Extension Of Fuzzy C-means Research Articles

Revisiting Possibilistic Fuzzy C-Means Clustering Using the Majorization-Minimization Method.

Possibilistic fuzzy c-means (PFCM) clustering is a kind of hybrid clustering method based on fuzzy c-means (FCM) and possibilistic c-means (PCM), which not only has the stability of FCM but also partly inherits the robustness of PCM. However, as an extension of FCM on the objective function, PFCM tends to find a suboptimal local minimum, which affects its performance. In this paper, we rederive PFCM using the majorization-minimization (MM) method, which is a new derivation approach not seen in other studies. In addition, we propose an effective optimization method to solve the above problem, called MMPFCM. Firstly, by eliminating the variable V∈Rp×c, the original optimization problem is transformed into a simplified model with fewer variables but a proportional term. Therefore, we introduce a new intermediate variable s∈Rc to convert the model with the proportional term into an easily solvable equivalent form. Subsequently, we design an iterative sub-problem using the MM method. The complexity analysis indicates that MMPFCM and PFCM share the same computational complexity. However, MMPFCM requires less memory per iteration. Extensive experiments, including objective function value comparison and clustering performance comparison, demonstrate that MMPFCM converges to a better local minimum compared to PFCM.

An Extended Fuzzy C-Means Segmentation for an Efficient BTD With the Region of Interest of SCP

Magnetic resonance imaging (MRI) is the primary source to diagnose a brain tumor or masses in the medical sciences. It is emerging to detect the tumors from the scanned MRI brain images at early stages for the best treatments. Existing image segmentation techniques, morphological, fuzzy c-means are wildly successful in the extraction region of interest (ROI) in brain image segmentation. Proper extraction of ROIs is useful for regularizing the regions of tumors from the brain image with effective binarization in the segmentation. However, the existing techniques are limiting the irregular boundaries or shapes in tumor segmentation. Thus, this paper presents the proposed work extending the FCM with the spatial correlated pixel (RSCP), known as FCM-RSCP. It overcomes the problem of irregular boundaries by assessing correlated spatial information during segmentation. Benchmarked MRI brain images are used in the experiment for demonstrating the efficiency of the proposed methodology.

$$L_{p}$$-norm probabilistic K-means clustering via nonlinear programming

Generalized fuzzy c-means (GFCM) is an extension of fuzzy c-means using $$L_{p}$$ -norm distances. However, existing methods cannot solve GFCM with m = 1. To solve this problem, we define a new kind of clustering models, called $$L_{p}$$ -norm probabilistic K-means ( $$L_{p}$$ -PKM). Theoretically, $$L_{p}$$ -PKM is equivalent to GFCM at m = 1, and can have nonlinear programming solutions based on an efficient active gradient projection (AGP) method, namely, inverse recursion maximum-step active gradient projection (IRMSAGP). On synthetic and UCI datasets, experimental results show that $$L_{p}$$ -PKM performs better than GFCM (m > 1) in terms of initialization robustness, p-influence, and clustering performance, and the proposed IRMSAGP also achieves better performance than the traditional AGP in terms of convergence speed.

Intuitionistic fuzzy c-means clustering algorithm based on a novel weighted proximity measure and genetic algorithm

In the era of big data, the research on clustering technologies is a popular topic because they can discover the structure of complex data sets with minimal prior knowledge. Among the existing soft clustering technologies, as an extension of fuzzy c-means (FCM) algorithm, the intuitionistic FCM (IFCM) algorithm has been widely used due to its superiority in reducing the effects of outliers/noise and improving the clustering accuracy. In the existing IFCM algorithm, the measurement of proximity degree between a pair of objects and the determination of parameters are two critical problems, which have considerable effects on the clustering results. Therefore, we propose an improved IFCM clustering technique in this paper. Firstly, a novel weighted proximity measure, which aggregates weighted similarity and correlation measures, is proposed to evaluate not only the closeness degree but also the linear relationship between two objects. Subsequently, genetic algorithms are utilized for identifying the optimal parameters. Lastly, experiments on the proposed IFCM technique are conducted on synthetic and UCI data sets. Comparisons with other approaches in cluster evaluation indexes indicate the effectiveness and superiority of our method.

Sequential Cluster Estimation: A Generalized Model for Finding Large Numbers of Clusters in Data

Clustering is an unsupervised learning method that partitions a set of objects into groups (clusters) of similar objects, where similarity is often computed from numerical object feature vectors (also called data points). An early (and still very popular) clustering algorithm, called k-means, finds clusters by minimizing the sum of the squared distances between data points and associated cluster centers. The k-means algorithm (like many other so-called hard clustering algorithms) assigns each object to one and only one of the considered clusters. In practice, however, cluster assignments may often be ambiguous. Objects may partially belong to several clusters or fit to none of these clusters. Such kinds of ambiguity can be mathematically handled by what is termed fuzzy set theory . A fuzzy variant of k -means called fuzzy c-means (FCM) has emerged to become one of the most popular fuzzy clustering methods, with hundreds of thousands of scientific publications. For a survey. Fuzzy clustering is often used to generate membership functions for fuzzy rule-based systems. Alternating cluster estimation (ACE)is an extension of FCM for arbitrary membership function shapes. This article introduces sequential cluster estimation (SCE), a variant of ACE that finds clusters sequentially and outperforms nonsequential clustering for data with many clusters.

Hierarchical granular hotspots detection

We present a hierarchical model based on the extended fuzzy C-means (EFCM) clustering algorithm to develop a granular view of hotspots on a geographic map. The objective is to establish an overview of the spatial distribution of a phenomenon when the relevant data are partitioned into different datasets. The EFCM algorithm is applied to each dataset to detect local hotspots, represented as circles, on the map. The local hotspots constitute information granules at lower level of abstraction in the model. A weighted EFCM algorithm is then applied to a dataset formed by the centers of all the local hotspots to extract circular prototypes, defined as global hotspots, which constitute information granules at the higher level, and hence, they deliver a global overview of the spatial distribution of the phenomenon on the map. Two indices related to the essential criteria of the principle of justifiable granularity are used. The results demonstrate that the most justifiable overview is obtained by using the radius of the local hotspot as weight. Comparisons with a hierarchical model based on FCM algorithm show that our algorithm gives a better granular view of the phenomenon with respect to the latter.

Robust fuzzy c‐means clustering algorithm using non‐parametric Bayesian estimation in wavelet transform domain for noisy MR brain image segmentation

The major drawback of the fuzzy c-means (FCM) algorithm is its sensitivity to noise. The authors propose a new extended FCM algorithm based a non-parametric Bayesian estimation in the wavelet transform domain for segmenting noisy MR brain images. They use the Bayesian estimator to process the noisy wavelet coefficients. Before segmentation based on FCM algorithm, they use an a priori statistical model adapted to the modelisation of the wavelet coefficients of a noisy image. The main objective of this wavelet-based Bayesian statistical estimation is to recover a good quality image, from a noisy image of poor quality. Experimental results on simulated and real magnetic resonance imaging brain images show that their proposed method solves the problem of sensitivity to noise and offers a very good performance that outperforms some FCM-based algorithms.

Extended Fuzzy C-Means hotspot detection method for large and very large event datasets

We present a hotspot detection method based on the Extended Fuzzy C-Means (EFCM) algorithm for large (L) and very large (VL) datasets of events. Extensions of four VL-FCM algorithms are presented. We test our method applying these algorithms to an L dataset composed from the epicenters of earthquakes happened in Italy since 1970. Comparison have been made with respect to the results obtained by applying the EFCM algorithm on the whole event dataset and two indices are used for measuring the performances of the algorithms proposed.

Spatiotemporal extended fuzzy C-means clustering algorithm for hotspots detection and prediction

We present a spatiotemporal clustering method, namely SEFCM, which is a generalization of the extended fuzzy C-Means (EFCM) method for detecting hotspots in spatial analysis. Each pattern is formed by three features: the geographical coordinates and the period in which a certain event is occurred. This method is applied to a spatial dataset (formed by earthquake epicenters occurred in Southern Italy since 2001 till to 2014) for prediction of the hotspots obtained in a given year. Comparisons of the prediction results are also made with the ones obtained by applying the known ST-DBSCAN algorithm.

Self-Organizing Map based Extended Fuzzy C-Means (SEEFC) algorithm for image segmentation

A Novel hybrid algorithm based on Self-Organizing-Map (SOM) and Extended Fuzzy C-Means (EFCM) named self-organizing-map based extended fuzzy c-means (SEEFC) has been designed and implemented for image segmentation. The proposed algorithm works in three stages. At first, the images are decomposed by discrete wavelet transform (DWT) into various frequencies and gradient, pixel value and statistical parameters are obtained to form a feature prototype. The feature prototypes are input to the Self Organizing Map (SOM). Finally, the codebook vectors of the trained SOM have been clustered automatically using Extended Fuzzy C-Means (EFCM). The clustered codebook vector centers are used for image segmentation based on minimum distance criterion. The proposed method has been tested with images from Berkeley’s database and results obtained are promising. The segmentation results are evaluated against the ground truth. Comparisons with another state of the art approaches indicate advantages of the SOM based EFCM algorithm.

A Fuzzy-Preconditioned GRBFN Model for Electricity Price Forecasting

This paper proposes a fuzzy-preconditioned ANN (Artificial Neural Network) model for electricity price forecasting. The deregulated electric power systems have been widely spread to trade electric power through electric power markets. The market players are interested in gaining the inside track to maximize the profits and minimize risks in advance. One of the most important tasks is how to forecast a complicated time series of electricity price that affects transmission network congestion. In practice, it is hard to forecast electricity price with the spikes due to the high nonlinearity. In this paper, GRBFN (General Radial Basis Function Network) of ANN is proposed for electricity price forecasting. It is an extension of RBFN of ANN in a way that the optimal parameters of the Gaussian functions are determined by the learning process in RBFN. To improve the model accuracy of GRBFN, FCE (fuzzy c-Elliptotypes) is introduced into GRBFN as a fuzzy precondition technique. FCE is an extension of FCM (fuzzy c-means) and plays a key role to classify input data into fuzzy clusters. The use of FCE contributes to the improvement of model accuracy for spikes of electricity price that bring about much higher price. This paper makes use of DA clustering to evaluate a better initial solution of the parameters of the Gaussian functions. Also, EPSO of evolutionary computation is used to evaluate better weights between neurons. The proposed method is successfully applied to real data of electricity price.

A novel automatic picture fuzzy clustering method based on particle swarm optimization and picture composite cardinality

Fuzzy clustering plays an important role in pattern recognition and knowledge discovery. Recently, there has been a great interest of developing fuzzy clustering algorithms on advanced fuzzy sets such as Picture Fuzzy Clustering (FC-PFS) which is an extension of Fuzzy C-Means on Picture Fuzzy Set. A major disadvantage of FC-PFS is how to define a prior number of clusters before clustering. Because each dataset has distinctive features and distributions of patterns, determining such the number for a clustering algorithm would result in good quality. In this paper, we propose a method called Automatic Picture Fuzzy Clustering (AFC-PFS) for determining the most suitable number of clusters for FC-PFS. It is a hybrid method between Particle Swarm Optimization (PSO) and FC-PFS where combined solutions consisting of the number of clusters and equivalent clustering centers and membership matrices are packed and optimized in PSO. A new term namely Picture Composite Cardinality is also given to determine a suitable number of clusters. AFC-PFS is empirically validated on benchmark datasets of UCI Machine Learning Repository by different clustering quality indices. The results show that AFC-PFS has better performance than the relevant methods.

Fuzzy Co-Clustering Induced by Multinomial Mixture Models

A close connection between fuzzyc-means (FCM) and Gaussian mixture models (GMMs) have been discussed and several extended FCM algorithms were induced by the GMMs concept, where fuzzy partitions are proved to be more useful for revealing intrinsic cluster structures than probabilistic ones. Co-clustering is a promising technique for summarizing cooccurrence information such as document-keyword frequencies. In this paper, a fuzzy co-clustering model is induced based on the multinomial mixture models (MMMs) concept, in which the degree of fuzziness of both object and item fuzzy memberships can be properly tuned. The advantages of the dual fuzzy partition are demonstrated through several experimental results including document clustering applications.

WebGIS based on spatio-temporal hot spots: an application to oto-laryngo-pharyngeal diseases

We present a web geo-spatial framework for analyzing and continuously monitoring the spatio-temporal evolution of disease hot spots for detecting spatial areas with high concentrations of events in a geographic information system (GIS). To detect the hot spots, we adopt Extended Fuzzy C-Means algorithm. Each event is given by the geo-positional coordinates of the place of residence of the patient. The analyst can insert event data directly on the map or digitizing the address of the residence of the patient and using geo-coding services for locating the event. In our experiments, the data consist of geo-referenced patterns corresponding to the residence of patients in the district of Naples (Italy) submitted to a surgical intervention concerning the oto-laryngo-pharyngeal apparatus between the years 2008 and 2012. The results show the presence of two greatest hot spots: the first covers a geographical area that affects the city of Naples, the second covers parts of various towns around the famous vulcan Vesuvius, respectively.

Spatio-temporal hotspots and application on a disease analysis case via GIS

Hotspot analysis is a spatial analysis that uses cluster techniques for determining areas with elevated concentrations of localized events. We use the consolidated Extended Fuzzy C-Means algorithm to determine the hotspot areas on the map as circles, moreover the advantages of this technique are the linear computational complexity, the robustness to noise and outliers, the automatic determination of the optimal number C of clusters (in the classical FCM algorithm C is chosen a priori). Furthermore it prevents the problem of shifting the clusters with low density area of data points in areas with higher density of such points. We apply this method to study the spatio-temporal variations of the hotspot areas by testing this process on a specific disease problem, precisely we have clusterized 5,000 point-events correspondent to cases of brain cancer detected in the state of New Mexico from 1973 to 1991. We also show that the same results are obtained by using the Extended Gustafson---Kessel algorithm which gives elliptical clusters. We have implemented both algorithms in a Geographic Information System environment. Thus we establish the areas which seem not interested from the incidence of the disease and those areas in which the phenomenon appears to be temporarily attenuated either increased or constant or quite disappeared.

Optimizing Query Results Integration Process Using an Extended Fuzzy C-Means Algorithm

Cleaning duplicate data is a major problem that persists even though many works have been done to solve it, due to the exponential growth of data amount treated and the necessity to use scalable and speed algorithms. This problem depends on the type and quality of data, and differs according to the volume of data set manipulated. In this paper we are going to introduce a novel framework based on extended fuzzy C-means algorithm by using topic ontology. This work aims to improve the OLAP querying process over heterogeneous data warehouses that contain big data sets, by improving query results integration, eliminating redundancies by using the extended classification algorithm, and measuring the loss of information.

Spatiotemporal Hotspots Analysis for Exploring the Evolution of Diseases: An Application to Oto-Laryngopharyngeal Diseases

This paper presents a spatiotemporal analysis of hotspot areas based on the Extended Fuzzy C-Means method implemented in a geographic information system. This method has been adapted for detecting spatial areas with high concentrations of events and tested to study their temporal evolution. The data consist of georeferenced patterns corresponding to the residence of patients in the district of Naples (Italy) to whom a surgical intervention to the oto-laryngopharyngeal apparatus was carried out between the years 2008 and 2012.

Comparison of FCM and FISODATA

In fuzzy clustering, the fuzzy c-means (FCM) clustering algorithm is the best known and used method. An interesting extension of FCM is the fuzzy ISODATA (FISODATA) algorithm; it updates cluster number during the algorithm. That’s why we can have more or less clusters than the initialization step. It’s the power of the fuzzy ISODATA algorithm comparing to FCM. The aim of this paper is to compare FCM and FISODATA results.

A fuzzy particle swarm optimization algorithm and its application to hotspot events in spatial analysis

A new Extended Fuzzy Particle Swarm Optimization (EFPSO) algorithm is presented and used for the determination of hotspot events in spatial analysis. In previous works (Di Martino et al. in Int J Hybrid Intell Syst 4:1–14, 2007; Di Martino and Sessa in Proceedings VISUAL 2008. LNCS 5188, Springer-Verlag, Berlin, pp. 92–95, 2008; Di Martino and Sessa in Expert Systems with Applications, to appear. doi:10.1016/j.eswa.2011.03.071, 2011) we have shown that the Extended Fuzzy C-Means (EFCM) can be used in the approximation of hotspot areas where the data are events geo-referenced as points on the geographic map and EFCM gives better results with respect to the classical Fuzzy C-Means. Here we compare EFPSO and EFCM, implementing both methods in a Geographic Information System. We apply the two methods to two specific datasets for crime analysis and forest fire point-events showing that EFPSO has the best performance with respect to EFCM.

The extended fuzzy C-means algorithm for hotspots in spatio-temporal GIS

In spatial analysis buffer impact areas are called hotspots and are determined by means of density clustering methods. In a previous work, we found these hotspots in the context of a Geographic Information System (GIS) by using the extended fuzzy C-means (EFCM). Here we show how the spatial distribution of the hotspots can evolve temporally and like applicational example, we present the spatial-temporal evolution in the period 2000–2006 of the fire point-events data of the Santa Fè district (NM) (downloaded from URL: www.fs.fed.us/r3/gis/sfe_gis.shtml).