Fuzzy Partition Clustering Research Articles

A social network user behaviour data recommendation system based on fuzzy partition clustering

A social network user behaviour data recommendation system based on fuzzy partition clustering

A social network user behaviour data recommendation system based on fuzzy partition clustering

A social network user behaviour data recommendation system based on fuzzy partition clustering

Robust hesitant fuzzy partitional clustering algorithms and their applications in decision making

Hesitant fuzzy sets (HFSs) are a powerful tool to describe uncertain and vague information, whose relationship can be analyzed and mined by clustering algorithms. The partitional idea is widely used in clustering analysis for real-number data but little for hesitant fuzzy data. After pointing out the weakness of the existing partitional clustering algorithms between HFSs, we modify the existing partitional clustering algorithms and propose four new algorithms with two types under hesitant fuzzy environment. One type, including the hesitant fuzzy K-medians (HFKME) and the hesitant fuzzy C-medians (HFCME) algorithms, is based on median but not mean. The other type, including the improved hesitant fuzzy K-means (IHFKM) and the improved hesitant fuzzy C-means (IFHCM) algorithms, is on the basis of a new and more robust distance measure which will be developed by HFSs. We find that these four new clustering algorithms are more robust than the existing ones and have better performance under the noise environment. After that, we compare our proposed partitional clustering algorithms with each other and also compare them with the existing methods, and then apply them to multi-attribute decision making and cluster analysis. Numerical results show that HFCME has better performance than HFKME, and IHFCM is better than IHFKM.

An improved approach to fuzzy clustering based on FCM algorithm and extended VIKOR method

Fuzzy C-means algorithm is a fuzzy partitional clustering algorithm. However, accuracy and easy to implement have converted this algorithm to the focus of research, and sensitivity to noisy data is an important and challenging issue in the algorithm, so that in recent years, many studies have been done to improve it. In this paper, a clustering algorithm named Fuzzy VIKOR C-means presented that by utilizing the extended VIKOR method based on targeted displacements in the centroids of the clusters seek to benefit from the flexibility property. Moreover, this algorithm also, considering Dunn’s index, means, and density measures as profit criteria, and DB index and the entropy measures as cost criteria, can reduce the sensitivity to noisy data and can enhance performance and quality of clusters. According to the simulation results and comparison with some recent well-known methods, this approach has an effective role in improving the assessment criteria.

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.

Geometric divergence based fuzzy clustering with strong resilience to noise features

In this article we consider the problem of fuzzy partitional clustering using a separable multi-dimensional version of the geometric distance which includes f-divergences as special cases. We propose an iterative relocation algorithm for the Fuzzy C Means (FCM) clustering that is guaranteed to converge to local minima. We also demonstrate, through theoretical analysis, that the FCM clustering with the proposed divergence based similarity measure, is more robust towards the perturbation of noise features than the standard FCM with Euclidean distance based similarity measure. In addition, we show that FCM with the suggested geometric divergence measure has better or comparable clustering performance to that of FCM with squared Euclidean distance on real world and synthetic datasets (even in absence of the noise features).

The bimodality of the 10k zCOSMOS-bright galaxies up toz ~ 1: a new statistical and portable classification based on optical galaxy properties

Our goal is to develop a new and reliable statistical method to classify galaxies from large surveys. We probe the reliability of the method by comparing it with a three-dimensional classification cube, using the same set of spectral, photometric and morphological parameters.We applied two different methods of classification to a sample of galaxies extracted from the zCOSMOS redshift survey, in the redshift range 0.5 < z < 1.3. The first method is the combination of three independent classification schemes, while the second method exploits an entirely new approach based on statistical analyses like Principal Component Analysis (PCA) and Unsupervised Fuzzy Partition (UFP) clustering method. The PCA+UFP method has been applied also to a lower redshift sample (z < 0.5), exploiting the same set of data but the spectral ones, replaced by the equivalent width of H$\alpha$. The comparison between the two methods shows fairly good agreement on the definition on the two main clusters, the early-type and the late-type galaxies ones. Our PCA-UFP method of classification is robust, flexible and capable of identifying the two main populations of galaxies as well as the intermediate population. The intermediate galaxy population shows many of the properties of the green valley galaxies, and constitutes a more coherent and homogeneous population. The fairly large redshift range of the studied sample allows us to behold the downsizing effect: galaxies with masses of the order of $3\cdot 10^{10}$ Msun mainly are found in transition from the late type to the early type group at $z>0.5$, while galaxies with lower masses - of the order of $10^{10}$ Msun - are in transition at later epochs; galaxies with $M <10^{10}$ Msun did not begin their transition yet, while galaxies with very large masses ($M > 5\cdot 10^{10}$ Msun) mostly completed their transition before $z\sim 1$.

A high-performing comprehensive learning algorithm for text classification without pre-labeled training set

In this paper, we investigate a comprehensive learning algorithm for text classification without pre-labeled training set based on incremental learning. In order to overcome the high cost in getting labeled training examples, this approach reforms fuzzy partition clustering to obtain a small quantity of labeled training data. Then the incremental learning of Bayesian classifier is applied. The model of the proposed classifier is composed of a Naive-Bayes-based incremental learning algorithm and a modified fuzzy partition clustering method. For improved efficiency, a feature reduction is designed based on the Quadratic Entropy in Mutual Information. We perform experiments to demonstrate the performance of the approach, and the results show that our approach is feasible and effective.