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: Kajian Self-Organizing Maps (SOM) dalam pengelompokan objek (studi kasus: pengelompokan desa/kelurahan di Kabupaten Wajo Sulawesi Selatan)
Abstrak: Clustering is a process of classifying objects into groups which have similarity. The result of clustering will show that objects in one cluster will be more homogeneous than others. There are two methods in classic clustering analysis i.e. hierarchical cluster method and non-hierarchical cluster method. Determination of the number of clusters which formed by them is done subjectively. The cluster other methods also developed by using artificial intelligence. Artificial neural network is an information processing paradigm that inspired by the biology systems, it is neuron. Like brain which process information. Self-organizing maps (SOM) is one of the topology of Unsupervised Artificial Neural Network (Unsupervised ANN) which process does not require monitoring in his training. Application clustering using SOM algorithm is expected to be used as a tool to analyze the data in order to obtain the characteristics of the data that will be grouped. Clustering is used to group the data naturally without based on the specific class target. In this study, SOM compared with clustering method with large data sizes, it was two-step cluster. According to Bacher (2004), two-step cluster method (TSC) was a cluster method which can resolve the problem clustering measurement scale, especially for large data with variables which have categorical and numerical data types. Performance clustering SOM and two-step cluster method compared by the simulation data, afterwards, applying the method of SOM on clustering villages/urbans in Wajo regency, South Sulawesi. The data in this study consisted of two sources i.e. simulated data and secondary data. Simulated data was generated data multivariate distribution (μ,Ʃ) which useful to measure the performance of two-step cluster method and SOM in classifying an object. Secondary data, which used in this study, BPS’s data in Wajo regency, South Sulawesi, was Village Potential Data (VPD) in 2011. Simulation data was the generated data numeric type (M) which consisted of three forms of the population i.e. a). a population consisted of three clusters were clearly separated, b). a population which consisted of three clusters of overlapping (overlap) each other in small numbers, and c). a population that consisted of three clusters of overlapping (overlap) each other in large numbers. The results of methods SOM and TSC showed that simulation data has the good ability to classify data, however, TSC provides better clustering results for large data sizes than SOM. In addition, it is also showed that the larger the number of data, the misclassification of SOM would become larger, nevertheless, the changes were relatively smaller. In the other hand, the larger the number of data the misclassification of TSC method was become smaller. Secondary data, which used in this study, written documentation and identification of used variables about areas/villages in Wajo regency, South Sulawesi, was Village Potential Data (VPD) in 2011 i.e. : X1 (total population), X2 (family farm), X3 (family farm laborer), X4 (family power user), X5 (fuel for daily cooking), X6 (educational facilities), X7 (health personnel), X8 (population mortality). Objects in this research were applied around the village/urbans in Wajo district. The results of clustering with SOM method, village/urbans in the Wajo regency produced
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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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