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: Comparison Study of Distance Measures in Nonlinear Panel Data Clustering with K-Means Method
Abstrak: Analisis penggerombolan digunakan untuk mengelompokkan objek berdasarkan kesamaan karakteristik antar objek. Analisis gerombol biasanya diterapakan pada data cross section akan tetapi pada penelitian ini analisis gerombol diterapkan pada data panel nonlinier dengan menggunakan metode k-means. Pemilihan metode jarak sangat berpengaruh terhadap optimasi penggerombolan. Data yang digunakan dalam penelitian ini ada dua yaitu data simulasi dan data riil. Sehingga, tahap pertama dilakukan simulasi data untuk mendapatkan metode jarak terbaik pada data panel nonlinier. Metode jarak yang digunakan adalah Euclidean, Manhattan, Maximum, Frechet, dan Dynamic Time Warping (DTW). Berdasarkan hasil evaluasi seluruh skenario data simulasi dapat ditarik kesimpulan bahwa jika objek datanya tidak tumpang tindih dan memiliki rentang waktu yang panjang maka sebaiknya menggunakan metode jarak maksimum. Akan tetapi, jika objek datanya tumpang tindih dan memiliki rentang waktu yang pendek maka sebaiknya menggunakan metode jarak dtw atau frechet. Selanjutnya, implementasinya pada data Indonesian Coronavirus Disease (COVID-19) dengan tujuan untuk mengelompokkan Provinsi berdasarkan jumlah kasus positif aktif. Hasilnya menunjukkan bahwa jumlah cluster yang optimal ketika dibentuk tiga gerombol dengan nilai kriteria Calinski Harabatz (CH) sebesar 143.459. Gerombol A beranggotakan 30 anggota Provinsi, Gerombol B tiga anggota Provinsi, sedangkan Gerombol C satu anggota yaitu Provinsi DKI Jakarta., Cluster analysis is used to group objects based on the similarity of characteristics between objects. Cluster analysis is usually applied to cross-sectional data, but in this study, cluster analysis was applied to nonlinear panel data using the K-Means method. The selection of the right distance measure affects the optimization of clustering. The data used in this study are simulation data and real data, so the first stage of the research was carried out by simulating data to obtain the best distance measure on nonlinear panel data. The distance measure used is Euclidean, Manhattan, Maximum, Fréchet, and Dynamic Time Warping (DTW). Based on the evaluation results of all simulation data scenarios, it can be concluded that if the data objects do not overlap and have a long time span, it is better to use the maximum distance measure. If the data objects overlap and have a short time span, then we recommend using the DTW or Fréchet spacing method. Furthermore, the implementation is carried out on Indonesian Coronavirus Disease (COVID-19) data with the aim of grouping Provinces based on the number of active positive cases. The results show that the number of clusters is optimal when three clusters are formed, with the value of the Calinski Harabatz (CH) criteria of 143,459. Cluster A consists of 30 provinces, Cluster B consists of three provinces, while Cluster C consists of one province, DKI Jakarta Province. Keywords: Coronavirus Disease; Calinski-
Keyword: Coronavirus Disease, Calinski-Harabatz, Dynamic Time Warping, Frechet, Maximum, K-Means

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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