Eigen Mathematics Journal
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Optimization of Classification Algorithms Performance with k-Fold Cross Validation
Get PDFSupervised learning is a predictive method used to make predictions or classifications. Supervised learning algorithms work by building a model using training data that includes both independent and dependent variables. Several methods for building classification include Logistic Regression, Naive Bayes, K-Nearest Neighbor (KNN), decision tree, etc. The lack of capacity of a classification algorithm to generalize certain data can be associated with the problem of overfitting or underfitting. K-fold cross-validation is a method that can help avoid overfitting or underfitting and produce a algorithm with good performance on new data. This study will test the Naive Bayes, K-Nearest Neighbor (KNN), Classification and Regression Tree (CART), and Logistic Regression methods with k-fold cross-validation on two different datasets. The values of k set for cross-validation are 2, 3, 5, 7, and 10. The analysis results concluded that each classification algorithm performed best at 10-fold cross-validation. In DATA 1, the Naive Bayes algorithm has the highest average accuracy of 0.67 (67%) and the error rate is 0.33 (33%), followed by the CART algorithm, KNN, and finally logistic regression. While DATA 2, the KNN algorithm has the highest average accuracy of 0.66 (66%) and an error rate of 0.34 (34%), followed by the CART algorithm, Naive Bayes, and finally logistic regressionbut can be a reference if you want to predict the growth direction of the accommodation and food service activities sector.Supervised learning is a predictive method used to make predictions or classifications. Supervised learning algorithms work by building a model using training data that includes both independent and dependent variables. Several methods for building classification include Logistic Regression, Naive Bayes, K-Nearest Neighbor (KNN), decision tree, etc. The lack of capacity of a classification algorithm to generalize certain data can be associated with the problem of overfitting or underfitting. K-fold cross-validation is a method that can help avoid overfitting or underfitting and produce a algorithm with good performance on new data. This study will test the Naive Bayes, K-Nearest Neighbor (KNN), Classification and Regression Tree (CART), and Logistic Regression methods with k-fold cross-validation on two different datasets. The values of k set for cross-validation are 2, 3, 5, 7, and 10. The analysis results concluded that each classification algorithm performed best at 10-fold cross-validation. In DATA 1, the Naive Bayes algorithm has the highest average accuracy of 0.67 (67%) and the error rate is 0.33 (33%), followed by the CART algorithm, KNN, and finally logistic regression. While DATA 2, the KNN algorithm has the highest average accuracy of 0.66 (66%) and an error rate of 0.34 (34%), followed by the CART algorithm, Naive Bayes, and finally logistic regressionbut can be a reference if you want to predict the growth direction of the accommodation and food service activities sector
Modeling of Economic Growth Rate in West Nusa Tenggara Province with Longitudinal Kernel Nonparametric Regression
Get PDFEconomic growth can indicate the success of economic development in people's lives, so it is essential to study the relationship between economic growth and factors that affect economic growth. Regression analysis is one of the most widely used statistical data analysis methods to determine the relationship pattern between the independent and dependent variables. Three methods can be used to estimate the regression curve, one of which is nonparametric regression. Economic growth data is one form of longitudinal data, with observations of independent subjects, with each subject being observed repeatedly over different periods. Kernel nonparametric regression model applications can be used for longitudinal data. This research aims to estimate the curve and get the best regression model. In this research, the smoothing technique chosen to estimate the nonparametric regression model for longitudinal data is the kernel triangle estimator, which can be obtained by minimizing the square of error using Weighted Least Squares (WLS) and selecting the optimum bandwidth using the Generalized Cross Validation (GCV) method. This study uses the economic growth rate in West Nusa Tenggara as the dependent variable and the human development index, population density, general allocation funds, local revenue, and labor force participation as independent variables. The result showed that the model is less accurate because of the low value of the coefficient for determination and the high value of the mean absolute percentage error (MAPE). This can be caused by the selection of bandwidth intervals that are too small
Solution of The Duffing Equation Using Exponential Time Differencing Method
Get PDFTo describe the spring stiffening effect that occurs in physics and engineering problems, Georg Duffing added the cubic stiffness term to the linear harmonic oscillator equation and is now known as the Duffing oscillator. Despite its simplicity, its dynamic behavior is very diverse. In this research, the Exponential Time Difference method is introduced to solve the Duffing oscillator numerically. To formulate the ETD method, we were using the integration factors. It is a function which, when multiplied by an ordinary differential equation, produces a differential equation that can be integrated. This method is an effective numerical method for solving complex differential equations, especially equations that have strong non-linearity The ETD method delivers highly accurate numerical solutions for the Duffing oscillator, with minimal discrepancy from the analytical results. Through parameter variation, the ETD method's applicability extends to diverse Duffing oscillator configurations
Solusi Numerik pada Persamaan Korteweg-De Vries Equation menggunakan Metode Beda Hingga
No full textThe Korteweg-de Vries (KdV) equation is a nonlinear partial differential equation that has a key role in wave physics and many other disciplines. In this article, we develop numerical solutions of the KdV equation using the finite difference method with the Crank-Nicolson scheme. We explain the basic theory behind the KdV equation and the finite difference method, and outline the implementation of the Crank-Nicolson scheme in this context. We also give an overview of the space and time discretization and initial conditions used in the simulation. The results of these simulations are presented through graphical visualizations, which allow us to understand how the KdV solution evolves over time. Through analysis of the results, we explore the behavior of the solutions and perform comparisons with exact solutions in certain cases. Our conclusion summarizes our findings and discusses the advantages and limitations of the method used. We also provide suggestions for future research in this area.Persamaan Korteweg-de Vries (KdV) adalah persamaan diferensial parsial nonlinear yang memiliki peran kunci dalam fisika gelombang dan banyak disiplin ilmu lainnya. Dalam artikel ini, kami mengembangkan solusi numerik persamaan KdV menggunakan metode beda hingga dengan skema Crank-Nicolson. Kami menjelaskan teori dasar di balik persamaan KdV dan metode beda hingga, serta menguraikan implementasi skema Crank-Nicolson dalam konteks ini. Kami juga memberikan gambaran tentang diskritisasi ruang dan waktu serta kondisi awal yang digunakan dalam simulasi. Hasil dari simulasi ini dipresentasikan melalui visualisasi grafis, yang memungkinkan kita untuk memahami bagaimana solusi KdV berkembang seiring berjalannya waktu. Melalui analisis hasil, kami mengeksplorasi perilaku solusi dan melakukan perbandingan dengan solusi eksak dalam kasus tertentu. Kesimpulan kami merangkum temuan kami dan mendiskusikan keuntungan dan keterbatasan metode yang digunakan. Kami juga memberikan saran untuk penelitian selanjutnya dalam bidang ini.
Kata kunci: Persamaan KdV, Soliton, Metode bedahingga, skema Crank-nicolso
Application of the Average Based Fuzzy Time Series Lee Method for Forecasting World Gold Prices
Get PDFGold is a investment that investors are interested in because it has relatively low risk and gold investment is not affected by inflation. Gold prices always change from time to time, so it is necessary to forecast gold prices as a basis for investors in making decisions. The forecasting method used in the fuzzy time series lee method. The purpose of this research is determine the world prices and determine the accuracy of the gold price forecasting value ortained using fuzzy time series lee method. The results of this research are forecasting gold prices in the period November 20, 2023 of US$ 63,89/grams and relatively the level of forecasting accuracy based on MAPE value of 0,540091% included in the very good criteria in forecasting gold prices
Numerical Analysis of Mathematical Model for Diabetes Mellitus Disease by Using Adam-Bashfort Moulton Method
Get PDFDiabetes mellitus is a metabolic disorder characterized by elevated blood glucose levels, known as hyperglycemia. The objective of this study is to develop a mathematical model of diabetes mellitus. The model will be analyzed in terms of its equilibrium points using the Adam-Bashforth Moulton numerical method. The numerical method that used is a multistep method. The predictor step employs the Runge-Kutta method, while the corrector step uses the Adam-Bashforth Moulton method. The mathematical model of diabetes mellitus is categorized into two classes: uncomplicated diabetes mellitus and complicated diabetes mellitus. The resulting model identifies two equilibrium points: the endemic equilibrium point (complicated) and the disease-free equilibrium point (uncomplicated). The eigenvalues of these equilibrium points are positive real numbers and negative real numbers. Therefore, the stability of the system is found to be unstable and asymptotically stable, indicating that the population of individuals with uncomplicated diabetes mellitus will continue to rise, whereas the population with complications will not increase significantly over time
Nowcasting of Indonesia's Gross Domestic Product Using Mixed Sampling Data Regression and Google Trends Data
Get PDFThis study aims to compare the results of the GDP nowcasting of the accommodation and food service activities sector without and with the pandemic time using the MIDAS method. The MIDAS method is an econometric approach used to predict economic development using real-time available high-level and low-frequency data. In this study, Google Trend acts as a predictor variable consisting of 16 search categories which are then reduced by Principal Component Analysis, resulting in several principal components. For GDP data, the data period collected is Quarter I 2010 to Quarter I 2023. This period will later be partitioned into the period before the COVID-19 pandemic, namely Quarter I 2010 to Quarter IV 2019 and a combined period, namely Quarter I 2010 to Quarter I of 2023. This partition was carried out to see the performance and sensitivity of the model before and after the shock due to the COVID-19 pandemic. From the models that have been made, nowcasting is carried out and it is found that the RMSE and MAE values for the pre-pandemic model are smaller than the combined model. The RMSE values for each of the pre-pandemic and combined models were 0.005753 and 0.056032 and the MAE values were 0.00359 and 0.048976 for the pre-pandemic and combined models. However, from this study it is not advisable to make predictions on the nominal GDP of the accommodation and food service activities sector because the results of the nowcasting predictions are still far from the actual value, but can be a reference if you want to predict the growth direction of the accommodation and food service activities sector
Comparison of Several Univariate Time Series Methods for Inflation Rate Forecasting
Get PDFForecasting inflation is very crucial for a country because inflation is one of indicator to measure development of the country. This study aims to evaluate the effectiveness of three univariate time series methods i.e., ARIMA (Autoregressive Integrated Moving Average), Double Exponential Smoothing (DES), and Trend Projection (TP), in forecasting Indonesia’s monthly inflation rates using data from 2018 to 2022. The analysis identifies DES as the most accurate method, evidenced by its lowest Root Mean Square Error (RMSE) value of 2.9296, outperforming ARIMA and TP, which have RMSE values of 13.1479 and 3.47053, respectively. Consequently, DES was selected as the preferred model for forecasting inflation over the next 36 month, with the forecasts indicating a consistent downward trend in inflation throughout the year. While these findings highlight DES's effectiveness, the study also acknowledges limitations, including its reliance on univariate models that do not incorporate other economic variables, and the potential limitations of the dataset’s specific time frame. To address these limitations, future research should consider multivariate models, integrate machine learning techniques, and conduct scenario analyses to improve forecast accuracy and robustness. Despite these constraints, the study provides valuable insights into inflation forecasting in Indonesia, offering a practical tool for policymakers and contributing to more informed economic decision-making.Forecasting inflation is very crucial for a country because inflation is one of indicator to measure development of the country. This study aims to evaluate the effectiveness of three univariate time series methods i.e., ARIMA (Autoregressive Integrated Moving Average), Double Exponential Smoothing (DES), and Trend Projection (TP), in forecasting Indonesia’s monthly inflation rates using data from 2018 to 2022. The analysis identifies DES as the most accurate method, evidenced by its lowest Root Mean Square Error (RMSE) value of 2.9296, outperforming ARIMA and TP, which have RMSE values of 13.1479 and 3.47053, respectively. Consequently, DES was selected as the preferred model for forecasting inflation over the next 36 month, with the forecasts indicating a consistent downward trend in inflation throughout the year. While these findings highlight DES's effectiveness, the study also acknowledges limitations, including its reliance on univariate models that do not incorporate other economic variables, and the potential limitations of the dataset’s specific time frame. To address these limitations, future research should consider multivariate models, integrate machine learning techniques, and conduct scenario analyses to improve forecast accuracy and robustness. Despite these constraints, the study provides valuable insights into inflation forecasting in Indonesia, offering a practical tool for policymakers and contributing to more informed economic decision-making
Forecasting Coffee Exports to the United States Using the Holt-Winters Exponential Method
No full textA study was conducted to estimate coffee exports to the United States using the Holt-Winters Exponential method. The aim of this research is to project coffee export activity over the next four periods. Data on coffee exports to the United States from 2000 to 2022 was obtained from the Indonesian Central Bureau of Statistics and used as a research object. The range of values used in this study is between 0.1 and 0.5 for α, between 0.1 and 0.5 for β, and between 0.1 and 0.9 for ϒ. The results of this research state that it is estimated that in 2023, Indonesia will export coffee to the United States amounting to 61,332.60 tons, in 2024 amounting to 60,661.50 tons, in 2025 amounting to 61,563.27 tons, and in 2026 amounting to 60,196.50 tonsSebuah studi telah dilakukan untuk meramalkan ekspor kopi ke Amerika Serikat menggunakan metode Holt-Winters Exponential. Tujuan dari penelitian ini adalah untuk memproyeksikan aktivitas ekspor kopi selama empat periode ke depan. Data ekspor kopi ke Amerika Serikat dari tahun 2000 hingga 2022 diperoleh dari Badan Pusat Statistik Indonesia dan dijadikan sebagai objek penelitian. Rentang nilai yang digunakan dalam studi ini adalah antara 0,1 dan 0,5 untuk α, antara 0,1 dan 0,5 untuk β, dan antara 0,1 dan 0,9 untuk ϒ. Hasil dari penelitian ini menyatakan bahwa diperkirakan pada tahun 2023, Indonesia akan mengekspor kopi ke Amerika Serikat sebesar 61.332,60 ton, pada tahun 2024 sebesar 60.661,50 ton, pada tahun 2025 sebesar 61.563,27 ton, dan pada tahun 2026 sebesar 60.196,50 ton
Modeling of the Spread of Malaria in the Bangka Belitung Islands Province Using the SEIR Method
Get PDFMalaria is an infectious disease caused by plasmodium through the bite of the Anopheles sp. female mosquito. (Roach, 2012). Malaria disease which hit the Bangka Belitung Islands Province in 2005 experienced a spike, reaching 36,901 people out of 981,573 residents and claimed the lives of 12 local residents. In 2011, the Bangka Belitung Islands Province was declared an endemic area for malaria. This research aims to model and interpret the spread of malaria using the SEIR model and predict the spread of malaria using parameter estimates. The steps in analyzing the SEIR model on the spread of malaria are making assumptions, forming a SEIR model, determining the equilibrium point and analyzing the stability of the equilibrium point, determining the basic reproduction number, and carrying out a simulation of the SEIR model that has been obtained. The SEIR model is classified into 4 classes, namely Susceptible (susceptible individuals), Exposed (individuals who have symptoms), Infected (infected individuals), and Recovered (recovered individuals). The data used in this research is data on the number of Susceptible, Exposed, Infected, and Recovered malaria cases in 2022 obtained from the Bangka Belitung Islands Provincial Health Service. The SEIR mathematical model is used to calculate the equilibrium point and basic reproduction number. Based on the SEIR model simulation results, it was found that the susceptible population decreased from the 0th month to the 48th month. As for the exposed population, there were 9,623 people in month 0, but in this condition the population decreased drastically per month. Furthermore, for the infected population there were 129 people in month 0, but in this condition the number of infected decreased drastically per month along with the decrease in the exposed population. For individuals who recovered, there was a increase from the 0th month to the 48th month.Malaria is an infectious disease caused by plasmodium through the bite of the Anopheles sp mosquito. female (Roach, 2012). Malaria disease which hit the Bangka Belitung Islands Province in 2005 experienced a spike, reaching 36,901 people out of 981,573 residents and claimed the lives of 12 local residents. In 2011, the Bangka Belitung Islands Province was declared an endemic area for malaria. This research aims to model and interpret the spread of malaria using the SEIR model and predict the spread of malaria using parameter estimates. The steps in analyzing the SEIR model on the spread of malaria are making assumptions, forming a SEIR model, determining the equilibrium point and analyzing the stability of the equilibrium point, determining the basic reproduction number, and carrying out a simulation of the SEIR model that has been obtained. The SEIR model is classified into 4 classes, namely Susceptible (susceptible individuals), Exposed (individuals who have symptoms), Infected (infected individuals), and Recovered (recovered individuals). The data used in this research is data on the number of Susceptible, Exposed, Infected and Recovered malaria cases in 2022 obtained from the Bangka Belitung Islands Provincial Health Service. The SEIR mathematical model is used to calculate the equilibrium point and basic reproduction number. Based on the SEIR model simulation results, it was found that the susceptible population decreased from the 0th month to the 48th month. As for the exposed population, there were 9,623 people in month 0, but in this condition the population decreased drastically per month. Furthermore, for the infected population there were 129 people in month 0, but in this condition the number of infected decreased drastically per month along with the decrease in the exposed population. For individuals who recovered, there was a decrease from the 0th month to the 48th month