General fuzzy C-means clustering algorithm using Minkowski metric

<span id="docs-internal-guid-94842888-7fff-2ae1-cd5c-026943b95b7f"><span>Cancer is one of the diseases with the highest mortality rate in the world. Cancer is a disease when abnormal cells grow out of control that can attack the body's organs side by side or spread to other organs. Lung cancer is a condition when malignant cells form in the lungs. To diagnose lung cancer can be done by taking x-ray images, CT scans, and lung tissue biopsy. In this modern era, technology is expected to help research in the field of health. Therefore, in this study feature extraction from CT images was used as data to classify lung cancer. We used CT scan image data from SPIE-AAPM Lung CT challenge 2015. Fuzzy C-Means and fuzzy kernel C-Means were used to classify the lung nodule from the patient into benign or malignant. Fuzzy C-Means is a soft clustering method that uses Euclidean distance to calculate the cluster center and membership matrix. Whereas fuzzy kernel C-Means uses kernel distance to calculate it. In addition, the support vector machine was used in another study to obtain 72% average AUC. Simulations were performed using different k-folds. The score showed fuzzy kernel C-Means had the highest accuracy of 74%, while fuzzy C-Means obtained 73% accuracy. </span></span>

Measures of similarity and detection of miniature foreign bodies in packaged foods

Multi-view collaborative locally adaptive clustering with Minkowski metric

Spectral clustering has become a typical and efficient clustering method used in a variety of applications. The critical step of spectral clustering is the similarity measurement, which largely determines the performance of the spectral clustering method. In this paper, we propose a novel spectral clustering algorithm based on the local similarity measure of shared neighbors. This similarity measurement exploits the local density information between data points based on the weight of the shared neighbors in a directed k $$ k $$ -nearest neighbor graph with only one parameter k $$ k $$ , that is, the number of nearest neighbors. Numerical experiments on synthetic and real-world datasets demonstrate that our proposed algorithm outperforms other existing spectral clustering algorithms in terms of the clustering performance measured via the normalized mutual information, clustering accuracy, and F $$ F $$ -measure. As an example, the proposed method can provide an improvement of 15.82% in the clustering performance for the Soybean dataset.

A current assumption of most clustering methods is that the training data and future data are taken from the same distribution. However, this assumption may not hold in most real-world scenarios. In this article, we propose an information theoretical importance sampling based approach for clustering problems (ITISC), which minimizes the worst case of expected distortions under the constraint of distribution deviation. The distribution deviation constraint can be converted to the constraint over a set of weight distributions centered on the uniform distribution derived from importance sampling. The objective of the proposed approach is to minimize the loss under maximum degradation hence the resulting problem is a constrained minimax optimization problem, which can be reformulated as an unconstrained problem using the Lagrange method. The optimization problem can be solved by either an alternating optimization algorithm or a general optimization routine by commercially available software. Experiment results on synthetic datasets and a real-world load forecasting problem validate the effectiveness of the proposed model. Furthermore, we demonstrate that fuzzy c-means is a special case of ITISC with the logarithmic distortion, and this observation provides an interesting physical interpretation for fuzzy exponent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m$</tex-math></inline-formula>.

Clustering is one of unsupervised classification method, that is, it classifies a data set into some clusters without any external criterion. Typical clustering methods, e.g. k-means (KM) and fuzzy c-means (FCM) are constructed based on optimization of the given objective function. Many clustering methods as well as KM and FCM are formulated as optimization problems with typical objective functions and constraints. The objective function itself is also an evaluation guideline of results of clustering methods. Considering together with its theoretical extensibility, there is the great advantage to construct clustering methods in the framework of optimization. From the viewpoint of optimization, some of the authors proposed an even-sized clustering method based on optimization (ECBO), which is with strengthened constraints of cluster size, and constructed some variations of ECBO. The constraint considered in ECBO is that each cluster size is K or K + 1. ECBO is based on KM and its algorithm is constructed as iterative optimization. The belongingness of each object to clusters are calculated by the simplex method in each iteration. The numerical experiments show that ECBO has higher classification accuracy than other similar clustering methods. It is considered that ECBO has the advantage in the viewpoint of clustering accuracy, cluster size, and optimization framework than other similar methods. However, the constraint of cluster sizes of ECBO is strict so that it may be inconvenient in case that the partition results, of which each cluster size need not be strictly even, but uneven, is desirable. Moreover, it is expected that new clustering algorithms of which each cluster size can be controlled can deal with more various datasets. In this paper, we first propose two new clustering algorithms based on ECBO. Each cluster size can be controlled in the proposed algorithms. Next, we estimate the new clustering algorithms through some numerical experiments.

Kernel-based fuzzy clustering and fuzzy clustering: A comparative experimental study

Hyperspectral image clustering is usually used for unsupervised learning in different applications. However, the traditional clustering methods have not been considered the complex relationships among neighbouring pixels. The Albedo and Shading elements can define pixel values in the HyperSpectral Images (HSIs). In HSIs, features are different from each other because of their natural physical characteristics and the physical nature of different image features can be described by the Albedo element. Therefore, in this paper, we generate the natural Albedo feature of the HSIs by applying Albedo recovery step to exploit main information from HSIs. Then, we utilized the Fuzzy C-means clustering method to cluster the natural Albedo dataset. In this paper, we propose a novel accurate Albedo Recovery based Fuzzy C-Means (ARFCM) method to cluster HSIs. In the dataset, each feature vector is processed by the Albedo recovery step to create a new feature vector. This new feature vector can describe the dataset better than the original one. Comparing clustering methods as one of the powerful clustering algorithms are widely used in the remote sensing fields of studying. The experiments conducted on several benchmark datasets demonstrated that the proposed clustering method achieves higher performance than other methods and present the efficiency and effectiveness of the proposed method. The results of experiments over different HSI datasets indicated that the proposed method could produce reliable and suitable results compared to the other methods. This shows the robustness of the proposed ARFCM algorithm over the various HSI datasets. Other methods may provide a good response in a given dataset and do not perform well in the other data. Consequently, the ARFCM method, regardless of the study area characteristics and the sensor features, always renders remarkable clustering accuracy.

Geometric divergence based fuzzy clustering with strong resilience to noise features

Fuzzy C-Means clustering based on dual expression between cluster prototypes and reconstructed data

Fuzzy c-means (FCM) is one of the most popular fuzzy clustering methods and it is used in various applications in computer science. Most clustering methods including FCM, suffer from bad initialization problem. If initial cluster centers (membership degree initialization in FCM) are not selected appropriately, it may yield poor results. In this paper we propose a method called MinMax FCM to overcome this problem. A new objective function is designed in MinMax FCM to this aim. We use maximum variance of clusters as objective function. In this regard, high-variance clusters are penalized. We compare MinMax FCM with FCM in terms of sum of clusters’ variances, maximum variance of clusters, and execution time using a number of UCI datasets.

Big data is technology that has the ability to manage very large amounts of data, in very fast time to allow real-time analysis and reactions. Several clustering methods which are used to group data are Fuzzy C-Means (FCM) and K-Means Clustering. K-Means Clustering algorithm is a method of partitioning existing data into two or more group. This research goal was to compare the performance of K-Means and Fuzzy C-Means algorithms in clustering data using big data technology. In this research, Hadoop and Hive were chosen the big data technology. The knowledge of Shia history on student and lecturer of Syarif Hidayatullah State Islamic University Jakarta were the data which used in this research, The testing was done by constructing application K-Means Fuzzy C-Means using Java language, Hadoop and Hive and then test the performance of K-Means and Fuzzy C-Means algorithms in data clustering. It compares both algorithms in terms of accuracy, execution time, and time complexity of the algorithms. In the application K-Means Fuzzy C-Means, evaluation were performed with data filter and the average accuracy difference result of K-Means and Fuzzy C-Means is 8.03% with the better accuracy owned by K-Means. The average execution time difference is 718.58 ms, which K-Means was faster than is Fuzzy C-Means. The time complexities of both algorithms have the same value O(n2) and the Big O equation resulted in an average difference of 93,568 with the smallest value on K-Means. Thus, K-Means algorithm is better than the Fuzzy C-Means in terms of accuracy, execution time, and the time complexity.

Exploring the uniform effect of FCM clustering: A data distribution perspective

Credal c-means clustering method based on belief functions

From the objective function of a generalized entropy-based fuzzy c-means (FCM) clustering, an algorithm was derived, which is a counterpart of Gaussian mixture models clustering. A drawback of the iterative clustering method is the slow convergence of the algorithm. Miyamoto et al. derived a hard clustering algorithm by defuzzifying the FCM clustering in which covariance matrices were introduced as decision variables. Taking into account this method, for quick and stable convergence of FCM type clustering, we propose the semi-hard clustering approach. The clustering result is used for a classifier and the free parameters of the membership function of fuzzy clusters are selected by particle swarm optimization (PSO). A high classification performance is achieved on a vehicle detection problem for outdoor parking lots.KeywordsParticle Swarm OptimizationMembership FunctionCluster CenterGaussian Mixture ModelMahalanobis DistanceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.