Possibilistic Clustering Algorithm Research Articles

Credibilistic Clustering: The Model and Algorithms

Fuzzy clustering is a widely used approach for data classification by using the fuzzy set theory. The probability measure and the possibility measure are two popular measures which have been used in the fuzzy [Formula: see text]-means algorithm (FCM) and the possibilistic clustering algorithms (PCAs), respectively. However, the numerical experiments revealed that FCM and its derivatives lack the intuitive concept of degree of belongingness, and PCAs suffer from the “coincident problem” and cannot provide very stable results for some data sets. In this study, we propose a new clustering algorithm, called the credibilistic clustering algorithm (CCA), based on the credibility measure. The credibility measure provides some unique properties which can solve the “coincident problem” and noise issue compared with the probability measure and possibility measure. Based on some randomly generated data sets, experimental results compared with FCM and PCA show that CCA can deal with the “coincident problem” with good clustering results, and it is more robust to noise than PCA.

Improved kernel possibilistic fuzzy clustering algorithm based on invasive weed optimization

Fuzzy c-means (FCM) clustering algorithm is sensitive to noise points and outlier data, and the possibilistic fuzzy c-means (PFCM) clustering algorithm overcomes the problem well, but PFCM clustering algorithm has some problems: it is still sensitive to initial clustering centers and the clustering results are not good when the tested datasets with noise are very unequal. An improved kernel possibilistic fuzzy c-means algorithm based on invasive weed optimization (IWO-KPFCM) is proposed in this paper. This algorithm first uses invasive weed optimization (IWO) algorithm to seek the optimal solution as the initial clustering centers, and introduces kernel method to make the input data from the sample space map into the high-dimensional feature space. Then, the sample variance is introduced in the objection function to measure the compact degree of data. Finally, the improved algorithm is used to cluster data. The simulation results of the University of California-Irvine (UCI) data sets and artificial data sets show that the proposed algorithm has stronger ability to resist noise, higher cluster accuracy and faster convergence speed than the PFCM algorithm.

Rapid Discrimination of Apple Varieties via Near-Infrared Reflectance Spectroscopy and Fast Allied Fuzzy C-Means Clustering

Abstract Discrimination of apple varieties plays an important role in apple post-harvest commercial processing. A fast allied fuzzy c-means (FAFCM) clustering algorithm was proposed to classify the apple varieties using near-infrared reflectance (NIR) spectroscopy technology and orthogonal linear discriminant analysis (OLDA) which was used as feature extraction and dimensionality reduction method. Our classification method: the high-dimensional NIR data were reduced to three-dimensional data by OLDA at first, and the FAFCM clustering algorithm was implemented to classify the reduced data. Furthermore, the principal component analysis (PCA) and linear discriminant analysis (LDA) combined with k-nearest neighbor classifier (KNNC), fuzzy c-means (FCM) clustering and unsupervised possibilistic clustering algorithm (UPCA), formed the other four classification methods to classify apple samples in comparison with our proposed method. The experimental results showed that FAFCM achieved the best performance of classification.

Credibilistic clustering algorithms via alternating cluster estimation

Credibilistic clustering is a new clustering method using the credibility measure in fuzzy clustering. Zhou et al. (2014) presented the clustering model of credibilistic clustering together with a credibilistic clustering algorithm for solving the optimization model. In this paper, a further investigation on credibilistic clustering is made. Within the solution architecture of alternating cluster estimation, a family of general credibilistic clustering algorithms are designed for solving the credibilistic clustering model. Moreover, a new credibilistic clustering algorithm is recommended for the real applications. Numerical examples based on randomly generated data sets and real data sets are presented to illustrate the performance and effectiveness of the credibilistic clustering algorithms from different aspects. Results comparing with the fuzzy $$c$$c-means algorithm and the possibilistic clustering algorithms show that the proposed credibilistic clustering algorithms can survive from the coincident problem and the noisy environments, and provide the clustering results with high overall accuracy.

A weighted kernel possibilistic c‐means algorithm based on cloud computing for clustering big data

SUMMARYPossibilistic c‐means (PCM) cluster algorithm has emerged as an important tool for data preprocessing widely used in data mining and knowledge discovery. Owning to the huge amount of data, high computational complexity, and noise‐corrupted data, the PCM algorithms scaled for big data find it difficult to produce a good result in real time. The paper proposes a weighted kernel PCM (wkPCM) algorithm to cluster data objects in appropriate groups. The proposed algorithm introduces weights to define the relative importance of each object in the kernel clustering solution, which reduces the corruption caused by noisy data. In order to improve the real time of the proposed algorithm, cloud computing technology is used to optimize wkPCM to propose a distributed wkPCM algorithm based on MapReduce, which can provide significant computation speed. Experiment demonstrates that the proposed possibilistic clustering algorithms can cluster big data in appropriate groups in real time. Copyright © 2014 John Wiley & Sons, Ltd.

A new heuristic possibilistic clustering algorithm for feature selection

The paper deals with the problem of selection of the most informative features. A new effective and efficient heuristic possibilistic clustering algorithm for feature selection is proposed. First, a brief description of basic concepts of the heuristic approach to possibilistic clustering is provided. A technique of initial data pre- processing is described and a fuzzy correlation measure is considered. The new algorithm is described and then illustrated on the well-known Iris data set benchmark and the results obtained are compared with those by us- ing the conventional, well-known and widely employed method of principal component analysis (PCA). Conclu- sions and suggestions for future research are given.

TWO PHASE CLUSTERING METHOD FOR LEACH PROTOCOL FOR EFFECTIVE CLUSTER HEAD SELECTION

A Wireless Sensor Networks (WSN) comprise of a huge quantity of clusters of sensor nodes that can inter communicate with all nodes and with the base station through a wireless link. All clusters are corresponding to a cluster head to provide a direct communication to the base station and in addition with other cluster heads. Obviously well-organized selection of cluster head is a significant problem in the performance of the wireless sensor network. In this study, a novel two stage clustering protocol based on Self Organizing Map (SOM) neural network and Modified Fuzzy Possibilistic Clustering Algorithm (MFPCM) with the purpose of balancing the energy consumption. The clustering is carried out based on two important condition, energy level and coordinates of sensor nodes. Consequently, this novel two stage clustering method can prevent from premature death of the nodes and permit for random death of them. The experimental observation reveals that the SOM-MFPCM based cluster- head selection algorithm performs better than the cluster head election approach used in LEACH and can enable the network lifetime longer with less number of dead nodes.

The SPoCA-suite: Software for extraction, characterization, and tracking of active regions and coronal holes on EUV images

Context. Precise localization and characterization of active regions (AR) and coronal holes (CH) as observed by extreme ultra violet (EUV) imagers are crucial for a wide range of solar and helio-physics studies.Aims. We introduce a set of segmentation procedures (known as the SPoCA-suite) that allows one to retrieve AR and CH properties on EUV images taken from SOHO-EIT, STEREO-EUVI, PROBA2-SWAP, and SDO-AIA.Methods. We build upon our previous work on the Spatial Possibilistic Clustering Algorithm (SPoCA), that we have improved substantially in several ways.Results. We apply our algorithm on the synoptic EIT archive from 1997 to 2011 and decompose this dataset into regions that can clearly be identified as AR, quiet Sun, and CH. An antiphase between AR and CH filling factor is observed, as expected. The SPoCA-suite is next applied to datasets from EUVI, SWAP, and AIA. The time series pertaining to ARs or CHs are presented.Conclusions. The SPoCA-suite enables the extraction of several long time series of AR and CH properties from the data files of EUV imagers and also allows tracking individual ARs or CHs over time. For AIA images, AR and CH catalogs are available in near-real time from the Heliophysics Events Knowledgebase. The full code, which allows processing any EUV images, is available upon request to the authors.

Segmentation of coronal features to understand the solar EUV and UV irradiance variability

Context. The study of solar irradiance variability is of great importance in heliophysics, the Earth’s climate, and space weather applications. These studies require careful identifying, tracking and monitoring of active regions (ARs), coronal holes (CHs), and the quiet Sun (QS). Aims. We studied the variability of solar irradiance for a period of two years (January 2011–December 2012) using the Large Yield Radiometer (LYRA), the Sun Watcher using APS and image Processing (SWAP) on board PROBA2, and the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). Methods. We used the spatial possibilistic clustering algorithm (SPoCA) to identify and segment coronal features from the EUV observations of AIA. The AIA segmentation maps were then applied on SWAP images, and parameters such as the intensity, fractional area, and contribution of ARs/CHs/QS features were computed and compared with the full-disk integrated intensity and LYRA irradiance measurements. Results. We report the results obtained from SDO/AIA and PROBA2/SWAP images taken from January 2011 to December 2012 and compare the resulting integrated full-disk intensity with PROBA2/LYRA irradiance. We determine the contributions of the segmented features to EUV and UV irradiance variations. The variations of the parameters resulting from the segmentation, namely the area, integrated intensity, and relative contribution to the solar irradiance, are compared with LYRA irradiance. We find that the active regions have a great impact on the irradiance fluctuations. In the EUV passbands considered in this study, the QS is the greatest contributor to the solar irradiance, with up to 63% of total intensity values. Active regions, on the other hand, contribute to about 10%, and off-limb structures to about 24%. We also find that the area of the features is highly variable suggesting that their area has to be taken into account in irradiance models, in addition to their intensity variations. Conclusions. We successfully show that the feature extraction allows us to use EUV telescopes to measure irradiance fluctuations and to quantify the contribution of each part to the EUV spectral solar irradiance observed with a calibrated radiometer. This study also shows that SPoCA is viable, and that the segmentation of images can be a useful tool. We also provide the measurement correlation between SWAP and AIA during this analysis.

Possibilistic biclustering algorithm for discovering value-coherent overlapping δ-biclusters

One of the important tools for analyzing gene expression data is biclustering method. It focuses on finding a subset of genes and a subset of experimental conditions that together exhibit coherent behavior. However, most of the existing biclustering algorithms find exclusive biclusters, which is inappropriate in the context of biology. Since biological processes are not independent of each other, many genes may participate in multiple different processes. Hence, nonexclusive biclustering algorithms are required for finding overlapping biclusters. In this regard, a novel possibilistic biclustering algorithm is presented here to find highly overlapping biclusters of larger volume with mean squared residue lower than a predefined threshold. It judiciously incorporates the concept of possibilistic clustering algorithm into biclustering framework. The integration enables efficient selection of highly overlapping coherent biclusters with mean squared residue lower than a given threshold. The detailed formulation of the proposed possibilistic biclustering algorithm, along with a mathematical analysis on the convergence property, is presented. Some quantitative indices are introduced for evaluating the quality of generated biclusters. The effectiveness of the algorithm, along with a comparison with other algorithms, is demonstrated both qualitatively and quantitatively on yeast gene expression data set. In general, the proposed algorithm shows excellent performance at finding patterns in gene expression data.

Fault Diagnosis of Metro Vehicle Auxiliary Inverter Based on PSO-KPCM Algorithm

In this paper, the principle of kernel-based possibilistic clustering algorithm and particle swarm optimization algorithm are introduced and the application of the algorithms in fault diagnosis of auxiliary inverter is studied. Several common fault types are simulated by MATALB software. By initializing clustering center of samples based on PSO algorithm, calculating the final membership matrix and the final clustering center matrix based on the KPCM algorithm, the fault samples can be classified finally. The simulation results show that the PSO-KPCM algorithm can be used in the field of fault diagnosis. The PSO-KPCM algorithm even has better results and faster convergence rate than FCM algorithm.

Research on the Variety Discrimination of Apple Using a Hybrid Possibilistic Clustering

Near infrared reflectance (NIR) spectroscopy has been used to obtain NIR spectra of two varieties of apple samples. The dimensionality of NIR spectra was reduced by principal component analysis (PCA), and discriminant information was extracted by linear discriminant analysis (LDA). Last, a hybrid possibilistic clustering algorithm (HPCA) was utilized as classifier to discriminate the apple samples of different varieties. HPCA integrates possibilistic clustering algorithm (PCA) and improved possibilistic c-means (IPCM) clustering algorithm, and produces not only the membership values but also typicality values by simple computation of the sample co-variance. Experimental results showed that HPCA, as an unsupervised learning algorithm, could quickly and easily discriminate the apple varieties.

On the convergence of some possibilistic clustering algorithms

In this paper, an analysis of the convergence performance is conducted for a class of possibilistic clustering algorithms (PCAs) utilizing the Zangwill convergence theorem. It is shown that under certain conditions the iterative sequence generated by a PCA converges, at least along a subsequence, to either a local minimizer or a saddle point of the objective function of the algorithm. The convergence performance of more general PCAs is also discussed.

On possibilistic clustering with repulsion constraints for imprecise data

In possibilistic clustering objects are assigned to clusters according to the so-called membership degrees taking values in the unit interval. Differently from fuzzy clustering, it is not required that the sum of the membership degrees of an object to all clusters is equal to one. This is very helpful in the presence of outliers, which are usually assigned to the clusters with membership degrees close to zero. Unfortunately, a drawback of the possibilistic approach is the tendency to produce coincident clusters. A remedy is to add a repulsion term among prototypes in the loss function forcing the prototypes to be far ‘enough’ from each other. Here, a possibilistic clustering algorithm with repulsion constraints for imprecise data, managed in terms of fuzzy sets, is introduced. Applications to synthetic and real fuzzy data are considered in order to analyze how the proposed clustering algorithm works in practice.

Possibilistic Exponential Fuzzy Clustering

Generally, abnormal points (noise and outliers) cause cluster analysis to produce low accuracy especially in fuzzy clustering. These data not only stay in clusters but also deviate the centroids from their true positions. Traditional fuzzy clustering like Fuzzy C-Means (FCM) always assigns data to all clusters which is not reasonable in some circumstances. By reformulating objective function in exponential equation, the algorithm aggressively selects data into the clusters. However noisy data and outliers cannot be properly handled by clustering process therefore they are forced to be included in a cluster because of a general probabilistic constraint that the sum of the membership degrees across all clusters is one. In order to improve this weakness, possibilistic approach relaxes this condition to improve membership assignment. Nevertheless, possibilistic clustering algorithms generally suffer from coincident clusters because their membership equations ignore the distance to other clusters. Although there are some possibilistic clustering approaches that do not generate coincident clusters, most of them require the right combination of multiple parameters for the algorithms to work. In this paper, we theoretically study Possibilistic Exponential Fuzzy Clustering (PXFCM) that integrates possibilistic approach with exponential fuzzy clustering. PXFCM has only one parameter and not only partitions the data but also filters noisy data or detects them as outliers. The comprehensive experiments show that PXFCM produces high accuracy in both clustering results and outlier detection without generating coincident problems.

Improvements to the quantum evolutionary clustering

In previous work, a novel approach to data clustering based on quantum evolutionary algorithm has been proposed. In a comparison to other evolutionary clustering algorithms, the approach showed a high performance in terms of effectiveness and quality of found clusters. Although the approach is sound, it tends to be trapped in local minima, which slows the convergence. The approach is based on degrees of belonging having a fixed relationship with the distance between the data points and the clusters. The fixed relationship ignores completely the dataset distribution. In this paper, we modify the approach to improve its convergence. We also modify the function calculating the degrees of belonging by taking inspiration from possibilistic clustering. Comparison has been done with approaches based on degrees of belonging like fuzzy, possibilistic, hybrid fuzzy possibilistic clustering and other quantum evolutionary algorithm. Results on both real and synthetic datasets show that the modifications brought to the approach enable a more efficient exploration of the search space which improves the convergence speed and quality.

Unsupervised Possibilistic Clustering Based on Kernel Methods

Abstract A new kernel based unsupervised clustering algorithm has been proposed. The proposed algorithm is called unsupervised kernel possibilistic clustering algorithm (UKPC), which is an extension of the previously proposed clustering algorithm of unsupervised possibilistic clustering algorithm (UPC). In UKPC, the sample points are mapped into the feature space by the introduced kernel function, and the final clustering partition is obtained by optimizing the objective function of UKPC, which adopts the same clustering rule with UPC clustering model. UKPC has the ability of revealing the non-convex cluster structure because the input data are mapped implicitly into a high-dimensional feature space where the nonlinear pattern now appears linear. The contrast experimental results with UPC and other typical fuzzy clustering algorithms show the better performance of the proposed algorithm.

Similarity Measure based Robust Possibilistic C-means Clustering Algorithms

Similarity Measure based Robust Possibilistic C-means Clustering Algorithms

A Multi-wavelength Analysis of Active Regions and Sunspots by Comparison of Automatic Detection Algorithms

Since the Solar Dynamics Observatory (SDO) began recording ≈ 1 TB of data per day, there has been an increased need to automatically extract features and events for further analysis. Here we compare the overall detection performance, correlations between extracted properties, and usability for feature tracking of four solar feature-detection algorithms: the Solar Monitor Active Region Tracker (SMART) detects active regions in line-of-sight magnetograms; the Automated Solar Activity Prediction code (ASAP) detects sunspots and pores in white-light continuum images; the Sunspot Tracking And Recognition Algorithm (STARA) detects sunspots in white-light continuum images; the Spatial Possibilistic Clustering Algorithm (SPoCA) automatically segments solar EUV images into active regions (AR), coronal holes (CH), and quiet Sun (QS). One month of data from the Solar and Heliospheric Observatory (SOHO)/Michelson Doppler Imager (MDI) and SOHO/Extreme Ultraviolet Imaging Telescope (EIT) instruments during 12 May – 23 June 2003 is analysed. The overall detection performance of each algorithm is benchmarked against National Oceanic and Atmospheric Administration (NOAA) and Solar Influences Data Analysis Center (SIDC) catalogues using various feature properties such as total sunspot area, which shows good agreement, and the number of features detected, which shows poor agreement. Principal Component Analysis indicates a clear distinction between photospheric properties, which are highly correlated to the first component and account for 52.86% of variability in the data set, and coronal properties, which are moderately correlated to both the first and second principal components. Finally, case studies of NOAA 10377 and 10365 are conducted to determine algorithm stability for tracking the evolution of individual features. We find that magnetic flux and total sunspot area are the best indicators of active-region emergence. Additionally, for NOAA 10365, it is shown that the onset of flaring occurs during both periods of magnetic-flux emergence and complexity development.

Image segmentation by fuzzy and possibilistic clustering algorithms for the identification of microcalcifications

Breast cancer is one of the leading causes of female mortality in the world, and early detection is an important means of reducing the mortality rate. The presence of microcalcification clusters has been considered as a very important indicator of malignant types of breast cancer, and its detection is important to prevent and treat the disease. This paper presents an effective approach, in order to detect microcalcification clusters in digitized mammograms, based on the synergy of image processing and partitional (hard and fuzzy) clustering techniques. Mathematical morphology has been used for image processing, and is used in this work as a first step, with the purpose of enhancing the contrast of microcalcifications. Image segmentation is an important task in the field of image processing, in order to identify regions with the same features. In the second step, we use image segmentation, using three partitional, hard and fuzzy clustering algorithms, such as k-Means, Fuzzy c-Means and Possibilistic Fuzzy c-Means, in order to make a comparison of the advantages and drawbacks offered by these algorithms, and which should help to improve the detection of microcalcification clusters in digitized mammograms.