In this paper, we present an approach to fit some Clustering Fuzzy linear regression models based on the Fuzzy response variables and Fuzzy parameters. In this approach, we first introduce a method for Clustering crisp/Fuzzy data based on Fuzzy c-means Clustering, and then, we fit some Clustering Fuzzy regression models based on the geometric mean. The optimal Clustering Fuzzy regression models are evaluated under two indices of goodness of fit. The applications of the proposed approach are studied in modeling some real data sets.

This paper presents an efficient hybrid method, namely Fuzzy particle swarm optimization (FPSO) and Fuzzy c-means (FCM) algorithms, to solve the Fuzzy Clustering problem, especially for large sizes. When the problem becomes large, the FCM algorithm may result in uneven distribution of data, making it difficult to find an optimal solution in reasonable amount of time. The PSO algorithm does find a good or near-optimal solution in reasonable time, but we show that its performance may be improved by seeding the initial swarm with the result of the c-means algorithm. Various Clustering simulations are experimentally compared with the FCM algorithm in order to illustrate the efficiency and ability of the proposed algorithms.

In this paper, we convert the Fuzzy Clustering ensemble consensus function problem into an optimization problem based on the reliability-based co-association matrix that minimize distance between co-association matrix of final Clustering and co-association matrix of base-Clusterings in the ensemble. The optimization problem is a constrained nonlinear objective function and we solve it by sparse sequential quadratic programming (SSQP).

Enhanced Oil Recovery (EOR) is a well-known method to increase oil production from oil reservoirs. Applying EOR to a new reservoir is a costly and time consuming process. Incorporating available knowledge of oil reservoirs in the EOR process eliminates these costs and saves operational time and work. This work presents a universal method to apply EOR to reservoirs based on the available data by Clustering the data into compact and well-separated groups. A label is then assigned to each cluster which is in fact class of the data points belonging to that cluster. When EOR is intended to be applied to a new reservoir, class of the reservoir is determined and then EOR method used for the reservoirs of that class is applied to this one with no further field studies and operations. In contrast to classification, Clustering is unsupervised and number of clusters within the data is not known a priori. Some well-known methods for determining number of clusters are tried but they failed. A novel method is presented in this work for number of clusters based on difference of membership grades of the data points in the clusters. It is applied to both synthetic and real life data including reservoirs data and it is shown that this method finds number of clusters accurately. It is also shown the raw data could be easily represented as Fuzzy rule-base for better understanding and interpretation of the data.

Nowadays, the Fuzzy C-Means method has become one of the most popular Clustering methods based on minimization of a criterion function. However, the performance of this Clustering algorithm may be significantly degraded in the presence of noise. This paper presents a robust Clustering algorithm called Bilateral Weighted Fuzzy CMeans (BWFCM). We used a new objective function that uses some kinds of weights for reducing the effect of noises in Clustering. Experimental results using, two artificial datasets, five real datasets, viz., Iris, Cancer, Wine, Glass and a speech corpus used in a GMM-based speaker identification task show that compared to three well-known Clustering algorithms, namely, the Fuzzy Possibilistic C-Means, Credibilistic Fuzzy C-Means and Density Weighted Fuzzy C-Means, our approach is less sensitive to outliers and noises and has an acceptable computational complexity.

Background & Aim: Microarray techniques are successfully used to investigate thousands of gene expression profiling in a variety of genomic analyses such as gene identification, drug discovery and clinical diagnosis, providing a large amount of genomic data for the overall research community. Statistical analysis of such databases included normalization, Clustering, classification, etc. The present study surveyed the application of Fuzzy Clustering technique in DNA microarray analysis. Materials & Methods: Golub, et al collected data bases of leukemia based on the method of oligonucleotide in 1999. The data are on the internet for free. In this paper we did analysis on this data set and gene expression data were clustered by Fuzzy Clustering. Data set included 20 Acute Lymphoblastic Leukemia (ALL) patients and 14 Acute Myeloid Leukemia (AML) patients. Efficiency of Clustering was compared with regard to real grouping (ALL & AML). We used R software for data analysis.Results: Specificity and sensitivity of Fuzzy Clustering in diagnosing of ALL patients are 90% and 93%, respectively. These results show a good accomplishment of both Clustering methods. It is considerable that, due to Clustering methods results, one of the samples was placed in ALL groups, which had been in AML group in clinical test. Conclusion: With regard to concordance of the results with real grouping of data, it could be said that we can use these methods in cases where we don't have accurate information of real data grouping. Moreover, results of Clustering might distinguish subgroups of data in such a way.

Distance-based Clustering methods categorize samples by optimizing a global criterion, finding ellipsoid clusters with roughly equal sizes. In contrast, density-based Clustering techniques form clusters with arbitrary shapes and sizes by optimizing a local criterion. Most of these methods have several hyper-parameters, and their performance is highly dependent on the hyper-parameter setup. Recently, a Gaussian Density Distance (GDD) approach was proposed to optimize local criteria in terms of distance and density properties of samples. GDD can find clusters with different shapes and sizes without any free parameters. However, it may fail to discover the appropriate clusters due to the interfering of clustered samples in estimating the density and distance properties of remaining unclustered samples. Here, we introduce Adaptive GDD (AGDD), which eliminates the inappropriate effect of clustered samples by adaptively updating the parameters during Clustering. It is stable and can identify clusters with various shapes, sizes, and densities without adding extra parameters. The distance metrics calculating the dissimilarity between samples can affect the Clustering performance. The effect of different distance measurements is also analyzed on the method. The experimental results conducted on several well-known datasets show the effectiveness of the proposed AGDD method compared to the other well-known Clustering methods.

The proposed IAFC neural networks have both the stability and the plasticity because they use the control structure which is similar to that of the ART-1(Adaptive Resonance Theory) neural network. The unsupervised IAFC neural network is the unsupervised neural network which uses the Fuzzy leaky learning rule. This Fuzzy leaky learning rule controls the updating amounts by membership values. The supervised IAFC neural networks are the supervised neural networks which use the fuzzified versions of Learning Vector Quantization (LVQ). In this paper, several important adaptive learning algorithms are also compared in the viewpoint of structure and learning rule. The performances of several adaptive learning algorithms are compared using Iris data.