Article Per Year (5 Year)
p-Index From 2021 - 2026
1.503
P-Index
This Author published in this journals
All Journal JTAM (Jurnal Teori dan Aplikasi Matematika) Jurnal Ilmiah Matematika Limits: Journal of Mathematics and Its Applications
Kafi, Rahmat Al
Department Of Mathematics, Faculty Of Mathematics And Natural Sciences, Universitas Indonesia
Computer Science & IT Mathematics

Published : 5 Documents Claim Missing Document
Claim Missing Document
Check
Articles

Found 5 Documents
Search

 1 
Analysis of diabetes mellitus gene expression data using two-phase biclustering method Rahmat Al Kafi; Alhadi Bustamam; Wibowo Mangunwardoyo
Jurnal Ilmiah Matematika Vol 8, No 2 (2021)
Publisher : Universitas Ahmad Dahlan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26555/konvergensi.v0i0.22111

Abstract

The purpose of this research is to find bicluster from Type 2 Diabetes Mellitus genes expression data which samples are obese and lean people using two-phase biclustering. The first step is to use Singular Value Decomposition to decompose matrix gene expression data into gene and condition based matrices. The second step is to use K-means to cluster gene and condition based matrices, forming several clusters from each matrix. Furthermore, the silhouette method is applied to determine the number of optimum clusters and measure the accuracy of grouping results. Based on the experimental results, Type 2 Diabetes Mellitus dataset with 668 selected genes produced optimal biclusters, with six biclusters. The obtained biclusters consist of 2 clusters on the gene-based matrix and 3 clusters on the sample-based matrix with silhouette values, respectively, are 0.7361615 and 0.7050163.
Analysis of diabetes mellitus gene expression data using two-phase biclustering method Rahmat Al Kafi; Alhadi Bustamam; Wibowo Mangunwardoyo
Jurnal Ilmiah Matematika Vol 8, No 2 (2021)
Publisher : Universitas Ahmad Dahlan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26555/konvergensi.v0i0.22111

Abstract

The purpose of this research is to find bicluster from Type 2 Diabetes Mellitus genes expression data which samples are obese and lean people using two-phase biclustering. The first step is to use Singular Value Decomposition to decompose matrix gene expression data into gene and condition based matrices. The second step is to use K-means to cluster gene and condition based matrices, forming several clusters from each matrix. Furthermore, the silhouette method is applied to determine the number of optimum clusters and measure the accuracy of grouping results. Based on the experimental results, Type 2 Diabetes Mellitus dataset with 668 selected genes produced optimal biclusters, with six biclusters. The obtained biclusters consist of 2 clusters on the gene-based matrix and 3 clusters on the sample-based matrix with silhouette values, respectively, are 0.7361615 and 0.7050163.
A Posteriori Premium Rate Calculation using Poisson-Gamma Hierarchical Generalized Linear Model for Vehicle Insurance Novkaniza, Fevi; Putri, Irene Devina; Kafi, Rahmat Al; Devila, Sindy
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.27837

Abstract

This study develops and applies the Poisson-Gamma Hierarchical Generalized Linear Model (PGHGLM) to address the challenge of determining accurate and fair premium rates in vehicle insurance. The PGHGLM models a mixture distribution for the response variable, influenced by random effects, and employs a logarithmic link function. Parameter estimation is conducted using the maximum likelihood method. However, since analytical estimation is not feasible, the numerical conjugate gradient method, specifically the Fletcher-Reeves algorithm, is utilized. The implementation of the PGHGLM uses the longitudinal Claimslong dataset, incorporating driver age as a covariate. The main contribution of this research lies in integrating a priori risk classification with a posteriori adjustment based on longitudinal claim frequency data. For datasets without covariates, trend parameters are incorporated into the model. For datasets with covariates, such as driver age, the average claim frequency is computed for each age category. Results show that posteriori premium rates increase with rising claim frequency from the previous year, with higher claim frequencies leading to larger rate adjustments in the subsequent year. Through the PGHGLM, a posteriori premium rate estimates are obtained for each age group of vehicle insurance policyholders. This study demonstrates the practical application of the PGHGLM in calculating precise premium rates. By analyzing a longitudinal vehicle insurance dataset, the model generates annual a posteriori premium rates tailored to age groups. These findings underscore the PGHGLM’s robust methodological framework and its potential to enhance premium fairness, enable risk-adjusted pricing, and better tailor insurance products to diverse policyholder profiles. 
Analysis of diabetes mellitus gene expression data using two-phase biclustering method Kafi, Rahmat Al; Bustamam, Alhadi; Mangunwardoyo, Wibowo
Jurnal Ilmiah Matematika Vol 8, No 2 (2021)
Publisher : Universitas Ahmad Dahlan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26555/konvergensi.v0i0.22111

Abstract

The purpose of this research is to find bicluster from Type 2 Diabetes Mellitus genes expression data which samples are obese and lean people using two-phase biclustering. The first step is to use Singular Value Decomposition to decompose matrix gene expression data into gene and condition based matrices. The second step is to use K-means to cluster gene and condition based matrices, forming several clusters from each matrix. Furthermore, the silhouette method is applied to determine the number of optimum clusters and measure the accuracy of grouping results. Based on the experimental results, Type 2 Diabetes Mellitus dataset with 668 selected genes produced optimal biclusters, with six biclusters. The obtained biclusters consist of 2 clusters on the gene-based matrix and 3 clusters on the sample-based matrix with silhouette values, respectively, are 0.7361615 and 0.7050163.
Pemodelan Harga Saham Berdasarkan Generalized Linear Model untuk Kejadian Multivariat Fevi Novkaniza; Jonathan Anthony; Rahmat Al Kafi
Limits: Journal of Mathematics and Its Applications Vol. 20 No. 3 (2023): Limits: Journal of Mathematics and Its Applications Volume 20 Nomor 3 Edisi No
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Kejadian multivariat adalah kejadian-kejadian yang memiliki tidak hanya satu peristiwa yang memengaruhi, tetapi bisa lebih banyak peristiwa yang memberi dampak pada peristiwa utamanya. Dampak yang dihasilkan dari suatu kejadian dapat berupa apa saja dan bisa diprediksi. Hal ini menyebabkan perlunya dibentuk sebuah model untuk memprediksi dampak dari sebuah kejadian sehingga dapat diambil keputusan penting berdasarkan kejadian tersebut. Saham merupakan salah satu contoh yang dapat direpresentasikan sebagai kejadian multivariat, seperti harga saham saat penutupan atau closing price, harga maksimal penutupan saham pada periode tertentu, dan durasi waktu (bulanan). Harga penutupan saham dan harga maksimal penutupan saham pada periode tertentu merupakan variabel acak kontinu yang masing-masing diasumsikan berdistribusi eksponensial dan truncated logistic. Durasi waktu (bulanan) merupakan variabel acak diskrit yang diasumsikan berdistribusi geometrik. Untuk mengakomodir kejadian multivariat yang melibatkan ketiga variabel acak tersebut digunakan distribusi trivariat yaitu, distribusi TETLG (Trivariate distribution with Exponential, Truncated Logistic, and Geometric marginals). Selanjutnya, untuk mengetahui pola hubungan antara ketiga variabel acak sebagai vektor respon dengan tiga kovariat yaitu, tingkat pengangguran, tingkat inflasi, dan tingkat obligasi 10 tahun, dikonstruksi sebuah Generalized Linear Model (GLM) untuk kejadian multivariat. Estimasi parameter model GLM kejadian multivariat, dilakukan menggunakan metode Maximum Likelihood. Sebagai implementasi pemodelan harga saham menggunakan GLM kejadian multivariat, diterapkan pada data harga penutupan saham dari Yahoo! Finance untuk periode 2 Januari 1958 hingga 17 April 2020. Berdasarkan uji likelihood ratio, diperoleh hasil bahwa hanya tingkat inflasi dan tingkat pengangguran yang memiliki pengaruh signifikan terhadap pemodelan harga saham.
Co-Authors Anggia Abygail Sihombing Bustamam, Alhadi Dian Maharani fevi novkaniza Jonathan Anthony Jonathan Anthony Kartika Chandra Dewi Putri, Irene Devina Sindy Devila Wibowo Mangunwardoyo WIBOWO MANGUNWARDOYO Yuni Rosita Dewi