Distance Functions Study in Fuzzy C-Means Core and Reduct Clustering

Fuzzy C-Means is a distance-based clustering process which applied by fuzzy logic concept. Clustering process worked in linear to the iteration process to minimizing the objective function. The objective function is an addition of the multiplication between the coordinates distance towards their closest cluster centroid and their membership degree. The more the iteration process, the objective function should get lower and lower. The objective of this research is to observe whether the distances which usually applied are able to fulfill the aforementioned hypothesis for determining the most suitable distance for Fuzzy C-Means clustering application. Few distance function was applied in the same dataset. 5 standard datasets and 2 random datasets were used to test the fuzzy c-means clustering performance with the 7 different distance function. Accuracy, purity, and Rand Index also applied to measure the quality of the resulted cluster. The observation result depicted that the distance function which resulted in the best quality of clusters are Euclidean, Average, Manhattan, Minkowski, Minkowski-Chebisev, and Canberra distance. These 6 distances were able to fulfill the basic hypothesis of the objective function behavior on Fuzzy C-Means Clustering method. The only distance who were not able to fulfill the basic hypothesis is Chebisev distance

Pemodelan Persamaan Navier-Stokes untuk Aliran Fluida Tidak Termampatkan

Kajian ini membahas pemodelan persamaan Navier-Stokes pada aliran fluida yang tidak termampatkan. Fluida diasumsikan tidak mengalami perubahan massa jenis(densitas) akibat aliran. Pemodelan persamaan ini didasarkan pada hukum-hukum dasar fisika yaitu hukum kekekalan massa dan hukum Newton dua. Tujuan skripsi ini adalah memodelkan aliran fluida ke dalam bentuk persamaan diferensial yang kemudian dapat dicari aproksimasi solusinya dan dapat disimulasikan secara numerik menggunakan metode beda hingga. Metode yang digunakan pada skripsi ini berupa studi pustaka dengan mengkaji dan mengembangkan literatur yang berhubungan dengan persamaan Navier-Stokes untuk aliran fluida yang tidak termampatkan dan ilmu mekanika fluida. Berdasarkan hukum kekekalan massa diperoleh persamaan kontinuitas kemudian berdasarkan hukum Newton ke-dua diperoleh persamaan momentum, kedua persamaan ini digabungkan menjadi suatu sistem persamaan diferensial parsiel nonlinear orde dua yang dikenal sebagai persamaan Navier-Stokes. Aliran dalam rongga disimulasikan secara grafis menggunakan persamaan yang telah diperoleh dan menghasilkan simulasi yang merepresentasikan aliran fluida sesungguhnya pada aliran dalam rongga

Similarity check Pemodelan Persamaan Navier-Stokes untuk Aliran Fluida Tidak Termampatkan

Kajian ini membahas pemodelan persamaan Navier-Stokes pada aliran fluida yang tidak termampatkan. Fluida diasumsikan tidak mengalami perubahan massa jenis(densitas) akibat aliran. Pemodelan persamaan ini didasarkan pada hukum-hukum dasar fisika yaitu hukum kekekalan massa dan hukum Newton dua. Tujuan skripsi ini adalah memodelkan aliran fluida ke dalam bentuk persamaan diferensial yang kemudian dapat dicari aproksimasi solusinya dan dapat disimulasikan secara numerik menggunakan metode beda hingga. Metode yang digunakan pada skripsi ini berupa studi pustaka dengan mengkaji dan mengembangkan literatur yang berhubungan dengan persamaan Navier-Stokes untuk aliran fluida yang tidak termampatkan dan ilmu mekanika fluida. Berdasarkan hukum kekekalan massa diperoleh persamaan kontinuitas kemudian berdasarkan hukum Newton ke-dua diperoleh persamaan momentum, kedua persamaan ini digabungkan menjadi suatu sistem persamaan diferensial parsiel nonlinear orde dua yang dikenal sebagai persamaan Navier-Stokes. Aliran dalam rongga disimulasikan secara grafis menggunakan persamaan yang telah diperoleh dan menghasilkan simulasi yang merepresentasikan aliran fluida sesungguhnya pada alira

The Suitable Distance Function for Fuzzy C-Means Clustering

Fuzzy C-Means clustering is a form of clustering based on distance which apply the concept of fuzzy logic. The clustering process works simultaneously with the iteration process to minimize the objective function. This objective function is the summation from the multiplication of the distance between the data coordinates to the nearest cluster centroid with the degree of which the data belong to the cluster itself. Based on the objective function equation, the value of the objective function will decrease by increasing the number of iteration process. This research provide how we choose the suitable distance for Fuzzy C-Means clustering. The right distance will meet the optimization problem in the Fuzzy CMeans Clustering method and produce good cluster quality. They are Euclidean, Average, Manhattan, Chebisev, Minkowski, Minkowski-Chebisev, and Canberra distance. We use five UCI Machine Learning dataset and two random datasets. We use the Lagrange multiplier method for the optimization of this method. The result quality of the cluster measure by their accuracy, Davies Bouldin Index, purity, and adjusted rand index. The experiment shows that the Canbera distances are the best distances which provide the optimum result by producing minimum objective function 378.185. The suitable distance for the application of the Fuzzy C-Means Clustering method are Euclidean distance, Average distance, Manhattan distance, Minkowski distance, Minkowski-Chebisev distance, and Canberra distance. These six distances produce a numerical simulation that derives the objective function fairly constant. Meanwhile, the Chebisev distance shows the movement of the value of the objective function that fluctuates, so it is not in accordance with the optimization problem in the Fuzzy C Means Clustering method

Similarity The Suitable Distance Function for Fuzzy C-Means Clustering

Fuzzy C-Means is a distance-based clustering process which applied by fuzzy logic concept. Clustering process worked in linear to the iteration process to minimizing the objective function. The objective function is an addition of the multiplication between the coordinates distance towards their closest cluster centroid and their membership degree. The more the iteration process, the objective function should get lower and lower. The objective of this research is to observe whether the distances which usually applied are able to fulfill the aforementioned hypothesis for determining the most suitable distance for Fuzzy C-Means clustering application. Few distance function was applied in the same dataset. 5 standard datasets and 2 random datasets were used to test the fuzzy c-means clustering performance with the 7 different distance function. Accuracy, purity, and Rand Index also applied to measure the quality of the resulted cluster. The observation result depicted that the distance function which resulted in the best quality of clusters are Euclidean, Average, Manhattan, Minkowski, Minkowski-Chebisev, and Canberra distance. These 6 distances were able to fulfill the basic hypothesis of the objective function behavior on Fuzzy C-Means Clustering method. The only distance who were not able to fulfill the basic hypothesis is Chebisev distance