Possibilistic Clustering Research Articles

Discriminative possibilistic clustering promoting cross-domain emotion recognition

Discriminative possibilistic clustering promoting cross-domain emotion recognition

Interval type-2 possibilistic picture C-means clustering incorporating local information for noisy image segmentation

Picture fuzzy C-means clustering is a novel computational intelligence method that has some advantages over fuzzy clustering in pattern analysis and machine intelligence. However, picture fuzzy clustering is easily affected by noise and weighting exponent, which seriously limits its widespread application. To address this issue, this paper proposes a new robust possibilistic clustering method called “interval type-2 possibilistic picture C-means clustering with local information”. This method combines interval type-2 fuzzy sets with possibilistic C-means clustering based on picture fuzzy sets, strengthening the noise resistance of picture fuzzy clustering. Firstly, this paper creatively extends an improved possibilistic clustering with double weighing exponents to picture fuzzy sets, solving the problem of consistency clustering in existing possibilistic picture clustering. Second, this paper originally introduces a new picture local information factor in possibilistic picture clustering and further enhances the anti-noise robustness of the method by using spatial possibilistic picture partition information. Finally, this paper skillfully extends this clustering method to interval type-2 fuzzy sets, which can handle more flexibly high-order uncertainties than type-1 clustering method. Experimental results indicate that this proposed method has better segmentation performance and stronger noise suppression ability compared with existing picture fuzzy clustering and interval type-2 fuzzy clustering. In summary, this work has made significant contributions to the development of picture fuzzy clustering theory and its applications.

Type2 soft biclustering framework for Alzheimer microarray

Microarray technology is a powerful tool that enables simultaneous analysis of the expression level of a large number of genes for different samples. Reliable information on gene expression level is much needed in the health system as it is widely used to predict, diagnose, and treat human diseases (e.g., Alzheimer's). For the analysis of the microarray dataset, biclustering is known to be a highly capable approach, however some characteristics of the dataset including high dimensionality, noise, uncertainty, and complex biological processes need to be handled properly. Concerning these characteristics, the current paper proposes a novel two-stage biclustering framework based on soft clustering and a metaheuristic technique. The integration of the two stages ensures a reliable search process to find similar expression patterns concerning gene expression characteristics. The proposed framework employs fuzzy and possibilistic clustering along with Type2-Fuzzy Sets theory to handle high-level uncertainty, noise, and outliers in microarray datasets. Considering the NP-hard nature of the biclustering method, the proposed framework incorporates the Genetic Algorithm with a unique chromosome representation, fitness function, and modification mechanisms. Real microarray datasets of Alzheimer's Disease have been used to evaluate the proposed framework. The comparative analysis of different versions of our proposed framework and some well-known biclustering methods demonstrates that the proposed framework is superior in terms of some indices including the mean squared residual and variance indices. The final results are further evaluated using the defined fitness function, which indicates the better performance of our possibilistic-based biclustering methods.

Possibilistic distribution distance metric: a robust domain adaptation learning method.

The affective Brain-Computer Interface (aBCI) systems, which achieve predictions for individual subjects through training on multiple subjects, often cannot achieve satisfactory results due to the differences in Electroencephalogram (EEG) patterns between subjects. One tried to use Subject-specific classifiers, but there was a lack of sufficient labeled data. To solve this problem, Domain Adaptation (DA) has recently received widespread attention in the field of EEG-based emotion recognition. Domain adaptation (DA) learning aims to solve the problem of inconsistent distributions between training and test datasets and has received extensive attention. Most existing methods use Maximum Mean Discrepancy (MMD) or its variants to minimize the problem of domain distribution inconsistency. However, noisy data in the domain can lead to significant drift in domain means, which can affect the adaptability performance of learning methods based on MMD and its variants to some extent. Therefore, we propose a robust domain adaptation learning method with possibilistic distribution distance measure. Firstly, the traditional MMD criterion is transformed into a novel possibilistic clustering model to weaken the influence of noisy data, thereby constructing a robust possibilistic distribution distance metric (P-DDM) criterion. Then the robust effectiveness of domain distribution alignment is further improved by a fuzzy entropy regularization term. The proposed P-DDM is in theory proved which be an upper bound of the traditional distribution distance measure method MMD criterion under certain conditions. Therefore, minimizing P-DDM can effectively optimize the MMD objective. Secondly, based on the P-DDM criterion, a robust domain adaptation classifier based on P-DDM (C-PDDM) is proposed, which adopts the Laplacian matrix to preserve the geometric consistency of instances in the source domain and target domain for improving the label propagation performance. At the same time, by maximizing the use of source domain discriminative information to minimize domain discrimination error, the generalization performance of the learning model is further improved. Finally, a large number of experiments and analyses on multiple EEG datasets (i.e., SEED and SEED-IV) show that the proposed method has superior or comparable robustness performance (i.e., has increased by around 10%) in most cases.

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.

Online Intrusion Detection for Internet of Things Systems With Full Bayesian Possibilistic Clustering and Ensembled Fuzzy Classifiers

The pervasive deployment of the Internet of Things (IoT) has significantly facilitated manufacturing and living. The diversity and continual updates of IoT systems make their security a crucial challenge, among which the detection of malicious network traffic turns out to be the most common yet destructive threat. Despite the efforts on feature engineering and classification backend designing, established intrusion detection systems sometimes lack robustness and are inflexible against the shift of the traffic distribution. To deal with these disadvantages, we design a fuzzy system for the online defense of IoT. Our framework incorporates a full Bayesian possibilistic clustering module for feature processing and an ensemble module motivated by reinforcement learning and adaptive boosting that dynamically fits the streaming data. The proposed clustering module overcomes the issue of determining the number of clusters and can dynamically identify new patterns. The classifier backend combines a collection of fuzzy decision trees that provide readable decision boundaries. The ensembled classifiers can accommodate the drift of data distribution to optimize the long-time performance. Our proposal is tested on settings including one dataset collected from real IoT systems and is compared to numerous competitors. Experimental results verified the advantage of our system regarding accuracy and stability.

Dynamic Evolving Cauchy Possibilistic Clustering Based on the Self-Similarity Principle (DECS) for Enhancing Intrusion Detection System

Dynamic Evolving Cauchy Possibilistic Clustering Based on the Self-Similarity Principle (DECS) for Enhancing Intrusion Detection System

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 self-learning iterative weighted possibilistic fuzzy c-means clustering via adaptive fusion

Considering that weighted possibilistic fuzzy clustering does not obtain significant performance compared with possibilistic fuzzy clustering, so this paper proposes an enhanced self-adaptive weighted possibilistic fuzzy clustering algorithm. Firstly, the principle of maximum entropy is introduced to weighted possibilistic fuzzy clustering, and the weighted coefficients of fuzzy clustering and possibilistic clustering are subject to regularization entropy constraint and a novel self-learning iterative weighted possibilistic fuzzy clustering is obtained, and its convergence is strictly proved by Zangwill theorem and bordered Hessian matrix. Secondly, a series of clustering validity functions for the proposed algorithm are constructed to determine the optimal number of clusters in the data set. In the end, to enhance the anti-noise robustness of the proposed algorithm, a robust loss function is applied in the adaptive weighted possibilistic fuzzy clustering, and a robust algorithm is obtained for noisy data clustering. Experimental results show that the proposed algorithm outperforms existing possibilistic fuzzy clustering-related algorithms, and the validity functions for the proposed algorithm can accurately determine the optimal number of clusters in the data set, meanwhile, the corresponding robust algorithm effectively enhances the performance of the algorithm in the presence of noise.

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.

A novel interval-valued data driven type-2 possibilistic local information c-means clustering for land cover classification

In the process of land cover classification, existing fuzzy clustering is not enough to describe the high-order fuzzy uncertainty, while possibilistic clustering has serious parameter dependence and cluster consistency, which makes them unable to effectively deal with the phenomena of “different objects with the same spectrum” and “different objects with the same spectrum”. Hence, this paper proposes a robust type-2 possibilistic C-means clustering with local information and interval-valued data model for remote sensing land cover classification. Firstly, according to the local neighborhood variance, remote sensing information is modeled as interval-valued data. Secondly, existing possibilistic C-means clustering is modified and an enhanced possibilistic C-means clustering is obtained. Once again, it is used to clustering interval-valued data and a single weighting exponent type-2 possibilistic C-means clustering with double distance measures is constructed. Finally, to further improve the robustness of clustering method, local information is embedded into the objective function of this enhanced type-2 possibilistic C-means clustering and a novel robust possibilistic clustering-related algorithm for remote sensing information classification is proposed. Experimental results show that the proposed algorithm outperforms existing state of the art type-2 clustering-related algorithms, and is of great significance to the interpretation of remote sensing images.

Multi-Model Adaptation Learning With Possibilistic Clustering Assumption for EEG-Based Emotion Recognition.

In machine learning community, graph-based semi-supervised learning (GSSL) approaches have attracted more extensive research due to their elegant mathematical formulation and good performance. However, one of the reasons affecting the performance of the GSSL method is that the training data and test data need to be independently identically distributed (IID); any individual user may show a completely different encephalogram (EEG) data in the same situation. The EEG data may be non-IID. In addition, noise/outlier sensitiveness still exist in GSSL approaches. To these ends, we propose in this paper a novel clustering method based on structure risk minimization model, called multi-model adaptation learning with possibilistic clustering assumption for EEG-based emotion recognition (MA-PCA). It can effectively minimize the influence from the noise/outlier samples based on different EEG-based data distribution in some reproduced kernel Hilbert space. Our main ideas are as follows: (1) reducing the negative impact of noise/outlier patterns through fuzzy entropy regularization, (2) considering the training data and test data are IID and non-IID to obtain a better performance by multi-model adaptation learning, and (3) the algorithm implementation and convergence theorem are also given. A large number of experiments and deep analysis on real DEAP datasets and SEED datasets was carried out. The results show that the MA-PCA method has superior or comparable robustness and generalization performance to EEG-based emotion recognition.

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.

Dynamic evidential clustering algorithm

In this paper, a dynamic evidential clustering algorithm (DEC) is introduced to address the computational burden of existing methods. To derive such a solution, an FCM-like objective function is first employed and minimized to obtain the support levels of the real singletons (specific) clusters to which the query objects belong, and then the query objects is initially adaptively assigned to outlier, precise or imprecise one via a new rule-based on the conflicts between the different support levels. For each imprecise object, it is finally reassigned to the singleton clusters or related meta-cluster by partial credal redistribution with the corresponding dynamic edited framework to reduce the computational burden. The proposed method can reduce the complexity to the level similar to that of the fuzzy and possibilistic clustering, which can effectively extend the application of evidential clustering, especially in big data. The effectiveness of the DEC method is tested by four experiments with artificial and real datasets.

Penalty term based suitable fuzzy intuitionistic possibilistic clustering: analyzing high dimensional gene expression cancer database

The aim of this paper is to identify the co-expressed potential genes that may serve for the development of the portions of normal or tumor. This paper differentiates the co-expressed genes into normal samples and tumor samples from gene expression dataset GSE25066. Since the dataset has vague boundaries and having common characteristics between the clusters, identifying the subgroups contain similar gene expression is really a tricky task one. Therefore, this paper introduces an effective fuzzy iterative clustering algorithm by incorporating kernel function, possibilistic c-means, fuzzy memberships, neighborhood information, median of neighboring objects and penalty term. The performances of the proposed clustering techniques have been shown through the succession experimental works on GSE25066. The effects of clustering results have been proved through comparing the resulted classes with ground truth.

An Intelligence EEG Signal Recognition Method via Noise Insensitive TSK Fuzzy System Based on Interclass Competitive Learning.

Epilepsy is an abnormal function disease of movement, consciousness, and nerve caused by abnormal discharge of brain neurons in the brain. EEG is currently a very important tool in the process of epilepsy research. In this paper, a novel noise-insensitive Takagi–Sugeno–Kang (TSK) fuzzy system based on interclass competitive learning is proposed for EEG signal recognition. First, a possibilistic clustering in Bayesian framework with interclass competitive learning called PCB-ICL is presented to determine antecedent parameters of fuzzy rules. Inherited by the possibilistic c-means clustering, PCB-ICL is noise insensitive. PCB-ICL learns cluster centers of different classes in a competitive relationship. The obtained clustering centers are attracted by the samples of the same class and also excluded by the samples of other classes and pushed away from the heterogeneous data. PCB-ICL uses the Metropolis–Hastings method to obtain the optimal clustering results in an alternating iterative strategy. Thus, the learned antecedent parameters have high interpretability. To further promote the noise insensitivity of rules, the asymmetric expectile term and Ho–Kashyap procedure are adopted to learn the consequent parameters of rules. Based on the above ideas, a TSK fuzzy system is proposed and is called PCB-ICL-TSK. Comprehensive experiments on real-world EEG data reveal that the proposed fuzzy system achieves the robust and effective performance for EEG signal recognition.

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.