Jurnal Riset dan Aplikasi Matematika (JRAM)

IMPLEMENTATION OF FRACTAL DIMENSIONS BOX COUNTING AND K-MEANS IN THE CLASSIFICATION OF EYE DISEASES BASED ON RETINAL FUNDUS IMAGES

Theresa Noriko Siregar, Dwi Juniati — Tue, 14 Nov 2023 00:00:00 +0700

The eyes are one part of the body that has an important role in human life. Like vision, the eye has parts that have their respective functions, both the outer parts such as the eyelids and eyebrows, and the inner parts of the eye such as the cornea, retina, and pupil. Visual impairment refers to any condition that affects the eye's ability to see clearly or function optimally. Visual impairment can affect various aspects of daily life and requires appropriate care and treatment. To differentiate between various types of eye disease, you can take pictures of the fundus of the retina. In this study, an introduction to the characteristics of each eye disease was carried out, namely Diabetic Retinopathy, Pathological Myopia, Hypertension Retinopathy, and Macular Degeneration. A total of 100 retinal fundus images were used in this research. The first step was to convert the image into RGB form and then carry out several image segmentation processes on the retinal fundus, namely green channel, CLAHE, morphological opening, and complement image (negative image). The image is then used to identify eye disease using edge detection using the Canny method. Furthermore, by using the
fractal dimension box-counting method, the resulting dimensional values are used in the clustering process. The resulting dimension values will be classified using the K-means grouping method with five clusters with an accuracy of 89%.
Keywords: Diabetic Retinopathy, Pathological Myopia, Hypertension Retinopathy, Age-related Macular Degeneration, Box Counting, K-Means.

DINAMIKA MODEL MANGSA-PEMANGSA LOTKA VOLTERRA DENGAN ADANYA KERJA SAMA BERBURU PADA PEMANGSA

Safinadin Indira Salwa, Lintang Alea Shakira, Dian Savitri — Tue, 14 Nov 2023 00:00:00 +0700

Artikel ini membahas model mangsa-pemangsa Lotka Volterra dengan adanya kerja sama berburu pada pemangsa. Sistem dianalisis dengan menentukan titik kesetimbangan dan kestabilan lokal masing-masing solusi yang menghasilkan analisis kestabilan sebanyak empat buah titik kestabilan, yaitu titik kepunahan semua populasi yang tidak stabil, titik kepunahan populasi pemangsa stabil dengan syarat, serta dua titik interior kedua populasi yang stabil dengan syarat tertentu. Simulasi numerik dilakukan untuk mengetahui kesesuaian hasil analisis dan perubahan solusi sistem karena adanya kerja sama berburu pada pemangsa berupa potret fase menggunakan P-Plane. Hasil analisis kestabilan dan simulasi numerik menunjukkan kestabilan ganda (bistabil) pada titik interior dan titik kepunahan populasi pemangsa saat parameter kerja sama berburu dengan dan Perubahan parameter kerja sama mempengaruhi titik kesetimbangan interior. Penurunan parameter kerjasama berburu pada pemangsa dapat menyebabkan perubahan titik interior.

This article discusses the Lotka Volterra prey-predator model in which predators cooperate in hunting. System analysis is carried out by determining the balance point and local stability of each solution which results in a stability analysis of four stability points, namely the extinction point of the entire unstable population, the extinction point of a stable predator population under certain conditions, and the extinction point of a stable predator population under certain condition, and two interior points of two populations that are stable under certain conditions. Numerical simulations were carried out to determine the suitability of the analysis results and changes in system solutions due to cooperative predator hunting in the form of phase portraits using P-Plane. The results of stability analysis and numerical simulations show dual stability (bistable) at the interior point and extinction point of the predator population when the hunting parameters are cooperative with and Changes in cooperation parameters affect the interior balance point. Decreased hunting cooperation parameters in predators can cause changes in interior points.

CLASSIFICATION OF NOCTURNAL BIRDS BASED ON SOUND USING HIGUCHI FRACTAL DIMENSION AND K-NEAREST NEIGHBOR

Agustina Surya Dewi, Dwi Juniati — Sat, 04 Nov 2023 00:00:00 +0700

Burung nokturnal merupakan jenis burung yang aktif di malam hari sehingga menjadi sulit untuk ditemui keberadaannya. Namun, suara khas yang dihasilkan setiap burung dapat dimanfaatkan untuk mendeteksi keberadaan suatu spesies burung nokturnal dengan mengklasifikasikan burung nokturnal menggunakan nilai dimensi fraktal. Pada penelitian ini akan diklasifikasikan burung nokturnal menggunakan metode Higuchi dan K-Nearest Neighbor (KNN). Pada penelitian ini digunakan sebanyak 120 data dengan masing-masing 15 data untuk 8 spesies burung yang berbeda, yaitu Eastern whip-poor-will, Eurasian stone-curlew, European nightjar, kowak-malam Abu, Pauraque, Short-tailed nighthawk, Striped owl, dan Long-tailed Potoo. Tahap pertama dilakukan pre-processing pada data dan dilanjutkan dengan ekstraksi ciri data sinyal suara menggunakan Discrete Wavelet Transform (DWT) dengan tipe mother wavelet Daubechies 4 dengan dekomposisi 5 level. Setelah itu, dicari nilai dimensi fraktalnya dengan metode Higuchi. Nilai dimensi fraktal yang diperoleh dibagi menjadi data latih dan data uji yang selanjutnya diklasifikasikan dengan metode KNN. Dari penelitian ini diperoleh akurasi tertinggi sebesar 87,5% pada K-max metode Higuchi 50 dan 60 dengan k=3 pada KNN. Hal ini menunjukkan bahwa dimensi fraktal Higuchi dan metode pengklasifikasian KNN dapat digunakan untuk mengklasifikasikan burung nokturnal berdasarkan suara.

Nocturnal birds are birds that are active at night, making them difficult to find. However, the distinctive sound produced by each bird can be utilized to detect the presence of nocturnal birds by classifying nocturnal birds using fractal dimension values. In this study, nocturnal birds will be classified using the Higuchi and K-Nearest Neighbor (KNN) methods. In this study, 120 data were used with 15 data each for 8 different bird species, i.e. Eastern whip-poor-will, Eurasian stone-curlew, European nightjar, black-crowned night heron, Pauraque, Short-tailed nighthawk, Striped owl, and Long-tailed Potoo. The first step is pre-processing the data and continuing with the extraction of sound signal data characteristics using Discrete Wavelet Transform (DWT) with Daubechies 4 mother wavelet type with 5-level decomposition. After that, the fractal dimension value is sought using the Higuchi method. The fractal dimension values obtained are divided into training data and test data which are then classified by the KNN method. From this study, the highest accuracy of 87.5% was obtained at K-max of Higuchi method 50 and 60 with k = 3 in KNN. This shows that the Higuchi fractal dimension and KNN method can be used to classify nocturnal birds based on sound.

PENGGUNAAN GEOGRAPHICALLY WEIGHTED REGRESSION PADA PENGELOMPOKAN KABUPATEN/KOTA PROVINSI JAWA TIMUR DIDASARKAN RATA-RATA LAMA SEKOLAH

Fenny Fitriani, SESIALIA INA, WARA PRAMESTI — Mon, 30 Oct 2023 00:00:00 +0700

Pada tahun 2022, rata-rata lama sekolah penduduk di Jawa Timur masih berada di bawah rata-rata lama sekolah keseluruhan penduduk Indonesia. Dimana kabupaten yang paling rendah rata-rata lama sekolahnya adalah Kabupaten Sampang sebesar 5,06 dan paling tinggi pada Kota Madiun sebesar 11,67. Perbedaan signifikan ini dimungkinkan karena adanya pengaruh faktor area. Hal ini membutuhkan suatu penelitian yang dapat mengelompokkan area-area yang memiliki kesamaan permasalahan rata-rata lama sekolah. Hasil pengelompokan ini bisa menjadi dasar untuk menentukan tindakan yang sesuai dengan faktor signifikan yang dibutuhkan pada area tersebut. Pada artikel ini dijabarkan pengelompokan faktor-faktor yang mempengaruhi rata-rata lama sekolah di Jawa Timur dengan menggunakan metode. Geographically Weighted Regression (GWR). Metode ini dipilih karena pada metode proses analisis dilakukan dengan memperhatikan efek area pengamatan yang dilakukan. Faktor-faktor yang dianggap mempengaruhi yaitu variabel harapan lama sekolah, pengeluaran per kapita riil disesuaikan, tingkat tengangguran terbuka, rata-rata upah/gaji bersih sebulan pekerja formal, dan tingkat partisipasi angkatan kerja. Dari hasil analisis, didapatkan faktor signifikan yang paling banyak mempengaruhi adalah harapan lama sekolah dan yang peling sedikit mempengaruhi adalah persentase tingkat tengangguran terbuka.

In 2022, the average years of schooling of the population in East Java is still below the overall average years of schooling of the Indonesian population. The district with the lowest average years of schooling is Sampang District at 5.06 and the highest is Madiun City at 11.67. This significant difference may be due to the influence of area factors. This requires a study that can group areas that have similar average years of schooling problems. The results of this grouping can be the basis for determining actions that are in accordance with the significant factors needed in the area. This article describes the clustering of factors that affect the average length of schooling in East Java using the method. Geographically Weighted Regression (GWR). This method was chosen because in the method the analysis process is carried out by considering the effect of the observation area. The factors that are considered to influence are expected years of schooling, adjusted real per capita expenditure, open unemployment rate, average monthly net wage/salary of formal workers, and labor force participation rate. From the results of the analysis, it was found that the most significant factor affecting the average years of schooling is the expected years of schooling and the least influential is the percentage of open unemployment rate.

PEMODELAN JUMLAH KASUS BARU HARIAN COVID-19 DI INDONESIA MENGGUNAKAN GAUSSIAN MIXTURE MODEL

Fevi Novkaniza, Nico, Rahmat Al Kafi — Mon, 30 Oct 2023 00:00:00 +0700

Penyakit COVID-19 adalah penyakit menular yang disebabkan oleh virus severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Selama masa pandemi COVID-19 terjadi beberapa kali lonjakan jumlah kasus baru COVID-19 yang menunjukkan adanya kesulitan dalam mengantisipasi peningkatan penyebaran COVID-19. Artikel ini membahas pemodelan jumlah kasus baru harian COVID-19 di Indonesia dari 1 Januari 2021 sampai 31 Maret 2022 menggunakan Gaussian Mixture Model (GMM). GMM merupakan salah satu mixture model dimana setiap komponen campuran diasumsikan berdistribusikan Gaussian. GMM dikonstruksi mengggunakan beberapa komponen campuran dan parameter dari setiap GMM diestimasi menggunakan metode maximum likelihood estimation (MLE) melalui algoritma Expectation-Maximization (EM). Berdasarkan nilai Akaike Information Criteria (AIC), diperoleh GMM dengan 4 komponen merupakan model terbaik untuk pemodelan data jumlah kasus baru harian COVID-19 di Indonesia. Berdasarkan menggunakan model GMM terbaik, diperoleh probabilitas jumlah kasus baru harian COVID-19 di Indonesia kurang dari jumlah kasus harian terendah adalah 0,01, lebih dari jumlah kasus harian rata-rata adalah 0,3 dan lebih dari jumlah kasus harian tertinggi adalah 0,017.

COVID-1 is an infectious disease caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). During the COVID-19 pandemic, there were several spikes in the number of new COVID-19 cases, which shows that there are difficulties in anticipating the increase in the spread of COVID-19. This article discusses modelling the number of daily new cases of COVID-19 in Indonesia from 1st January 2021 to March 31, 2022, using the Gaussian Mixture Model (GMM). GMM is a mixture model where each mixture component is assumed to have a Gaussian distribution. GMM is constructed using several mixed components, and the parameters of each GMM are estimated using the maximum likelihood estimation (MLE) method via the Expectation-Maximization (EM) algorithm. Based on the Akaike Information Criteria (AIC) values, it was found that GMM with 4 components is the best model for modelling data on the number of daily new cases of COVID-19 in Indonesia. Based on the best GMM model, the probability that the number of new daily COVID-19 cases in Indonesia is less than the lowest number of daily cases is 0.01, more than the average number of daily cases is 0.3, and more than the highest number of daily cases is 0.017.