Possibilistic Clustering Algorithm Research Articles

A Novel Possibilistic Clustering Algorithm for Measurement Data of Vehicle MMW Radar

A Novel Possibilistic Clustering Algorithm for Measurement Data of Vehicle MMW Radar

Generalized possibilistic c-means clustering with double weighting exponents

Considering that the improved possibilistic c-means (PCM) algorithms are sensitive to noise while addressing the issue of consistency clustering in PCM, this paper proposes the generalized possibilistic c-means clustering with double weighting exponents. Firstly, double weighting exponents are introduced into the PCM algorithm, and the generalized possibilistic c-means clustering model is established. Secondly, the difference between the double weighting exponents in the generalized possibilistic clustering model is set to 1 or −1; two improved single-exponent possibilistic clustering algorithms called IPCM1 and IPCM2 are proposed, and their local convergence is strictly proven by the Zangwill theorem. Finally, the reasonable range of the weighting exponent in IPCM1 and IPCM2 algorithms is determined by mathematical optimization. Experimental results indicate that IPCM1 and IPCM2 outperform existing PCM-related algorithms; they achieve excellent clustering performance, significantly improve the robustness to noise, and decrease the sensitivity to the weighting exponent. The work of this paper has far-reaching significance for promoting the development of the possibilistic c-means clustering theory.

A Sparse Framework for Robust Possibilistic K-Subspace Clustering

Clustering noisy, high-dimensional, and structurally complex data have always been a challenging task. As most existing clustering methods are not able to deal with both the adverse impact of noisy samples and the complex structures of data, in this article, we propose a novel robust and sparse possibilistic K-subspace (RSPKS) clustering algorithm to integrate subspace recovery and possibilistic clustering algorithms under a unified sparse framework. First, the proposed method sparsifies the membership matrix and the subspace projection vector under a dual-sparse framework to handle high-dimensional noisy data. This unifies dimensionality reduction and clustering using one objective function for which the optimization can be realized through synchronous iteration. Second, the reconstruction error of each sample in the local subspace is used as the distance metric for classification. That is, each sample itself is treated as a clustering prototype so as not to be affected by the structure of the overall data distribution. Therefore, the clustering prototype construction problem of the data with complex structures can be better addressed. Finally, to deal with nonlinear regions, our RSPKS method is further extended into a kernelized version, namely the kernelized RSPKS clustering algorithm. The experimental results on both synthetic and real-world datasets demonstrate that our proposed method outperforms state-of-the-art algorithms in terms of clustering accuracy.

Two novel outlier detection approaches based on unsupervised possibilistic and fuzzy clustering.

Outliers are data points that significantly deviate from other data points in a data set because of different mechanisms or unusual processes. Outlier detection is one of the intensively studied research topics for identification of novelties, frauds, anomalies, deviations or exceptions in addition to its use for data cleansing in data science. In this study, we propose two novel outlier detection approaches using the typicality degrees which are the partitioning result of unsupervised possibilistic clustering algorithms. The proposed approaches are based on finding the atypical data points below a predefined threshold value, a possibilistic level for evaluating a point as an outlier. The experiments on the synthetic and real data sets showed that the proposed approaches can be successfully used to detect outliers without considering the structure and distribution of the features in multidimensional data sets.

A new stochastic gradient descent possibilistic clustering algorithm

Several well known clustering algorithms have their own online counterparts, in order to deal effectively with the big data issue, as well as with the case where the data become available in a streaming fashion. However, very few of them follow the stochastic gradient descent philosophy, despite the fact that the latter enjoys certain practical advantages (such as the possibility of (a) running faster than their batch processing counterparts and (b) escaping from local minima of the associated cost function), while, in addition, strong theoretical convergence results have been established for it. In this paper a novel stochastic gradient descent possibilistic clustering algorithm, called O- PCM 2 is introduced. The algorithm is presented in detail and it is rigorously proved that the gradient of the associated cost function tends to zero in the L 2 sense, based on general convergence results established for the family of the stochastic gradient descent algorithms. Furthermore, an additional discussion is provided on the nature of the points where the algorithm may converge. Finally, the performance of the proposed algorithm is tested against other related algorithms, on the basis of both synthetic and real data sets.

Origin of the Solar Rotation Harmonics Seen in the EUV and UV Irradiance

Long-term periodicities in the solar irradiance are often observed with periods proportional to the solar rotational period of 27 days. These periods are linked either to some internal mechanism in the Sun or said to be higher harmonics of the rotation without further discussion of their origin. In this article, the origin of the peaks in periodicities seen in the solar extreme ultraviolet (EUV) and ultraviolet (UV) irradiance around the 7, 9, and 14 days periods is discussed. Maps of the active regions and coronal holes are produced from six images per day using the Spatial Possibilistic Clustering Algorithm (SPoCA), a segmentation algorithm. Spectral irradiance at coronal, transition-region/chromospheric, and photospheric levels are extracted for each feature as well as for the full disk by applying the maps to full-disk images (at 19.3, 30.4, and 170 nm sampling in the corona/hot flare plasma, the chromosphere/transition region, and the photosphere, respectively) from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO) from January 2011 to December 2018. The peaks in periodicities at 7, 9, and 14 days as well as the solar rotation around 27 days can be seen in almost all of the solar irradiance time series. The segmentation also provided time series of the active regions and coronal holes visible area (i.e. in the area observed in the AIA images, not corrected for the line-of-sight effect with respect to the solar surface), which also show similar peaks in periodicities, indicating that the periodicities are due to the change in area of the features on the solar disk rather than to their absolute irradiance. A simple model was created to reproduce the power spectral density of the area covered by active regions also showing the same peaks in periodicities. Segmentation of solar images allows us to determine that the peaks in periodicities seen in solar EUV/UV irradiance from a few days to a month are due to the change in area of the solar features, in particular, active regions, as they are the main contributors to the total full-disk irradiance variability. The higher harmonics of the solar rotation are caused by the clipping of the area signal as the regions rotate behind the solar limb.

Segmentation of Coronal Features to Understand the Solar EUV and UV Irradiance Variability III. Inclusion and Analysis of Bright Points

The study of solar irradiance variability is of great importance in heliophysics, Earth’s climate, and space weather applications. These studies require careful identifying, tracking and monitoring of features in the solar photosphere, chromosphere, and corona. Do coronal bright points contribute to the solar irradiance or its variability as input to the Earth atmosphere? We studied the variability of solar irradiance for a period of 10 years (May 2010 – June 2020) using the Large Yield Radiometer (LYRA), the Sun Watcher using APS and image Processing (SWAP) on board PROBA2, and the Atmospheric Imaging Assembly (AIA), and applied a linear model between the segmented features identified in the EUV images and the solar irradiance measured by LYRA. Based on EUV images from AIA, a spatial possibilistic clustering algorithm (SPoCA) is applied to identify coronal holes (CHs), and a morphological feature detection algorithm is applied to identify active regions (ARs), coronal bright points (BPs), and the quiet Sun (QS). The resulting segmentation maps were then applied on SWAP images, images of all AIA wavelengths, and parameters such as the intensity, fractional area, and contribution of ARs/CHs/BPs/QS features were computed and compared with LYRA irradiance measurements as a proxy for ultraviolet irradiation incident to the Earth atmosphere. We modeled the relation between the solar disk features (ARs, CHs, BPs, and QS) applied to EUV images against the solar irradiance as measured by LYRA and the F10.7 radio flux. A straightforward linear model was used and corresponding coefficients computed using a Bayesian method, indicating a strong influence of active regions to the EUV irradiance as measured at Earth’s atmosphere. It is concluded that the long- and short-term fluctuations of the active regions drive the EUV signal as measured at Earth’s atmosphere. A significant contribution from the bright points to the LYRA irradiance could not be found.

Brain Magnetic Resonance Imaging Segmentation Using Possibilistic Clustering Algorithm Combined with Context Constraints

Because the FCM method is simple and effective, a series of research results based on this method are widely used in medical image segmentation. Compared with the traditional FCM, the probability clustering (PCM) algorithm cancels the constraint on the normalization of each sample membership degree in the iterative process, and the clustering effect of the method is improved within a certain range. However, the above two methods only use the gray value of the image pixels in the iterative process, ignoring the context constraint relationship between the high-dimensional image pixels. The two are easily affected by image noise during the segmentation process, resulting in poor robustness, which will affect the segmentation accuracy in practical applications. In order to alleviate this problem, this paper introduces the context constraint information of image based on PCM, and proposes a PCM algorithm that combines context constraints (CCPCM) and successfully applies it to human brain MR image segmentation to further improve the noise immunity of the new algorithm. Expand the applicability of new algorithms in the medical field. Through simulation results on medical images, it is found that compared with the previous classical clustering methods, such as FCM, PCM, etc., the CCPCM has better anti-interference to different noises, and the segmentation boundary is clearer. At the same time, CCPCM algorithm introduces the spatial neighbor information adaptive weighting mechanism in the clustering process, which can adaptively adjust the constraint weight of spatial information and optimize the clustering process, thus improving the segmentation efficiency.

Coronal Holes during the Period of Maximum Asymmetry in the 24th Solar Activity Cycle

The current 24th solar activity cycle differs substantially from previous cycles in a number of parameters, especially in terms of a large asymmetry in the number of sunspots (Sp) during the second peak of its maximum. From March 2013 through December 2015. a significant predominance was observed in the number of sunspots in the southern hemisphere. The main purpose of this paper is to clarify the behavior of coronal holes (CH) during this period. This study is based on an analysis of data recorded by the 19.3 nm channel of the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamic Observatory (SDO). Two methods of detecting CH (simplified visual and the Spatial Possibilistic Clustering Algorithm (SPoCA)) are used to obtain time series of daily total CH areas for the Sun’s northern and southern hemispheres. The two methods agree on the estimated areas of the CH. A comparison of the observed variations in the areas of the CH with the numbers and areas of sunspots showed that in this period, activity predominates in the S-hemisphere both in terms of sunspots and in terms of the total CH area. Here a rise in the area of the CH follows a rise in sunspot activity by roughly half a year. It is suggested that the CH and spots are associated elements of the overall magnetic activity of the Sun, in qualitative agreement with studies of activity complexes. A dipole poloidal field in the form of open CH fields and a toroidal field in the form of active regions are related on time scales substantially shorter than the solar cycle.

Images Sub-segmentation by Fuzzy and Possibilistic Clustering Algorithm

In this work, an alternative new methodology to segment regions in an image is proposed. The method takes the advantages offered by hybrid algorithms, as the Possibilistic Fuzzy c-Means (PFCM) clustering algorithm, which has the qualities of both the Fuzzy c-Means (FCM) and the Possibilistic c-Means (PCM). The method is called sub-segmentation, and it consists of finding some clusters in an image through the segmentation of the image and, within these clusters, the less representative pixels or atypical pixels. These elements very frequently represent the zones of interest during image analysis. Three different cases are used in order to illustrate the method. The first one is an image of a drop of milk, where the generality of the method is tested in a simple but representative image. The second case corresponds to digital mammograms, where the potentiality of the method is tested in a critical application, such as anomalies identification in mammograms for cancer detection. The last case gives an idea of its range of applications, as the method is applied to an industrial case of classification of wood boards according to their quality. As can be seen from the three cases used in this work, the results are very interesting and promising.

Network Traffic Anomaly Detection Based on Incremental Possibilistic Clustering Algorithm

This paper proposed a Mahalanobis distance based Incremental Possibilistic Clustering (IPC) algorithm to detect abnormal flow. Firstly, the attributes of network flow is extracted by damped incremental statistics. Then the model of normal traffic will be generated by IPC algorithm. To extract the model of high-dimensional data without pre-known number of cluster centers, the algorithm gradually choose outliers as new clustering centers and merges the overlapping clustering centers. Finally, the data that doesn’t belong to any normal model is regarded as abnormal data. By using the Mahalanobis distance instead of the traditional Euclidean distance, the defect that the possibilistic clustering tends to find the features of hypersphere is solved. The experiments show that this method can distinguish normal flow and abnormal flow effectively and reaches the detection rate of 98%.

Fuzzy Clustering for Exploratory Analysis of EEG Event-Related Potentials

We introduce an analysis method for electroencephalography (EEG) data, focused on event-related potentials (ERPs). Our approach is unsupervised and makes use of a fuzzy clustering algorithm based on the possibilistic framework and includes a data-driven noise and artifact rejection phase. Our contribution provides a general analysis tool, applicable to any ERP dataset, which can uncover the dataset's internal structure. The fuzzy clustering algorithm is the core of our method, since its fine-grained membership grades how much a sample belongs to a given cluster, making the method applicable even when groups have a certain overlap. Prior to the clustering step, we apply weights to the feature vectors, optimizing them in order to enhance the variance within the dataset, and we extract time-window-interval-based features inspired by interval arithmetic. We apply the data processing workflow to the analysis of a set of ERPs recorded during an emotional Go/NoGo task. We evaluate the performance of the unsupervised analysis by computing a measure based on the clusterization rate of trials in different experimental conditions. The results of the studied dataset show that the proposed method obtains a difference of clusterization rate of 69% in Go versus NoGo trials, when weights and interval features are applied to the data, improving previous work not including weights and interval features, which had a rate of 31%. Furthermore, when compared with the standard fuzzy c-means, our proposed possibilistic clustering algorithm outperforms it in terms of the clusterization rate. We also examine the effect of preprocessing the data with independent component analysis and removing noise-related components and observe that this does not improve significantly the obtained results. These findings demonstrate that our proposed method provides a valuable data processing workflow robust to EEG artifacts and able to produce a clustering that is coherent with the experimental conditions represented in the ERP dataset.

Cutset-type possibilistic c-means clustering algorithm

The possibilistic c-means (PCM) clustering algorithm was introduced to avoid the sensitivity of the fuzzy c-means (FCM) clustering algorithm to outliers by relaxing the column sum constraint of the membership matrix of the FCM, namely the between-class relationships. The membership value is then interpreted as the typicality value of a data point in the PCM which reflects the absolute distance of data point to one cluster well. However, the PCM has a significant defect of coincident clustering problem because of relaxing the relations of clusters. In this paper, a novel cutset-type possibilistic clustering (C-PCM) algorithm is proposed. The C-PCM firstly generates a cluster core resulting from a β-cutset for each cluster and searches for data points located inside the cluster core. Then, the typicalities of these points to other clusters are modified, thus introducing the between-class relationships and avoiding coincident clusters. Simultaneously an adaptive determination method is also given for the parameter β in the C-PCM. Moreover, a novel segmentation method for images corrupted by salt-and-pepper noise is proposed by taking advantage of the strong robustness of the C-PCM to outliers. Several experiments are done on synthetic data-sets, high dimensional data sets, noisy images, which demonstrate the good performance of the proposed algorithm.

Segmentation of photospheric magnetic elements corresponding to coronal features to understand the EUV and UV irradiance variability

Context. The magnetic field plays a dominant role in the solar irradiance variability. Determining the contribution of various magnetic features to this variability is important in the context of heliospheric studies and Sun-Earth connection. Aims. We studied the solar irradiance variability and its association with the underlying magnetic field for a period of five years (January 2011–January 2016). We used observations from the Large Yield Radiometer (LYRA), the Sun Watcher with Active Pixel System detector and Image Processing (SWAP) on board PROBA2, the Atmospheric Imaging Assembly (AIA), and the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO). Methods. The Spatial Possibilistic Clustering Algorithm (SPoCA) is applied to the extreme ultraviolet (EUV) observations obtained from the AIA to segregate coronal features by creating segmentation maps of active regions (ARs), coronal holes (CHs) and the quiet sun (QS). Further, these maps are applied to the full-disk SWAP intensity images and the full-disk (FD) HMI line-of-sight (LOS) magnetograms to isolate the SWAP coronal features and photospheric magnetic counterparts, respectively. We then computed full-disk and feature-wise averages of EUV intensity and line of sight (LOS) magnetic flux density over ARs/CHs/QS/FD. The variability in these quantities is compared with that of LYRA irradiance values. Results. Variations in the quantities resulting from the segmentation, namely the integrated intensity and the total magnetic flux density of ARs/CHs/QS/FD regions, are compared with the LYRA irradiance variations. We find that the EUV intensity over ARs/CHs/QS/FD is well correlated with the underlying magnetic field. In addition, variations in the full-disk integrated intensity and magnetic flux density values are correlated with the LYRA irradiance variations. Conclusions. Using the segmented coronal features observed in the EUV wavelengths as proxies to isolate the underlying magnetic structures is demonstrated in this study. Sophisticated feature identification and segmentation tools are important in providing more insights into the role of various magnetic features in both the short- and long-term changes in the solar irradiance.

On the unification of possibilistic fuzzy clustering: Axiomatic development and convergence analysis

Fuzzy partitional clustering algorithms like Fuzzy C-means (FCM) are sensitive to noise points or outliers because of the probabilistic constraint (the sum of the membership values of a specific data point to all the clusters is 1), which enables it to classify any noise or outlier in a specific cluster. This, not only hampers the clustering performance corresponding to that specific point, but also leaves a huge impact on the overall clustering process by deviating the cluster centroids through a significant amount. In order to improve this weakness, possibilistic approach relaxes the probabilistic constraints. Nevertheless, due to lack of constraints imposed on the typicality matrix, depending on initialization, possibilistic clustering algorithms suffer from coincident clusters because their membership expressions do not consider the distance to other cluster representatives. Fuzzy possibilistic clustering which puts a linear constraint on the sum of all the typicality values, takes care of this problem, but if the number of data points is high, the generated typicality values are very small due to the linear constraint on their sums. In order to do away with that problem, the possibilistic fuzzy clustering algorithm was developed. In this article, we present an axiomatic development and extension of the possibilistic fuzzy clustering algorithm in three directions: choice of the dissimilarity measure, joint contribution function, and the penalty function. We provide a thorough convergence analysis of the proposed generalized possibilistic fuzzy clustering algorithm. We investigate the relationships of the proposed generalization with the existing variations of the Possibilistic C-Means (PCM), Fuzzy Possiblistic C-Means (FPCM) and Possibilistic Fuzzy C-Means (PFCM) algorithms in literature. To the best of our knowledge, this is the first article of its kind to provide a unification to the long list of possibilistic, fuzzy possiblistic, and possibilistic fuzzy clustering methods.

Statistical properties of coronal hole rotation rates: Are they linked to the solar interior?

The present paper discusses results of a statistical study of the characteristics of coronal hole (CH) rotation in order to find connections to the internal rotation of the Sun. The goal is to measure CH rotation rates and study their distribution over latitude and their area sizes. In addition, the CH rotation rates are compared with the solar photospheric and inner layer rotational profiles. We study coronal holes observed within $\pm 60$ latitude and longitude degrees from the solar disc centre during the time span from the 1 January 2013 to 20 April 2015, which includes the extended peak of solar cycle 24.We used data created by the Spatial Possibilistic Clustering Algorithm (SPoCA), which provides the exact location and characterisation of solar coronal holes using SDO=AIA 193 {\AA} channel images. The CH rotation rates are measured with four-hour cadence data to track variable positions of the CH geometric centre. North-south asymmetry was found in the distribution of coronal holes: about 60 percent were observed in the northern hemisphere and 40 percent were observed in the southern hemisphere. The smallest and largest CHs were present only at high latitudes. The average sidereal rotation rate for 540 examined CHs is $13:86 (\pm 0:05)$ degrees/d. Conclusions. The latitudinal characteristics of CH rotation do not match any known photospheric rotation profile. The CH angular velocities exceed the photospheric angular velocities at latitudes higher than 35-40 degrees. According to our results, the CH rotation profile perfectly coincides with tachocline and the lower layers of convection zone at around 0.71 $R_{\odot}$; this indicates that CHs may be linked to the solar global magnetic field, which originates in the tachocline region.

Sparsity-Aware Possibilistic Clustering Algorithms

In this paper, two novel possibilistic clustering algorithms are presented, which utilize the concept of sparsity. The first one, called sparse possibilistic c-means, exploits sparsity and can deal well with closely located clusters that may also be of significantly different densities. The second one, called sparse adaptive possibilistic c-means, is an extension of the first, where now the involved parameters are dynamically adapted. The latter can deal well with even more challenging cases, where, in addition to the above, clusters may be of significantly different variances. More specifically, it provides improved estimates of the cluster representatives, while, in addition, it has the ability to estimate the actual number of clusters, given an overestimate of it. Extensive experimental results on both synthetic and real datasets support the previous statements.

An Analysis of Distributed Fuzzy K-Prototype Clustering Techniques over Peer to Peer Network Environment

The challenging problems in recent years is the Distributed Data clustering over Peer-to-Peer network (P2P). In this paper, there is a presentation of peer-to-peer based K-prototype framework named MEKPFCM, by incorporating kernel fuzzy c-means and possibilistic fuzzy clustering algorithms. This work also considers the distributed clustering problem where the data and computing resources are spread over the large Peer-to-Peer network. It offers two algorithms which produce an approximate result produced by the MEKPFCM clustering algorithm. In the dynamic P2P network, the distributed fuzzy k-prototype clustering algorithm is played a major role. This can produce clustering's by local synchronization only. The second algorithm uses sampled peers that are reliable and present analytical guarantees regarding the accuracy of clustering on a P2P network. The performance of the proposed method evaluation is done through accuracy and computation time and the experimentation shows that the proposed method gives good performance compared to the existing method.

Possibilistic Clustering Algorithm Incorporating Grey-Level Histogram and Spatial Information for Image Segmentation

Image segmentation is a process of segmenting an image into non-intersecting regions containing homogeneous pixels that are inhomogeneous with those in other adjacent regions. In this paper, a possibilistic clustering algorithm incorporating grey-level histogram and spatial information (PCA_HS) for image segmentation is proposed. The grey-level histogram speeds up the algorithm and the spatial information enhances its robustness to noise and outliers. To assess the proposed algorithm, four widely used validity indexes are computed and discussed. As the experimental quantitative and qualitative results on real images with and without noise show, PCA_HS can preserve the homogeneity and integrality of the regions and hence is more effective and efficient than traditional PCA.

Rederivation of the fuzzy–possibilistic clustering objective function through Bayesian inference

Unsupervised clustering of a set of datums into homogeneous groups is a primitive operation required in many signal and image processing applications. In fact, different incarnations and hybrids of Fuzzy C-Means (FCM) and Possibilistic C-means (PCM) have been suggested which address additional requirements such as accepting weighted sets and being robust to the presence of outliers. Nevertheless, arriving at a general framework, which is independent of the datum model and the notion of homogeneity of a particular problem class, is a challenge. However, this process has not been followed organically and clustering algorithms are generally based on exogenous objective functions which are heuristically engineered and are believed to lead to the satisfaction of a required behavior. These techniques also commonly depend on regularization coefficients which are to be set “prudently” by the user or through separate processes. In contrast, in this work, we utilize Bayesian inference and derive a robustified objective function for a fuzzy–possibilistic clustering algorithm by assuming a generic datum model and a generic notion of cluster homogeneity. We utilize this model for the purpose of cluster validity assessment as well. We emphasize the epistemological importance of the theoretical basis on which the developed methodology rests. At the end of this paper, we present experimental results to exhibit the utilization of the developed framework in the context of four different problem classes.