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<![CDATA[CLUSTERING DISTRICTS/CITIES IN EAST JAVA PROVINCE BASED ON HIV CASES USING K-MEANS, AGNES, AND ENSEMBLE ]]>
<![CDATA[Lusia, Dwi Ayu]]>;
<![CDATA[Salsabila, Imelda]]>;
<![CDATA[Kusdarwati, Heni]]>;
<![CDATA[Astutik, Suci]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 1 (2025): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol19iss1pp63-72
<![CDATA[Cluster analysis is a method of grouping data into certain groups based on similar characteristics. This research aims to group districts/cities in East Java Province in 2021 based on HIV cases using hierarchical cluster analysis (AGNES), non-hierarchical cluster analysis (K-means), and ensemble clustering. The study found that the ensemble clustering solution forms four clusters, consistent with the results of AGNES clustering. This suggests that ensemble clustering improves the quality of cluster solutions by leveraging both hierarchical and non-hierarchical methods. The grouping of districts/cities based on HIV cases provides a clear distribution pattern for more targeted interventions. The study is limited to HIV cases in East Java Province and may not be generalizable to other regions with different epidemic characteristics. Additionally, the study focuses on clustering methods without investigating temporal changes in HIV case distribution. This research is one of the few studies that applies ensemble clustering to HIV cases in East Java Province. It combines hierarchical and non-hierarchical methods to improve the clustering process and provides a practical approach for regional HIV control planning.]]>
<![CDATA[THE UNINFORMATIVE PRIOR OF JEFFREYS’ DISTRIBUTION IN BAYESIAN GEOGRAPHICALLY WEIGHTED REGRESSION ]]>
<![CDATA[Faisal, Fachri]]>;
<![CDATA[Pramoedyo, Henny]]>;
<![CDATA[Astutik, Suci]]>;
<![CDATA[Efendi, Achmad]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol18iss2pp1229-1236
<![CDATA[When using the Bayesian method for estimating parameters in a geographically weighted regression model, the choice of the prior distribution directly impacts the posterior distribution. The distribution known as the Jeffreys prior is an uninformative type of prior distribution and is invariant to reparameterization. In cases where information about the parameter is not available, the Jeffreys' prior is utilized. The data was fitted with an uninformative Jeffreys' prior distribution, which yielded a posterior distribution that was utilized for estimating parameters. This study aims to derive the prior and marginal posterior distributions of the Jeffreys' and in Bayesian geographically weighted regression (BGWR). The marginal posterior distributions of and can be obtained by integrating the other parameters of a common posterior distribution. Based on the results and discussion, the Jeffreys prior in BGWR with the likelihood function is . On the other hand, the marginal posterior distribution of follows a normal multivariate distribution, that is, , while the marginal posterior distribution of follows an inverse gamma distribution, that is, . As further research, it is necessary to follow up on several limitations of the results of this research, namely numerical simulations and application to a particular case that related to the results of the analytical studies that we have carried out.]]>
<![CDATA[MIXED GEOGRAPHICALLY WEIGHTED REGRESSION (MGWR) WITH ADAPTIVE WEIGHTING FUNCTION IN POVERTY MODELING IN NTT PROVINCE ]]>
<![CDATA[Ola, Petrus Kanisius]]>;
<![CDATA[Iriany, Atiek]]>;
<![CDATA[Astutik, Suci]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 3 (2024): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol18iss3pp2035-2046
<![CDATA[Poverty modeling is a crucial economic and social development issue in various regions, including in East Nusa Tenggara (NTT) Province. This research proposes using the Mixed Geographically Weighted Regression (MGWR) model with an adaptive Bisquare weighting function to analyze variables influencing poverty levels in NTT Province. The MGWR model is an extension of the Geographically Weighted Regression (GWR), which allows some variables in the model to have local effects while others have global effects. The adaptive weighting function in the MGWR model enhances the analysis by providing different weights at each location according to its local characteristics, thus making the results more accurate and representative for each area. The data includes economic, social, and infrastructure variables from 22 districts/cities in NTT Province for 2023. The MGWR model with an adaptive weighting function is applied to model the relationship between these variables and poverty levels. The analysis integrates statistical software to manage and analyze spatial data. The study findings show that the MGWR model with an adaptive weighting function offers better estimates than the global regression and GWR models. The results revealed the smallest AIC value for the MGWR model at 104.1888, compared to the global regression model at 140.1427 and the GWR model at 117.6174. This model successfully identifies significant local and global variables and shows variations in influence at different locations in NTT Province. These findings provide valuable insights for policymakers and practitioners in designing and implementing more effective poverty alleviation strategies tailored to local conditions in NTT Province.]]>
<![CDATA[ENHANCING WEIGHTED FUZZY TIME SERIES FORECASTING THROUGH PARTICLE SWARM OPTIMIZATION ]]>
<![CDATA[Zamelina, Armando Jacquis Federal]]>;
<![CDATA[Astutik, Suci]]>;
<![CDATA[Fitriani, Rahma]]>;
<![CDATA[Fernandes, Adji Achmad Rinaldo]]>;
<![CDATA[Ramifidisoa, Lucius]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 4 (2024): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol18iss4pp2675-2684
<![CDATA[Climate change is a complex process that has far-reaching consequences for daily living. Temperature is one of the climatic features. Knowing its future value through a forecasting model is critical, as it aids in earlier strategic decision-making. Without considering spatial factors, this study investigates an Air Temperature variable forecasting. Weighted Fuzzy Time Series (WFTS) is one of the forecasting techniques. Furthermore, the length of the interval and the extent to which previous values (Order length) are utilized in predicting the subsequent value are pivotal factors in WFTS modelization and its forecasting accuracy. Therefore, this research investigates the interval length and the Order length of the WFTS through the Particle Swarm Optimization (PSO) approach. The variable used is the air temperature in Malang, Indonesia. The dataset is taken from BMKG-Indonesia. The forecasting performance of classical WFTS is enhanced by setting an appropriate order level and employing Particle Swarm Optimization (PSO) to determine the optimal interval fuzzy length. As indicated by the Evaluation matrices in the result section, the proposed optimization overtaken the classical WFTS in term of accuracy. The evaluation indicates a Mean Absolute Percentage Error (MAPE) value of 1.25 and a Root Mean Square Error (RMSE) of 0.32 for the Proposed model. In contrast, the classical WFTS demonstrates a MAPE of 2.26 and RMSE of 0.58. The implementation of the PSO provides solid insights for Air temperature forecasting accuracy.]]>
<![CDATA[DEVELOPMENT OF NONPARAMETRIC PATH FUNCTION USING HYBRID TRUNCATED SPLINE AND KERNEL FOR MODELING WASTE-TO-ECONOMIC VALUE BEHAVIOR ]]>
<![CDATA[Rohma, Usriatur]]>;
<![CDATA[Fernandes, Adji Achmad Rinaldo]]>;
<![CDATA[Astutik, Suci]]>;
<![CDATA[Solimun, Solimun]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 1 (2025): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol19iss1pp331-344
<![CDATA[Waste management remains a challenge, including in Batu City, East Java, Indonesia. Rapid population growth and economic activities in the city have resulted in a substantial increase in waste volume. One of the key factors in solving waste problems is the mindset of the community towards waste management. The application of statistical analysis methods can be an effective approach to solving problems related to waste management from an economic point of view. Nonparametric path analysis is a statistical method that does not rely on the assumption that the curve is known. Nonparametric path analysis is performed if the data does not fulfill the linearity assumption. This study aims to determine the best nonparametric path function with a hybrid truncated spline and kernel approach among EV values of 0.5; 0.8; and 1. In addition, this study also aims to test the significance of the best path function obtained. The data used in this study are timer data obtained from the Featured Basic Research Grant. The results showed that the best model of hybrid truncated spline and kernel nonparametric path analysis is a hybrid model of truncated spline nonparametric path of linear polynomial degree 1 knot and kernel triangle nonparametric path at EV 0.5. In addition, the significance of the best nonparametric truncated spline and kernel hybrid path function estimation using jackknife resampling shows that all exogenous variables have a significant effect on endogenous variables as evidenced by a p-value smaller than (0.05).]]>
<![CDATA[META-REGRESSION OF SOCIOECONOMIC FACTORS AND THE PREVALENCE OF PHYSICAL DISORDERS IN HYPERTENSIVE PATIENTS ]]>
<![CDATA[Rahmi, Nur Silviyah]]>;
<![CDATA[Astutik, Suci]]>;
<![CDATA[Surya Wardhani, Ni Wayan]]>;
<![CDATA[Maharani, Adinda Gita]]>;
<![CDATA[Fakhrunnisa, Atmadani Rahayu]]>;
<![CDATA[Khatimah, Husnul]]>;
<![CDATA[Aulia, Silvia Intan]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol19iss4pp2275-2286
<![CDATA[Hypertension is a common degenerative disease with a high mortality rate and a significant impact on quality of life and productivity. Education level plays a crucial role in understanding and managing hypertension, where higher education levels can contribute to reducing the risk of hypertension. This study utilized meta-analysis and meta-regression to explore the relationship between education level and hypertension prevalence. Secondary data from eight previous studies conducted between 2015 and 2023 were analyzed. Heterogeneity analysis was performed to determine the appropriate meta-analysis model, with a random-effect model selected based on the test results. Of the eight studies analyzed, five showed a negative odds ratio, indicating that individuals with higher education levels have a lower likelihood of developing hypertension compared to those with lower education levels. The heterogeneity test showed significant variability among the studies (I2 = 91.38%). The random-effect model estimated a combined effect size with an ln odds ratio of -0.1777 and a 95% confidence interval of -0.3228 to -0.0326. These findings suggest that higher education levels are associated with a lower risk of hypertension. This underscores the importance of improving access to quality education as part of public health strategies to reduce the incidence of hypertension and enhance overall community well-being.]]>
<![CDATA[Dual Optimization of Weighted Fuzzy Time-Series Forecasting: Particle Swarm Optimization and Lagrange Quadratic Programming ]]>
<![CDATA[Zamelina, Armando Jacquis Federal]]>;
<![CDATA[Astutik, Suci]]>;
<![CDATA[Fitriani, Rahma]]>
<![CDATA[ JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 3 (2024): July ]]>
Publisher : <![CDATA[Universitas Muhammadiyah Mataram ]]>
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DOI: 10.31764/jtam.v8i3.22554
<![CDATA[Time series Forecasting is one of crucial techniques that helps with strategic decision-making and mitigating potential risks –One of which is Weighted fuzzy time series (WFTS). Moreover, the interval length of the WFTS plays a crucial role in its modelization and accuracy in predicting future values. Therefore, this research implements a dual optimization on WFTS, which are (1) Particle Swarm Optimization to find the optimum interval length of the WFTS and (2) a Lagrange quadratic to optimize the weight of the fuzzy interval. In this research, a univariate Average Air Temperature located in Malang is used to perform forecasting model. The dataset is taken from BMKG-Indonesia. This research aims to acquire an optimized interval length on fuzzy time series forecasting, i.e., improving its accuracy by finding the optimal interval length. Based on the result, the proposed dual optimization model outperforms the classical WFTS on forecasting. The proposed model excels based on the evaluation matrix values. It has been noticed also that implementing PSO to find the optimum interval length has improved the accuracy of the classical WFTS. The classical WFTS has MAPE and RMSE of 2.4 and 0.73, respectively, while the proposed dual optimized model has 1.01 and 0.3. This approach identifies the best interval values and provides optimum weights related to each data point, providing solid insights for air temperature forecasting. ]]>
<![CDATA[A Combined Truncated Spline and Kernel Semiparametric Path Model Development ]]>
<![CDATA[Rohma, Usriatur]]>;
<![CDATA[Fernandes, Adji Achmad Rinaldo]]>;
<![CDATA[Astutik, Suci]]>;
<![CDATA[Solimun, Solimun]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/cauchy.v10i1.29849
<![CDATA[Semiparametric path analysis is a combination of parametric and nonparametric path analysis performed when the linearity assumption in some relationships is not met. In this study, the development of semiparametric path function estimation was carried out by combining two truncated spline and kernel approaches. In addition, the purpose of this study is to determine the significance of function estimation using t-test statistics at the jackknife resampling stage. This research was conducted in 135 Junrejo sub-districts of Batu district. The results showed that the development of a combined semiparametric path function estimation of truncated spline and kernel with weighted least square allows a more flexible and accurate estimation in modeling waste management behavior patterns. 2. The significance of the best truncated spline nonparametric path estimation in the model of the effect of Environmental Quality and the Use of Waste Banks on the Economic Benefits of Waste through the Use of the 3R Principles using t test statistics at the jackknife resampling stage shows that all exogenous variables have a significant effect on endogenous variables.]]>
<![CDATA[Geographically Weighted Random Forest Model for Addressing Spatial Heterogeneity of Monthly Rainfall with Small Sample Size ]]>
<![CDATA[Damayanti, Rismania Hartanti Putri Yulianing]]>;
<![CDATA[Astutik, Suci]]>;
<![CDATA[Astuti, Ani Budi]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/cauchy.v10i1.32161
<![CDATA[Rainfall modeling often involves complex spatial patterns that vary across locations. Traditional spatial models such as Geographically Weighted Regression (GWR) assume linear relationships and may fall short in capturing nonlinear interactions among predictors and the small sample size is more challenging to fix the assumptions. To address this limitation, this study applies the Geographically Weighted Random Forest (GWRF) method is a hybrid approach that integrates Random Forest (RF), a non-parametric machine learning algorithm with geographically weighted modeling. GWRF is advantageous as it accommodates both spatial heterogeneity and nonlinear relationships, making it suitable for modeling monthly rainfall, which is inherently spatially varied and influenced by complex factors. This study aims to implement and evaluate the performance of the GWRF model in monthly rainfall prediction across East Java. The model is tested using various numbers of trees to determine the optimal structure, and its performance is assessed using Root Mean Square Error (RMSE), Akaike Information Criterion (AIC), and corrected AIC (AICc). Results indicate that the model tends to overestimate the Out-of-Bag (OOB) Error at all tree variations, with the smallest RMSE (85.68) achieved at 750 trees. Humidity emerges as the most influential variable in predicting monthly rainfall in the region, based on variable importance analysis]]>
<![CDATA[Hyperparameter Optimization Approach in GRU Model: A Case Study of Rainfall Prediction in DKI Jakarta ]]>
<![CDATA[Mashfia, Fidia Raaihatul]]>;
<![CDATA[Astutik, Suci]]>;
<![CDATA[Sumarminingsih, Eni]]>
<![CDATA[ CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI ]]>
Publisher : <![CDATA[Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang ]]>
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DOI: 10.18860/cauchy.v10i1.32277
<![CDATA[Rainfall is a crucial factor in water resource management and disaster mitigation. This study develops a rainfall prediction model for DKI Jakarta using a Gated Recurrent Unit (GRU) with hyperparameter optimization to enhance prediction accuracy. Daily rainfall data is processed using a sliding window technique, where 30 days of historical data serve as input to predict rainfall on the 31st day. The model is trained with various configurations of batch sizes and the number of neurons in hidden layers to determine the optimal performance. The results of hyperparameter tuning show that the batch size configuration of 64, hidden layer 1 with 32 neurons, and hidden layer 2 with 128 neurons produces an MAE of 6.66 and an RMSE of 13.94. The model is quite good at capturing daily rainfall patterns but still has difficulty in predicting extreme rainfall spikes]]>
