Judul: Optimization of Provincial Clustering Based on Sustainable Development Goals with Hierarchical Clustering, K-Medoids, and DBSCAN
Abstrak: Analisis gerombol merupakan teknik statistika untuk mengidentifikasi gerombol bermakna dari objek data multivariat berdasarkan ukuran kemiripan. Selain memilih ukuran kemiripan, ketepatan dalam menerapkan metode pembentukan gerombol juga menjadi hal fundamental. Karakteristik data dapat memengaruhi performa analisis gerombol. Data multidimensional dengan jumlah dimensi yang besar memiliki tantangan adanya curse of dimensionality. Salah satu cara mengatasi masalah tersebut adalah dengan melakukan reduksi dimensi. Penelitian ini mengevaluasi performa metode reduksi dimensi analisis komponen utama dan t-SNE, serta membandingkan tiga metode penggerombolan yaitu metode hierarki, metode partisi dengan algoritma K-Medoids, dan metode berbasis kepekatan dengan algoritma Density-Based Spatial Clustering of Applications with Noise (DBSCAN) pada data multidimensi, studi kasus penggerombolan provinsi berdasarkan tujuan pembangunan berkelanjutan (TPB). Evaluasi kinerja hasil penggerombolan didasarkan pada tiga indeks validitas. Hasil penelitian menunjukkan bahwa kombinasi t-SNE dengan algoritma hierarki pautan tunggal atau dengan DBSCAN menghasilkan gerombol paling optimal dengan nilai Silhouette tertinggi (0,56), indeks Davies-Bouldin terendah (0,47), dan indeks Calinski-Harabasz tertinggi (75,04) dibandingkan hasil penggerombolan algoritma lainnya. Penggerombolan optimal tersebut menghasilkan tujuh gerombol provinsi dengan karakteristik pencapaian TPB yang berbeda. Terdapat dua gerombol yang menunjukkan pencapaian TPB rendah, sehingga memerlukan perhatian ekstra sesuai dengan karakteristiknya masing-masing. Gerombol-gerombol tersebut terdiri atas provinsi di wilayah timur Indonesia., Cluster analysis is a statistical technique used to identify meaningful clusters from multivariate data objects based on similarity measures. In addition to choosing the right similarity measures, the accuracy in applying clustering methods is also fundamental. The characteristics of the data can influence the performance of cluster analysis. Multidimensional data with many dimensions face the challenge known as the curse of dimensionality. Dimensionality reduction helps address this issue. This study evaluates the performance of two dimensionality reduction methods, principal component analysis and t-SNE, and compares three clustering methods: hierarchical clustering, K-Medoids, and Density-Based Spatial Clustering of Applications with Noise (DBSCAN). The study focuses on clustering provinces based on sustainable development goals (SDGs). Clustering performance is evaluated using three validity indices. Results indicate that combining t-SNE with the single-linkage hierarchical algorithm or DBSCAN produces the most optimal clusters. These methods achieve the highest Silhouette score (0.56), the lowest Davies-Bouldin index (0.47), and the highest Calinski-Harabasz index (75.04) compared to other algorithms. The optimal clustering results in seven distinct clusters of provinces with different SDGs achievement characteristics. Two clusters, comprising provinces in eastern Indonesia, show low SDGs achievement and require extra attention based on their specific characteristics.
Keyword: cluster analysis, DBSCAN, principal component analysis, sustainable development goals, t-SNE

Judul: Application of the DBSCAN Algorithm for Clustering City/Regency in West Java Based on Food Insecurity Indicators
Abstrak: Terdapat beberapa permasalahan umum ketika melakukan analisis gerombol, diantaranya adalah adanya “curse of dimensionality” di ruang dimensi tinggi dan adanya bentuk gerombol yang tidak beraturan (arbitrary) serta kehadiran outlier. Permasalahan tersebut dapat diatasi dengan melakukan reduksi dimensi terlebih dahulu dan menggunakan analisis gerombol yang berbasis kepadatan. Kerawanan pangan merupakan salah satu permasalahan utama yang menjadi isu global bagi sebagian besar negara. Di Indonesia terdapat FSVA (Food Security and Vulnerability Atlas) yang merupakan peta tematik visualisasi geografis wilayah rentan terhadap kerawanan pangan. Penentuan status rawan pangan suatu daerah pada FSVA diukur dengan analisis yang relatif sederhana yaitu metode pembobotan pada sembilan indikator kerawanan pangan kronis. Pada penelitian kali ini, penggerombolan wilayah yang rentan terhadap kerawanan pangan untuk kota/kabupaten di Jawa Barat dilakukan dengan metode machine learning dan indikator yang digunakan lebih beragam (25 peubah) untuk menghasilkan gerombol yang lebih baik. Penggerombolan dilakukan dengan metode DBSCAN (DensityBased Spatial Clustering of Applications with Noise) pada data yang telah direduksi dimensi terlebih dahulu menggunakan metode t-SNE (t-Distributed Stochastic Neighbor Embedding). Data yang digunakan dalam penelitian ini adalah data Susenas (Survei Sosial Ekonomi Nasional) tahun 2020 untuk provinsi Jawa Barat. Hasil penggerombolan terbaik ditentukan berdasarkan parameter optimal yang dievaluasi menggunakan koefisien Silhouette dan indeks DBCV (Density Based Clustering Validation). Parameter optimal yang menghasilkan koefisien Silhouette dan indeks DBCV tertinggi diperoleh pada perplexity = 1, epsilon = 31, dan minPts = 2. Penggerombolan terbaik menghasilkan lima gerombol dengan tidak ada outlier., There are several common problems when performing cluster analysis, including the existence of a “curse of dimensionality” in high-dimensional space and the presence of arbitrary cluster shapes, and also the presence of outliers. These problems can be solved by reducing the dimensions first and using density-based cluster analysis. Food insecurity is one of the main problems that become a global issue for most countries. In Indonesia, there is an FSVA (Food Security and Vulnerability Atlas) which is a thematic map visualizing geographical areas vulnerable to food insecurity. Determination of the food insecurity status of an area on the FSVA is measured by relatively simple analysis, namely the weighting method on nine indicators of chronic food insecurity. In this study, clustering of areas that are vulnerable to food insecurity for cities/districts of West Java is carried out using machine learning methods and the indicators used are more diverse (25 variables) to produce better clusters. Clustering is performed using the DBSCAN (Density-Based Spatial Clustering of Applications with Noise) method on data that has been reduced in dimensions first using t-SNE (t-Distributed Stochastic Neighbor Embedding). The data used in this study is the 2020 Susenas (Survei Sosial Ekonomi Nasional) data for the province of West Java. The best clustering result is determined based on the optimal parameters evaluated using the Silhouette coefficient and the DBCV (Density-Based Clustering Validation) index. Optimal parameters that produce the highest Silhouette coefficient and DBCV index are obtained at perplexity = 1, epsilon = 31, and minPts = 2. The best clustering results in five clusters with no outliers.
Keyword: cluster analysis, DBSCAN, dimensionality reduction, food insecurity, t-SNE

Judul: Hamiltonian formulation for linear waves motion in two layers fluid
Abstrak: The surface wave could be considered as a wave that separates two fluids, namely water and air. Based on this assumption, it is introduced the interfacial wave, a wave between two layers of fluid with different density. The formulation of interfacial waves motion begins with deriving the base equation of irrotational ideal fluid. Furthermore, according to irrotational fluid assumption, the base equation can be stated in velocity potential. In this derivation, the fluids domain is assumed to be restricted by rigid lid boundary conditions, both at the upper and lower limit. Therefore, the interfacial waves motion can be explained in a hamiltonian formulation. In the hamiltonian formulation, total energy is defined as the sum of kinetic and potential energy. The hamiltonian system is obtained from reduction of kinetic energy by using the Dirichlet Neumann Operator. The resulted kinetic energy equation is nonlinear. Therefore, this form is linearized by first part of the Taylor expansion. This linearization gives a dispersion relation of linear wave. Based on this dispersion relation, the phase speed of the linear wave depends on the density ratio of the two layers fluid.
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