Judul: Integrasi Self Organizing Maps dan Algoritme K-means untuk Clustering Data Ketahanan Pangan Kabupaten di Wilayah Provinsi Bali, Nusa Tenggara Barat, dan Nusa Tenggara Timur
Abstrak: The assessment of food security as a measure of development is very important. Food security in a region has multidimentional characteristics that need to be analyzed. The purpose of this research is to implement the S-K algorithm (combination of Self organizing maps -SOM- and K-means algorithm) for data clustering and to gain data characteristics as the result of data clustering. The used data is the indicator for the food security from 30 districts in the provinces of Bali, Nusa Tenggara Barat, and Nusa Tenggara Timur. These data are the input for S-K algorithm. SOM clustering result is validated using Davies-Bouldin Index (DBI). Centroid and the number of cluster from SOM are utilized as the input for K-means algorithm, which is used to refine the final cluster. In this research, these data are also clustered by K-means algorithm with randomly generated initial centroids. The value of DBI results of SOM, S-K, K-means clustering has been compared and it is found that S-K algorithm has the minimum value of DBI. Thus, it is proved that the S-K algorithm gives good clustering results. Based on the data analysis, the districts in the Province of Nusa Tenggara Timur are categorized as the areas with food insecurity. Meanwhile, the districts in the Province of Nusa Tenggara Barat are included in the relatively food insecurity areas. Food security in all districts in the Province of Bali are satisfactory.
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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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