Statistical Modeling of RPCA-FCM in Spatiotemporal Rainfall Patterns Recognition

Abstract

This study was conducted to identify the spatiotemporal torrential rainfall patterns of the East Coast of Peninsular Malaysia, as it is the region most affected by the torrential rainfall of the Northeast Monsoon season. Dimension reduction, such as the classical Principal Components Analysis (PCA) coupled with the clustering approach, is often applied to reduce the dimension of the data while simultaneously performing cluster partitions. However, the classical PCA is highly insensitive to outliers, as it assigns equal weights to each set of observations. Hence, applying the classical PCA could affect the cluster partitions of the rainfall patterns. Furthermore, traditional clustering algorithms only allow each element to exclusively belong to one cluster, thus observations within overlapping clusters of the torrential rainfall datasets might not be captured effectively. In this study, a statistical model of torrential rainfall pattern recognition was proposed to alleviate these issues. Here, a Robust PCA (RPCA) based on Tukey’s biweight correlation was introduced and the optimum breakdown point to extract the number of components was identified. A breakdown point of 0.4 at 85% cumulative variance percentage efficiently extracted the number of components to avoid low-frequency variations or insignificant clusters on a spatial scale. Based on the extracted components, the rainfall patterns were further characterized based on cluster solutions attained using Fuzzy C-means clustering (FCM) to allow data elements to belong to more than one cluster, as the rainfall data structure permits this. Lastly, data generated using a Monte Carlo simulation were used to evaluate the performance of the proposed statistical modeling. It was found that the proposed RPCA-FCM performed better using RPCA-FCM compared to the classical PCA coupled with FCM in identifying the torrential rainfall patterns of Peninsular Malaysia’s East Coast.