Zuherman Rustam

This paper presents a rigorous investigation of Mercer-compliant kernels through both theoretical analysis and extensive empirical validation. We present a unified theoretical analysis of Mercer’s condition across six fundamental kernel classes, including radial basis function (RBF), Matérn ( ν = 0.5, 1.5, 2.5), Nyström-based approximations (Nyström-RBF and Nyström-Matérn), and Gaussian Process formulations. This framework integrates established proofs and spectral properties from the literature into a coherent analytical perspective. Our analysis further provides characterization of eigenvalue behavior and examination of positive definiteness properties for each kernel type. Through comprehensive SVM classification experiments on seven diverse datasets (Breast Cancer Wisconsin, Wine, Digits, Iris, Spiral, Moons, and Circles), we demonstrate how theoretical kernel properties translate into practical performance. Key findings indicate that Matérn ( ν = 0.5) kernels achieve strong and often near-perfect accuracy on datasets with complex nonlinear geometric structures (e.g., Moons and Spiral), while RBF kernels excel (99.8 %) on relatively well-separated data. The Nyström approximation provides significant computational speed-up and maintains competitive accuracy on synthetic datasets, though its performance degrades on more complex real-world data. Statistical validation using the Friedman test and post-hoc Nemenyi tests indicates statistically significant differences among kernel types ( p < 0.001). This work bridges the gap between kernel theory and practical machine learning by providing: (1) a unified analysis of Mercer condition properties across kernel types, (2) empirical performance benchmarks, and (3) practical insights for kernel selection based on data characteristics and computational constraints.

Context: Financial system stability is determined by the condition of the banking system. A bank failure can destroy the stability of the financial system, as banks are subject to systemic risk, affecting not only individual banks but also segments or the entire financial system. Calculating the probability of a bank going bankrupt is one way to ensure the banking system is safe and sound. Existing literature and limitations: Statistical models, such as Altman's Z-Score, are one of the common techniques for developing a bankruptcy prediction model. However, statistical methods rely on rigid and sometimes irrelevant assumptions, which can result in low forecast accuracy. New approaches are necessary. Objective of the research: Bankruptcy models are developed using machine learning techniques, such as logistic regression (LR), random forest (RF), and support vector machines (SVM). According to several studies, machine learning is also more accurate and effective than statistical methods for categorising and forecasting banking risk management. Present Research: The commercial bank data are derived from the annual financial statements of 44 active banks and 21 bankrupt banks in Turkey from 1994 to 2004, and the rural bank data are derived from the quarterly financial reports of 43 active and 43 bankrupt rural banks in Indonesia between 2013 and 2019. Five rural banks in Indonesia have also been selected to demonstrate the feasibility of analysing bank bankruptcy trends. Findings and implications: The results of the research experiments show that RF can forecast data from commercial banks with a 90% accuracy rate. Furthermore, the three machine learning methods proposed accurately predict the likelihood of rural bank bankruptcy. Contribution and Conclusion: The proposed innovative machine learning approach help to implement policies that reduce the costs of bankruptcy.

COVID-19 is a new type of ailment caused by the strenuous acute respiratory syndrome, namely SARS-CoV-2, also frequently well-known as the Coronavirus. An early tendency of COVID-19 for some sufferers can cause no symptoms at all as no experience is referred to as asymptomatic confirmation cases, yet these sufferers can still transmit COVID-19 to other people. Therefore, the authors developed a program using Machine Learning that sustains data to be analyzed based on the input served under the proposed methods of Convolutional Neural Network-Support Vector Machine (CNNSVM) and Convolutional Neural Network-Random Forest(CNNRF), along with several optimizers to be compared. Convolutional Neural Networks is a deep learning algorithm that can train large data sets with millions of parameters and has attracted attention in various fields that are commonly used for the classification and detection of Convolution in Neural Networks. In amalgamation with Support Vector Machines, a technique that uses two vectors to form a dividing line or side and fairly high accuracy,y random forests classification. In the manner of image data obtained from ChestX-ray images of people with COVID-19 from the Italian Society of Medical and Interventional Radiology (SIRM), a total of 1750 observations consisting of 1000 data for COVID¬-19 images and 750 data for non-COVID-19 images. This research aims to determine which optimizer is better for analyzing COVID-19 ChestX-ray images by evaluating both methods. Hopefully, both methods can provide higher accuracy for future studies with wider databases to provide better results for analyzing different ailments.

Lung cancer is the deadliest cancer worldwide. Correct diagnosis of lung cancer is one of the main tasks that is challenging tasks, so the patient can be treated as soon as possible. In this research, we proposed a hybrid model based on convolutional neural networks (CNN) and fuzzy kernel k-medoids (FKKM) for lung cancer detection, where the magnetic resonance imaging (MRI) images are transmitted to CNN, and then the output is used as new input for FKKM. The dataset used in this research consist of MRI images taken from someone who had lung cancer with the treatment of anti programmed cell death-1 (anti-PD1) immunotherapy in 2016 that obtained from the cancer imaging archive. The proposed method obtained accuracy, sensitivity, precision, specificity, and F1-score 100% by using radial basis function (RBF) kernel with sigma of {10_­­^-8, 10_­­^-4, 10_­­^-3, 5x10_­­^-2, 10_­­^-1, 1, 10­­⁴} in 20-fold cross-validation. The computational time is only taking less than 10 seconds to forward dataset to CNN and 3.85 ± 0.6 seconds in FKKM model. So, the proposed method is more efficient in time and has a high performance for detecting lung cancer from MRI images.

Cervical cancer classification using convolutional neural network-support vector machine