Gözde Ulutagay

A new unsupervised approach for fuzzy clustering

In this paper, a new level-based (hierarchical) approach to the fuzzy clustering problem for spatial data is proposed. In this approach each point of the initial set is handled as a fuzzy point of the multidimensional space. Fuzzy point conical form, fuzzy α-neighbor points, fuzzy α-joint points are defined and their properties are explored. It is known that in classical fuzzy clustering the matter of fuzziness is usually a possibility of membership of each element into different classes with different positive degrees from [0,1]. In this study, the fuzziness of clustering is evaluated as how much in detail the properties of classified elements are investigated. In this extent, a new Fuzzy Joint Points (FJP) method which is robust through noises is proposed. Algorithm of FJP method is developed and some properties of the algorithm are explored. Also sufficient condition to recognize a hidden optimal structure of clusters is proven. The main advantage of the FJP algorithm is that it combines determination of initial clusters, cluster validity and direct clustering, which are the fundamental stages of a clustering process. It is possible to handle the fuzzy properties with various level-degrees of details and to recognize individual outlier elements as independent classes by the FJP method. This method could be important in biological, medical, geographical information, mapping, etc. problems.

Robustness of density-based clustering methods with various neighborhood relations

Cluster analysis is one of the most crucial techniques in statistical data analysis. Among the clustering methods, density-based methods have great importance due to their ability to recognize clusters with arbitrary shape. In this paper, robustness of the clustering methods is handled. These methods use distance-based neighborhood relations between points. In particular, DBSCAN (density-based spatial clustering of applications with noise) algorithm and FN-DBSCAN (fuzzy neighborhood DBSCAN) algorithm are analyzed. FN-DBSCAN algorithm uses fuzzy neighborhood relation whereas DBSCAN uses crisp neighborhood relation. The main characteristic of the FN-DBSCAN algorithm is that it combines the speed of the DBSCAN and robustness of the NRFJP (noise robust fuzzy joint points) algorithms. It is observed that the FN-DBSCAN algorithm is more robust than the DBSCAN algorithm to datasets with various shapes and densities.

Fuzzy and crisp clustering methods based on the neighborhood concept: A comprehensive review

The aim of this paper has twofold: i to explore the fundamental concepts and methods of neighborhood-based cluster analysis with its roots in statistics and decision theory, ii to provide a compact tool for researchers. Since DBSCAN is the first method which uses the concept of neighborhood and it has many successors, we started our discussion by exploring it. Then we compared some of the successors of DBSCAN algorithm and other crisp and fuzzy methods on the basis of neighborhood strategy.

On the analysis of BIS stage epochs via fuzzy clustering.

Abstract Among various types of clustering methods, partition-based methods such as k-means and FCM are widely used in the analysis of such data. However, when duration between stimuli is different, such methods are not able to provide satisfactory results because they find equal size clusters according to the fundamental running principle of these methods. In such cases, neighborhood-based clustering methods can give more satisfactory results because measurement series are separated from one another according to dramatic breaking points. In recent years, bispectral index (BIS) monitoring, which is used for monitoring the level of anesthesia, has been used in sleep studies. Sleep stages are classically scored according to the Rechtschaffen and Kales (R&K) scoring system. BIS has been shown to have a strong correlation with the R&K scoring system. In this study, fuzzy neighborhood/density-based spatial clustering of applications with noise (FN-DBSCAN) that combines speed of the DBSCAN algorithm and robustness of the NRFJP algorithm is applied to BIS measurement series. As a result of experiments, we can conclude that, by using BIS data, the FN-DBSCAN method estimates sleep stages better than the fuzzy c-means method.

OWA aggregation based CxK-nearest neighbor classification algorithm

A new OWA (Ordered Weighted Averaging) distance based CxK-nearest neighbor algorithm (CxK-NN) is proposed. In this approach, K-nearest neighbors from each of the classes are taken into account instead of the well-known K-nearest neighbor (K-NN) algorithm in which only the total number, K of neighbors are considered. Distance between the classified point and its K-nearest set is determined based on the OWA operator. After experiments with well-known classification datasets, we conclude that average accuracy results of the OWA distance-based CxK-NN algorithm are better than that of K-NN and weighted K-NN algorithms.

An Extension of Fuzzy L-R Data Classification with Fuzzy OWA Distance

K‐Nearest neighbor (K‐NN) algorithm is a classification algorithm widely used in machine learning, statistical pattern recognition, data mining, etc. Ordered weighted averaging (OWA) distance based CxK nearest neighbor algorithm is a kind of K‐NN algorithm based on OWA distance. In this study, the aim is two‐fold: i) to perform the algorithm with two different fuzzy metric measures, which are Diamond distance, and weighted dissimilarity measure composed by spread distances and center distances, and ii) to evaluate the effects of different metric measures. K neighbors are searched for each class, and OWA distance is used to aggregate the information. The OWA distance can behave as intercluster distance approaches single, complete, and average linkages by using different weights. The experimental study is performed on well‐known three classification data sets (iris, glass, and wine). N‐fold cross‐validation is used for the evaluation of performances. It is seen that single linkage approach by using two different metric measures has significant different results.

Ranking Fuzzy Numbers and Its Extensions

Ranking fuzzy numbers plays a prominent role in management, engineering, and basic sciences. Fuzzy numbers are represented by a membership function, and despite the real numbers that can be linearly ordered, fuzzy numbers might overlap with each other; thus, their ordering seems impossible or very difficult. Varieties of methods have been proposed for ranking fuzzy numbers in the recent years. Due to nonintuitive and nondiscriminating results of these methods that cause inconsistency in outputs, generalization of them is limited and there are some extenuations associated with them. Some of the ranking methods use defuzzification methods, while others are based on themembership function ormetric distance methods. This issue’s papers study the following areas.

Combining the Information of Multiple Ranker in Ranked Set Sampling with Fuzzy Set Approach

Ranked set sampling (RSS) is a useful alternative sampling method for parameter estimation. Compared to other sampling methods, it uses the ranking information of the units in the ranking mechanism before the actual measurement. The ranking mechanism can be described as a visual inspection of an expert or a highly-correlated concomitant variable. Accuracy for ranking of the sample units affects the precision of the estimation. This study proposes an alternative approach, called Fuzzy-weighted Ranked Set Sampling (FwRSS), to RSS for dealing with the uncertainty in ranking using fuzzy set. It assumes that there are K (\(K>1\)) rankers for rank decisions and uses three different fuzzy norm operators to combine the decisions of all rankers in order to provide the accuracy of ranking. A simulation study is constructed to see the performance of the mean estimators based on RSS and FwRSS.

Mean Estimation Based on FWA Using Ranked Set Sampling with Single and Multiple Rankers

The Ranked Set Sampling (RSS) is an advanced sampling method which improves the precision and accuracy of the mean estimator. In RSS, the units in the random sets which are drawn from a population are ranked by a ranking mechanism, and one of these ranked units is sampled from each set with a specific scheme. Ranking the units (visually or by a concomitant variable) could not be perfect because there is an uncertainty in decision making about the rank of a unit. In this study, we propose a fuzzy set perspective for RSS and an estimator for the population mean based on Fuzzy Weighted Average (FWA) operator. A real data application is given to illustrate the new approach for the single and multiple rankers.

Challenges and possible solutions to density based clustering

Clustering is an interdisciplinary-studied subject of statistical data analysis. In this study, among various types of clustering algorithms, the algorithms derived from Density Based Spatial Clustering of Applications with Noise (DBSCAN) are investigated. Although DBSCAN is the well-known density-based algorithms it has some bottlenecks. So, enhanced versions of DBSCAN are developed to provide some solutions and to ameliorate the algorithm. In this study, we provide a compact source of DBSCAN-based algorithms for the mentioned challenges.