Genetically derived fuzzy c-means clustering algorithm for segmentation

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.

The identification of fuzzy models for classification is a very complex task. Often, real world databases have a large number of features and the most relevant ones must be chosen. Recently, a new automatic feature selection for classification problems was proposed to construct compact fuzzy classification models. This technique used the classical fuzzy c-means algorithm. However, other fuzzy clustering algorithms, such as possibilistic c-means, fuzzy possibilistic c-means or possibilistic fuzzy c-means can be used to cluster the data. An open topic of research is what clustering algorithms can be used to derive fuzzy models for classification. This paper addresses this topic, by comparing fuzzy clustering algorithms in terms of computational efficiency and accuracy in classification problems. The algorithms were tested in well-known data sets: iris plant, wine, hepatitis, breast cancer and in a difficult real-world problem: the prediction of bankruptcy.

Bias-correction fuzzy clustering algorithms

Partition-and-merge based fuzzy genetic clustering algorithm for categorical data

Comparison of two fuzzy algorithms in geodemographic segmentation analysis: The Fuzzy C-Means and Gustafson–Kessel methods

Forecasting activities play an important role in our daily life. In recent years, fuzzy time series (FTS) methods were developed to deal with forecasting problems. FTS attracted researchers because of its ability to predict the future values in some critical situations where most standard forecasting models are doubtfully applicable or produce bad fittings. However, some critical issues in FTS are still open; these issues are often subjective and affect the accuracy of forecasting. In this paper, we focus on improving the accuracy of FTS forecasting methods. The new method integrates the fuzzy clustering and genetic algorithm with FTS to reduce subjectivity and improve its accuracy. In the new method, the genetic algorithm is responsible for selecting the proper model. Also, the fuzzy clustering algorithm is responsible for fuzzifying the historical data, based on its membership degrees to each cluster, and using these memberships to defuzzify the results. This method provides better forecasting accuracy when compared with other extant researches.

Several criminal profiling systems have been developed to assist the Law Enforcement Agencies in solving crimes but the techniques employed in most of the systems lack the ability to cluster criminal based on their behavioral characteristics. This paper reviewed different clustering techniques used in criminal profiling and then selects one fuzzy clustering algorithm (Expectation Maximization) and two hard clustering algorithm (K-means and Hierarchical). The selected algorithms were then developed and tested on real life data to produce "profiles" of criminal activity and behavior of criminals. The algorithms were implemented using WEKA software package. The performance of the algorithms was evaluated using cluster accuracy and time complexity. The results show that Expectation Maximization algorithm gave a 90.5% clusters accuracy in 8.5s, while K-Means had 62.6% in 0.09s and Hierarchical with 51.9% in 0.11s. In conclusion, soft clustering algorithm performs better than hard clustering algorithm in analyzing criminal data.
 Keywords: Clustering Algorithm, Profiling, Crime, Membership value

Over the years, research on fuzzy clustering algorithms has attracted the attention of many researchers, and they have been applied to various areas, such as image segmentation and data clustering. Various fuzzy clustering algorithms have been put forward based on the initial Fuzzy C-Means clustering (FCM) with Euclidean distance. However, the existing fuzzy clustering approaches ignore two problems. Firstly, clustering algorithms based on Euclidean distance have a high error rate, and are more sensitive to noise and outliers. Secondly, the parameters of the fuzzy clustering algorithms are hard to determine. In practice, they are often determined by the user’s experience, which results in poor performance of the clustering algorithm. Therefore, considering the above deficiencies, this paper proposes a novel fuzzy clustering algorithm by combining the Gaussian kernel function and Grey Wolf Optimizer (GWO), called Kernel-based Picture Fuzzy C-Means clustering with Grey Wolf Optimizer (KPFCM-GWO). In KPFCM-GWO, the Gaussian kernel function is used as a symmetrical measure of distance between data points and cluster centers, and the GWO is utilized to determine the parameter values of PFCM. To verify the validity of KPFCM-GWO, a comparative study was conducted. The experimental results indicate that KPFCM-GWO outperforms other clustering methods, and the improvement of KPFCM-GWO is mainly attributed to the combination of the Gaussian kernel function and the parameter optimization capability of the GWO. What is more, the paper applies KPFCM-GWO to analyzes the value of an airline’s customers, and five levels of customer categories are defined.

In order to develop quantitative seafloor sediment classification techniques it is important to acknowledge that by nature the boundaries between soft sediments are characterized by transition zones and therefore are indeterminate and gradual. A fuzzy clustering method, fuzzy c-means (FCM), was used to identify these transition zones within a subset of the data used to generate the Australian Seascapes classification model. The overlapping classes and gradual boundaries resulting from the fuzzy c-means algorithm provided estimates of sediment boundaries that are a closer model of reality than sharp boundaries. FCM output is given in the form of membership layers for each class, hard classes for each grid cell based on the maximum membership value, and a confusion index layer quantifying uncertainty in class attribution. The confusion index layer provided a spatial representation of transition zones and overlap between seafloor classes and highlighted areas of greatest uncertainty. We extended the standard FCM algorithm by applying the new FMLE fuzzy clustering algorithm that takes into account spatial relationships in the data. In addition, we implemented and applied new cluster validity techniques, PCAES, PBMF, and XB to determine the optimal number of clusters in the data, which is a novel pattern recognition application for seabed mapping. The 5-class FCM classification provided the most reliable result. The results of this research were tested and validated on a simulated dataset and then the clustering and validation algorithms were applied to marine sediment data to identify Seascapes. The new results were compared with previously published Seascapes classes identified with hard ISODATA clustering techniques from GeoScience Australia's Seascapes classification result. With the increasing use of physical surrogates to explain marine biodiversity, this research plays a crucial role in the development of techniques to identify habitat zones on the seabed.

Clustering is a potential tool of data mining. A clustering method analyzes the pattern of a data set and groups the data into several clusters based on the similarity among themselves. Clusters may be either crisp or fuzzy in nature. The present chapter deals with clustering of some data sets using Fuzzy C-Means (FCM) algorithm and Entropy-based Fuzzy Clustering (EFC) algorithm. In FCM algorithm, the nature and quality of clusters depend on the pre-defined number of clusters, level of cluster fuzziness and a threshold value utilized for obtaining the number of outliers (if any). On the other hand, the quality of clusters obtained by the EFC algorithm is dependent on a constant used to establish the relationship between the distance and similarity of two data points, a threshold value of similarity and another threshold value used for determining the number of outliers. The clusters should ideally be distinct and at the same time compact in nature. Moreover, the number of outliers should be as minimum as possible. Thus, the above problem may be posed as an optimization problem, which will be solved using a Genetic Algorithm (GA). The best set of multi-dimensional clusters will be mapped into 2-D for visualization using a Self-Organizing Map (SOM).

Fuzzy C-means (FCM) clustering algorithm tries to get the memberships of each sample to each Cluster by optimizing an objective function, and then assign each of the samples to an appropriate class. The Fuzzy C-means algorithm doesn’t fit for clusters with different sizes and different densities, and it is sensitive to noise and anomaly. We present two improved fuzzy c-means algorithms, Clusters-Independent Relative Density Weights based Fuzzy C-means (CIRDWFCM) and Clusters-Dependent Relative Density Weights based Fuzzy C-means (CDRDWFCM), according to the various roles of different samples in clustering. Several experiments of them are done on four datasets from UCI and UCR. Experimental results shows that this two presented algorithms can increase the similarity or decrease the iterations to some extent, and get better clustering results and improve the clustering quality.

This chapter presents two novel approaches for the identification of Takagi-Sugeno fuzzy models with time variant and time invariant features. The mixed fuzzy clustering (MFC) algorithm is used for determining the parameters of Takagi-Sugeno fuzzy models (FMs) in two different ways: (1) MFC FM, where the antecedent fuzzy sets are determined based on the partition matrix generated by the mixed fuzzy clustering algorithm; (2) FCM–UMFC FM, where the input features are transformed using MFC and the antecedent fuzzy sets are derived using fuzzy c-means (FCM). The fuzzy modeling approaches are tested on four health care applications for the classification of critically ill patients: administration of vasopressors in pancreatitis and pneumonia patients, mortality in septic shock and early readmissions. Both approaches increase the performance of Takagi-Sugeno based on FCM, in all datasets. In particular, the best performer, FCM–UMFC FM, achieves notable improvements in the four datasets.

Brain Magnetic Resonance Imaging (MRI) image segmentation is one of the critical technologies of clinical medicine, and is the basis of three-dimensional reconstruction and downstream analysis between normal tissues and diseased tissues. However, there are various limitations in brain MRI images, such as gray irregularities, noise, and low contrast, reducing the accuracy of the brain MRI images segmentation. In this paper, we propose two optimization solutions for the fuzzy clustering algorithm based on local Gaussian probability fuzzy C-means (LGP-FCM) model and anisotropic weight fuzzy C-means (AW-FCM) model and apply it in brain MRI image segmentation. An FCM clustering algorithm is proposed based on AW-FCM. By introducing the new neighborhood weight calculation method, each point has the weight of anisotropy, effectively overcomes the influence of noise on the image segmentation. In addition, the LGP model is introduced in the objective function of fuzzy clustering, and a fuzzy clustering segmentation algorithm based on LGP-FCM is proposed. A clustering segmentation algorithm of adaptive scale fuzzy LGP model is proposed. The neighborhood scale corresponding to each pixel in the image is automatically estimated, which improves the robustness of the model and achieves the purpose of precise segmentation. Extensive experimental results demonstrate that the proposed LGP-FCM algorithm outperforms comparison algorithms in terms of sensitivity, specificity and accuracy. LGP-FCM can effectively segment the target regions from brain MRI images.

Fuzzy clustering partitions data points of a dataset into clusters in which one data point can belong to more than one cluster. In the literature, a number of fuzzy clustering algorithms have been proposed. This paper reviews various fuzzy clustering algorithms such as Fuzzy C-Means (FCM), Possibilistic C-Means (PCM), Possibilistic Fuzzy C-Means (PFCM), Intuitionistic Fuzzy C-Means (IFCM), Kernel Fuzzy C-Means (KFCM), and Density-Oriented Fuzzy C-Means (DOFCM). We have demonstrated the experimental performance of these algorithms on some standard and synthetic datasets which include—Bensaid, Square (DUNN), D15, and D45 dataset. Then, the results are analyzed and compared to see the effectiveness of these algorithms in presence of noise and outliers.

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.