Identifying the local time scale of the torrential rainfall pattern through Singular Spectrum Analysis (SSA) is useful to separate the trend and noise components. However, SSA poses two main issues which are torrential rainfall time series data have coinciding singular values and the leading components from eigenvector obtained from the decomposing time series matrix are usually assesed by graphical inference lacking in a specific statistical measure. In consequences to both issues, the extracted trend from SSA tended to flatten out and did not show any distinct pattern. This problem was approached in two ways. First, an Iterative Oblique SSA (Iterative OSSA) was presented to make adjustment to the singular values data. Second, a measure was introduced to group the decomposed eigenvector based on Robust Sparse K-means (RSK-Means). As the results, the extracted trend using modification of SSA appeared to fit the original time series and looked more flexible compared to SSA...

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Principal Component Analysis (PCA) is a popular method used for reduction of large scale data sets in hydrological applications. Typically, PCA scores are applied to hierarchical cluster analysis to redefine region. However, the choice of cumulative percentage of variance for PCA scores and identifying the best number of clusters can be difficult. In this paper, we investigate the effect of determining the number of clusters by comparing (i) standardized and unstandardized PCA scores on different cumulative percentages of variance (ii) to determine number of clusters using Calinski and Harabasz Index. We have found that Calinski and Harabasz Index is most appropriate to determine the best number of clusters and that standardized PCA scores within the range of 65% to 70% cumulative percentage of variance give the most reasonable number of clusters...

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One of the popular approaches in modifying the Conjugate Gradient (CG) Method is hybridization. In this paper, a new hybrid CG is introduced and its performance is compared to the classical CG method which are RivaieMustafa-Ismail-Leong (RMIL) and Syarafina-Mustafa-Rivaie (SMR) methods. The proposed hybrid CG is evaluated as a convex combination of RMIL and SMR method. Their performance are analyzed under the exact line search. The comparison performance showed that the hybrid CG is promising and has outperformed the classical CG of RMIL and SMR in terms of the number of iterations and central processing unit per time..

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In this study, hybrid RPCA-spectral biclustering model is proposed in identifying the Peninsular Malaysia rainfall pattern. This model is a combination between Robust Principal Component Analysis (RPCA) and biclustering in order to overcome the skewness problem that existed in the Peninsular Malaysia rainfall data. The ability of Robust PCA is more resilient to outlier given that it assesses every observation and downweights the ones which deviate from the data center compared to classical PCA. Meanwhile, two way-clustering able to simultaneously cluster along two variables and exhibit a high correlation compared to one-way cluster analysis. The experimental results showed that the best cumulative percentage of variation in between 65%-70% for both Robust and classical PCA. Meanwhile, the number of clusters has improved from six disjointed cluster in Robust PCA-kMeans to eight disjointed cluster for the proposed model. Further analysis shows that the proposed model has smaller variatio.....

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The objective of this study is to identify the main spatial distribution patterns associated with torrential rainfall days that linked to the topography of Peninsular Malaysia.This is done by applying cluster analysis on the most relevant principal directions extracted from a principal components analysis of the between day correlation. However, the characteristic of rainfall data in Peninsular Malaysia involve skewed observations which only take positive values and are skewed towards higher values. Thus, applying PCA based Pearson correlation on rainfall data set could affect cluster partitions and generate extremely unbalanced clusters. Tukey's biweight correlation is introduced to overcome the problem where the weight function down weights data values that is far from the center of the data. The findings indicate that ten rainfall patterns obtained are quite definite and clearly display the dominant role extended by the complex topography and exchange monsoons of the peninsular.  .....

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- The coronavirus disease 2019 (COVID-19) outbreak in December 2019 had affected the way of living for people around the world including students in educational institutions. These students had to prepare for the continuity of their study mentally and phy..

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This paper presents a modified correlation in principal component analysis (PCA) for selection number of clusters in identifying rainfall patterns. The approach of a clustering as guided by PCA is extensively employed in data with high dimension especially in identifying the spatial distribution patterns of daily torrential rainfall. Typically, a common method of identifying rainfall patterns for climatological investigation employed T mode-based Pearson correlation matrix to extract the relative variance retained. However, the data of rainfall in Peninsular Malaysia involved skewed observations in the direction of higher values with pure tendencies of values that are positive. Therefore, using Pearson correlation which was basing on PCA on rainfall set of data has the potentioal to influence the partitions of cluster as well as producing exceptionally clusters that are eneven in a space with high dimension. For current research, to resolve the unbalanced clusters challenge regarding t.....

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Identifying local time scale to determine when the torrential rainfall events occur at a particular location is critically important. This can be detected by observing the trend which is characterized by the shape of time series data in order to detect the abnormally heavy rainfall that can cause torrential rainfall events. One of the methods in identifying the range of local time scale according to the trend is based on Singular Spectrum Analysis (SSA).The variations in the time series observations can be decomposed and reconstructed to locate the time period in which the extreme rainfall events occur when using SSA approach. However, in torrential rainfall time series data, the daily amount of rainfall is approximately similar over a period of time. This situation leads to a problem when using SSA since there are coinciding singular values. It might cause disjoint sets of singular values and different series components to mix up with each other. Besides, using SSA, leading component .....

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Monthly precipitation data during the period of 1970 to 2019 obtained from the Mete-orological, Climatological and Geophysical Agency database were used to analyze regionalized precipitation regimes in Yogyakarta, Indonesia. There were missing values in 52.6% of the data, which were handled by a hybrid random forest approach and bootstrap method (RF-Bs). The present approach addresses large missing values and also reduces the Root Mean Square Error (RMSE) and the Mean Absolute Error (MAE) in the search for the optimum minimal value. Cluster analysis was used to classify stations or grid points into different rainfall regimes. Hierarchical clustering analysis (HCA) of rainfall data reveal the pattern of behavior of the rainfall regime in a specific region by identifying homogeneous clusters. According to the HCA, four distinct and homogenous regions were recognized. Then, the principal component analysis (PCA) technique was used to homog-enize the rainfall series and optimally reduce th.....

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In high dimensional data, Principal Component Analysis (PCA)-based Pearson correlation remains broadly employed to reduce the data dimensions and to improve the effectiveness of the clustering partitions. Besides being prone to sensitivity on non-Gaussian distributed data, in a high dimensional data analysis, this algorithm may influence the partitions of cluster as well as generate exceptionally imbalanced clusters due to its assigned equal weight to each observation pairs. To solve the unbalanced clusters in hydrological study caused by skewed character of the dataset, this study came out with a robust method of PCA in term of the correlation. This study will explain a RPCA to be proposed as an alternative to classical PCA in reducing high dimensional dataset to a lower form as well as obtain balance clustering result. This study improved where RPCA managed to downweigh the far-from-center outliers and develop the cluster partitions. The results for both methods are compared in term .....

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