had missing data, and 716 pieces of data had conflicting information, leading to the data removal process. Thus, 12,000 records were considered for processing, whereas 1103 records were removed. It is essential to identify significant attributes that contribute better to the knowledge discovery process of groundwater levels.