Limits: Journal of Mathematics and Its Applications

Evaluasi Kinerja Metode CLARA dan FCM dalam Analisis Gerombol untuk Data Berjumlah Besar dengan Pencilan

Indahwati Indahwati — 2025-11-20

Analisis gerombol adalah suatu metode statistika yang mengidentifikasi gerombol objek berdasarkan karakteristik serupa. Masalah yang sering terjadi dalam analisis gerombol adalah keberadaan data pencilan. Keberadaan pencilan dapat mengakibatkan output yang tidak sesuai dengan gambaran yang sebenarnya, sehingga gerombol yang dihasilkan tidak merepresentasikan objek dengan tepat. Masalah lain yang dapat muncul dalam analisis gerombol adalah besarnya jumlah amatan, sehingga diperlukan metode analisis yang efisien dalam penggerombolan. Penelitian ini juga memperdalam tentang kinerja keduanya terhadap jarak antara pusat gerombol dan kondisi penggerombolan melalui kajian simulasi, dimana masing-masing faktor terdiri dari tiga level yang diobservasi. Metode Clustering Large Applications (CLARA) dan Fuzzy C-Means (FCM) adalah metode yang kekar (robust) terhadap pencilan dan mampu menganalisis dataset besar. Metode FCM menggunakan nilai pembobot (w) yang optimal agar kekar terhadap pencilan. Metode CLARA memiliki sifat kekar dikarenakan menggunakan medoid sebagai pusat gerombol dan penggunaan jarak Manhattan dalam perhitungan jarak antara objek dan pusat gerombol. Metode tersebut akan dievaluasi menggunakan beberapa kriteria evaluasi kebaikan yaitu berdasarkan akurasi penggerombolan serta rasio simpangan baku dalam gerombol dan antar gerombol. Hasil analisis menunjukkan pengaruh signifikan pada masing-masing faktor dan interaksi antar faktor. Visualisasi menunjukkan bahwa peningkatan persentase pencilan mengurangi akurasi penggerombolan, sementara jumlah data yang lebih besar meningkatkan akurasi. Jarak yang lebih besar antara pusat gerombol dan kondisi gerombol yang terpisah menghasilkan rasio simpangan baku gerombol yang lebih kecil. Hasil penelitian menunjukkan bahwa metode FCM lebih efektif dalam menangani data dengan variasi yang signifikan.

Bilangan Kromatik Lokasi Amalgamasi Sisi Graf Lingkaran $amal_s(C_n^j;v_{j,1}v_{j,n})$ dengan $n=3,4$, dan $m\geq2$

Des Welyyanti — 2025-11-20

Let G be a connected graph and {S_1,S_2,…,S_k} be an ordered partition of V(G). Let S_i is a set of color classes using colors 1,2,...,k where k as positive integer. The color code c_ (v) of vertex v in G with respect to is defined as k-vector, c_ (v)=(d(v,S_1 ),d(v,S_2 ),…,d(v,S_i )) where d(v,S_i ). If each of vertices in G have distinct color codes, then c is called as locating coloring of G. The minimum number of colors that are used for locating coloring is called as locating chromatic number of G, denoted by X_L (G).

Pemodelan Harga Emas Berdasarkan Kurs Rupiah Terhadap USD dengan Pendekatan Regresi Polinomial Lokal

Fitria Halimatuzzahro — 2025-11-20

Modeling gold prices based on the exchange rate of the rupiah against the USD is important because it can be used in making investment decisions as well as a reference for formulating economic policy. This study aims to apply local polynomial regression in modeling gold prices in Indonesia based on the rupiah exchange rate against the USD. In this study, gold price modeling was carried out using nonparametric regression with local polynomials. The data used in the study are monthly data of exchange rates as predictor variables (X) and gold prices as response variables (Y) observed from January 2014 to October 2024. Applying local polynomial regression starts with collecting data, analyzing data descriptively, and then modeling and estimating gold price data in Indonesia based on the rupiah exchange rate against the USD using the R program. The results showed that gold price modeling based on the rupiah exchange rate against the USD was obtained on insample data with the best local polynomial estimator of order 2 with an optimal bandwidth of 800 with a MAPE of 9.85% which was classified as very good while for outsample data the MAPE value was 24.87% so that the model estimate for outsample data was classified as sufficient. Overall, the MAPE value related to the prediction of gold prices in January 2014 - October 2024 is 11.01% which is classified as good.

Optimasi Komposisi Makanan Penderita Diabetes dengan Hybrid Genetic Algorithm dan Modified Simulated Annealing

Achmad Suryadi Nasution — 2025-11-20

Diabetes mellitus is one of the deadliest diseases. Factors that can cause diabetes mellitus are irregular eating patterns and unhealthy lifestyles. Patients with diabetes mellitus must have a healthy diet by identifying the optimal food composition so as not to trigger complications with various other deadly diseases. Identification of food composition was carried out using a hybrid adaptive genetic algorithm and modified simulated annealing. Based on the patient testing results, the average accuracy for carbohydrates, protein, fat, sodium, fiber, and calories was 99.90%, 99.72%, 99.33%, 99.99%, 99.29%, and 99.86%, respectively.

Dinamika Solusi dan Kontrol Optimal Model Penyakit ISPA di Kota Malang

Lukman Hakim — 2025-11-20

The current research provides a mathematical model utilizing nonlinear ordinary differential equations to represent the spread of acute respiratory infections (ARI). The model is divided into five compartments: the susceptible population, the vaccinated population, the latent population, the infected population, and the recovered population. Through dynamic analysis, two equilibrium points were determined. The disease-free equilibrium point is stable under conditions, while the endemic equilibrium point exhibits asymptotic stability. The lsqcurvefit methods was implemented to estimate the parameters, facilitating accurate parameter approximation. The acquisition of estimated values was implemented in the sensitivity analysis, and several parameters sensitive to were obtained: the vaccination rate, the natural death rate, the mortality cause infection rate, and recovery rate. An optimal control problem was designed by incorporating two control variables: firstly, reducing the direct contact between the susceptible and infected populations, and the other focused on increasing the intensity of infected individuals. The solution of optimal control problem was derived using Pontryagin's Principle. The objective function was formulated as a Lagrange to minimize the number of latent and infected individuals, and maximizing the vaccinated and recovered populations. Finally, numerical simulations were performed to validate the theoretical analysis, demonstrating that the results in line with the objective function of optimal control and effectively support the proposed strategies for controlling the disease.

Kontrol Optimal Model Dinamik Penyebaran Penyakit Tuberkulosis dengan Kekambuhan di Kota Semarang

Lathifatul Inayah Alhusna — 2025-11-20

In this study, we modified the SVIR (Susceptible, Vaccinated, Infectious, Recovered) dynamic model by considering relapse in the spread of Tuberculosis (TB). To reduce the spread of TB, we applied optimal control theory using Pontryagin's Minimum Principle. Two control variables were used: TB prevention education and treatment for actively infected individuals. This optimal control system was solved through numerical simulations using the Forward-Backward Sweep and fourth-order Runge-Kutta methods. The results of the numerical simulations were used to illustrate the difference between implementing a control strategy and no control. The results showed that the education intervention was able to reduce the actively infected subpopulation by 99.74%, while if the treatment intervention alone was given, the number of infected individuals showed a decrease of 99.69%. However, when both interventions were implemented simultaneously, the actively infected subpopulation was able to be reduced by up to 99.90%. In this case, implementing education and treatment controls simultaneously was more effective than implementing the controls separately and was able to significantly increase the recovered subpopulation, indicating more optimal disease control

Identifikasi Preferensi Konsumen pada Pembelian Produk Skincare menggunakan Analisis Konjoin

Eileen Lyana Putri — 2025-11-20

Skincare products are beauty care products used to prevent, improve, and treat skin problems such as acne, acne scars, blemishes, or to brighten the skin, treat dark skin, delay aging, or brighten the skin. The purpose of this study was to determine consumer preferences for purchasing skincare products based on three main characteristics, namely product origin (local or international), product benefits (brightening, moisturizing, anti-aging), and price. Data were analyzed using a conjoint analysis approach to determine consumer preferences in choosing skincare products. The results of the analysis showed that the products most preferred by consumers were local products that were useful for brightening the skin, with prices below fifty thousand. The majority of respondents were women who lived on the island of Java, with an average age of 23 years 9 months and were students. They purchased skincare products once every one to two months. Based on the model obtained, it shows that the benefits and origin of the product are more considered than the price.

Evaluasi Regresi Terklaster Fuzzy Spasial Simultan dengan Pendekatan Simulasi

Siti Hasanah — 2025-11-20

Spatial data refers to data that contains information related to the geographical characteristics of a region. As spatial data evolves into large-scale datasets, efficient analytical methods are required for processing the data. One such method suitable for analyzing large-scale spatial data is spatial fuzzy clustering. This method allows for the adjustment of cluster weights based on data likelihood, making it more capable of capturing the actual local variations present in spatial data. In this study, two types of spatial fuzzy clustering methods were evaluated through simulation: the method with a spatial penalty, Spatial Fuzzy Clustered Regression (SFCR), and the method without a spatial penalty, Fuzzy Geographically Weighted Clustering Regression (FGWCR). SFCR is a method that combines spatial clustering and regression modeling simultaneously, resulting in more efficient computation time. FGWCR produces clusters by considering both spatial proximity and attribute similarity, making it effective for spatial data analysis. The data were designed to form six clusters during the simulation process. The simulation results showed that the SFCR method was more capable of accurately capturing data variation and cluster distribution. The R² values for SFCR at a fuzziness degree of 2 and under weak, moderate, and strong spatial autocorrelation were 99.7%, 99.6%, and 99.5%, respectively, while the R² values for FGWCR were 98.5%, 98.6%, and 98.1%. Model performance was evaluated using RMSE, where lower RMSE values indicate better performance. The RMSE values for the SFCR method at a fuzziness degree of 2 and under weak, moderate, and strong spatial autocorrelation were 0.30, 0.289, and 0.298, respectively, while the RMSE values for the FGWCR method were 0.659, 0.541, and 0.551.

Perbandingan Kinerja Hybrid Classification SVM-RF dan SVM-NN Terhadap Faktor Risiko Anemia Ibu Hamil di Indonesia dengan Pendekatan Clustering K-Means

Asyifah Qalbi — 2025-11-20

Classification is one of the most researched topics by researchers from the field of machine learning and data mining. Machine learning methods that are often used include Support Vector Machine (SVM), Random Forest (RF) and Neural Network (NN). However, SVM does not always provide good accuracy. For example, when applied to highly imbalanced data, SVM will experience challenges. In addition, there is no single best method that can be applied to all classification problems. Currently, hybrid method approaches for data mining applications are becoming increasingly popular such as hybrid SVM-RF, SVM-NN and KMeans-SVM methods. In this study, a hybrid method of SVM-RF and SVM-NN was used to classify risk factors for anemia in pregnant women in Indonesia with a K-Means approach to cluster data misclassified by SVM. The results showed that the hybrid method can improve the performance of the SVM model. Hybrid SVM-RF provides a higher evaluation metric value compared to SVM-NN. The four evaluation metrics used, namely accuracy, balanced accuracy, sensitivity and specificity in SVM-RF are worth 0,989; 0,989; 0,988; and 0,989, respectively. The variables that contribute generally based on SHAP Global to the classification of risk factors for anemia in pregnant women in order are Age, Fe Tablet, Working Status, Education, Nutritional Status and ANC.

Komparasi Spline Kubik Not-a-Knot dan Natural pada Lompatan En-Nesyri Piala Dunia 2022

Delfia Hidayatul Fitri — 2025-11-20

The jumping motion when heading the ball in football varies depending on the conditions. This study aims to analyze the phenomenal jump of En-Nesyri at the 2022 World Cup from a kinematic perspective. The data was collected through digitization techniques from a demonstration of the jump and analyzed using cubic spline interpolation with two boundary conditions: natural and not-a-knot. The object of this study is En-Nesyri’s jump, which reached 2.78 meters when heading the ball during the match againts Portugal. The results show the kinematics of the jumping motion, including position, velocity, and acceleration. Additionally, differences between cubic spline interpolation with the two boundary conditions were observed. At 1.5 seconds, the head reaches its maximum height. The analysis indicates that the cubic spline with the not-a-knot boundary condition is more suitable for modeling phenomenal jump that do not start from a stationary position