Spatial Assessment of Water River Pollution Using the Stochastic Block Model: Application in Different Station in the Litani River, Lebanon - ATOUI, Alya; El Haj, Abir; Slaoui, Yousri; Fadel, Ali; Slim, Kamal; Andaloussi, Samir Abbad; Moilleron, Régis; KHRAIBANI, Zaher (Statistics, Optimization & Information Computing, 2022)
Water pollution is a major global environmental problem. In Lebanon, water pollution threatens public health and biological diversity. In this work, a non-classical classification method was used to assess water pollution in a Mediterranean River. A clustering proposal method based on the stochastic block model (SBM) was used as an application on physicochemical parameters in three stations of the Litani River to regroup these parameters in different clusters and identify the evolution of the physicochemical parameters between the stations. Results showed that the used method gave advanced findings on the distribution of parameters between inter and intra stations. This was achieved by calculating the estimated connection matrices between the obtained clusters and the probability vector of belonging of the physicochemical parameters to each cluster in the different stations. In each of the three stations, the same two clusters were obtained, the difference between them was in the estimated connection matrices and the estimated cluster membership vectors. The power of SBM proposed methods is demonstrated in simulation studies and a new real application to the sampling physicochemical parameters in Litani River. First, we compare the proposed method to the classical principal component analysis (PCA) method then to the Hierarchical and the K-means clustering methods. Results showed that these classical methods gave the same two clusters as the proposed method. However, unlike the proposed SBM method, classical approaches are not able to show the blocks structure of the three stations.