Hard Clustering Methods Research Articles

Bagged fuzzy clustering for fuzzy data: An application to a tourism market

Segmentation has several strategic and tactical implications in marketing products and services. Despite hard clustering methods having several weaknesses, they remain widely applied in marketing studies. Alternative segmentation methods such as fuzzy methods are rarely used to understand consumer behaviour. In this study, we propose a strategy of analysis, by combining the Bagged Clustering (BC) method and the fuzzy C-means clustering method for fuzzy data (FCM-FD), i.e., the Bagged fuzzy C-means clustering method for fuzzy data (BFCM-FD). The method inherits the advantages of stability and reproducibility from BC and the flexibility from FCM-FD. The method is applied on a sample of 328 Chinese consumers revealing the existence of four segments (Admirers, Enthusiasts, Moderates, and Apathetics) of the perceived images of Western Europe as a tourist destination. The results highlight the heterogeneity in Chinese consumers’ place preferences and implications for place marketing are offered.

Kernel-based hard clustering methods in the feature space with automatic variable weighting

This paper presents variable-wise kernel hard clustering algorithms in the feature space in which dissimilarity measures are obtained as sums of squared distances between patterns and centroids computed individually for each variable by means of kernels. The methods proposed in this paper are supported by the fact that a kernel function can be written as a sum of kernel functions evaluated on each variable separately. The main advantage of this approach is that it allows the use of adaptive distances, which are suitable to learn the weights of the variables on each cluster, providing a better performance. Moreover, various partition and cluster interpretation tools are introduced. Experiments with synthetic and benchmark datasets show the usefulness of the proposed algorithms and the merit of the partition and cluster interpretation tools.

Clustering Sentence-Level Text Using a Novel Fuzzy Relational Clustering Algorithm

In comparison with hard clustering methods, in which a pattern belongs to a single cluster, fuzzy clustering algorithms allow patterns to belong to all clusters with differing degrees of membership. This is important in domains such as sentence clustering, since a sentence is likely to be related to more than one theme or topic present within a document or set of documents. However, because most sentence similarity measures do not represent sentences in a common metric space, conventional fuzzy clustering approaches based on prototypes or mixtures of Gaussians are generally not applicable to sentence clustering. This paper presents a novel fuzzy clustering algorithm that operates on relational input data; i.e., data in the form of a square matrix of pairwise similarities between data objects. The algorithm uses a graph representation of the data, and operates in an Expectation-Maximization framework in which the graph centrality of an object in the graph is interpreted as a likelihood. Results of applying the algorithm to sentence clustering tasks demonstrate that the algorithm is capable of identifying overlapping clusters of semantically related sentences, and that it is therefore of potential use in a variety of text mining tasks. We also include results of applying the algorithm to benchmark data sets in several other domains.

Soft and hard clustering methods for delineation of hydrological homogeneous regions in the southern strip of the Caspian Sea Watershed

AbstractRegionalisation is a fundamental task for transferring hydrological information from gauged to un‐gauged catchments. This study employs several soft and hard clustering approaches for regionalisation of the 61 catchments located in the southern strip of the Caspian Sea Watershed. Factor analysis using Principal Component Analysis resulted to four out of 16 catchment's attributes relating to flooding which were then used for regionalisation. Hierarchical and Non‐Hierarchical Clustering, K‐Means, Fuzzy C‐Means and Kohonen methods were studied and compared by L‐Moment tests. While in hard clustering approach, distinct clusters of catchments were formed, soft clustering techniques allocated catchments to more than one cluster according to their membership probability. The performance of different clustering methods resulted to the similar number of homogeneous groups. However, the number of sites allocated to the clusters is different. Hard clustering resulted in three clusters at 38, 10 and 13 sites, while Soft clustering allocated 26, 20 and 15 sites to the clusters, respectively. Results indicate a superiority of the soft clustering in the study area where deriving hydrologic groups by hard clustering is problematic.

MO‐E‐330A‐03: Automated Texture Based CT Segmentation by Gabor Filtering and Fuzzy Clustering

Purpose: To automate segmentation of lesion and organs at risk in lung patients by using Gabor filtering and fuzzy clustering for 4D CT image data and to check the usefulness of segmentation by using these methods. Method and Materials: Image was pre‐processed with contrast enhancement and median filtering in order to prepare it for feature extraction. By filtering the enhanced image by Gabor filtering, texture features were extracted. Three fuzzy segmentation algorithms were selected including Fuzzy C‐Means (FCM), Gustaffson Kessel and Gath Geva (GG). Optimal number of clusters is determined by using validity criterion including Partition coefficient (F), Classification entropy (H), Xie Beni index (XB) and Partition index (SC). Images were then clustered and clusters visualized by using Principle Component Analysis (PCA). Finally, Performance of the algorithms was calculated by plotting the Receiver Operating Curves (ROC). Results: It was found that different clustering algorithms are best suited for different tissue/Organ segmentations. Furthermore, ROC curves indicated that FCM segmented the left lung with a True Positive (TP) rate of 94.72%, GK segmented Lesion with a TP rate of 88% and GG segmented heart with a TP rate of 74.8%. Fuzzy clustering methods in conjunction with Gabor filters are seen to completely outperform traditional Hard clustering methods like K‐Means and KMediod. Finally, there is a marked difference seen between the fuzzy clustered regions and oncologist marked GTV. Conclusion: Texture based segmentation using Gabor filtering and fuzzy clustering perform quite well for Lesion and organs at risk segmentation, however, different fuzzy clustering methods should be combined for optimal segmentation. As Gabor filters use different frequencies and orientation for filtering, they reveal hidden structure, which may contribute to a more precise delineation of tissue/lesion structure.

Fuzzy Bayesian validation for cluster analysis of yeast cell-cycle data

Clustering for the analysis of the genes organizes the patterns into groups by the similarity of the dataset and has been used for identifying the functions of the genes in the cluster and analyzing the functions of unknown genes. Since the genes usually belong to multiple functional families, fuzzy clustering methods are more appropriate than the conventional hard clustering methods which assign a sample to only one group. In this paper, a Bayesian-like validation method selecting a fuzzy partition is proposed to evaluate the fuzzy partitions effectively. The theoretical interpretation of the obtained memberships is beyond the scope of this paper, and an empirical evaluation of the proposed method is conducted by comparing to the four representative conventional fuzzy cluster validity measures in four well-known datasets. Analysis of yeast cell-cycle data follows to evaluate the proposed method.

Rainfall Patterns over India: Classification with Fuzzy c-Means Method

Seasonal (June through September) percentage departure from normal rainfall patterns over India for the period 1871–1994 have been classified using Fuzzy c-means method (FCM) to identify the dominant modes of spatio-temporal variability in the Indian monsoon rainfall. Unlike the hard clustering methods, for example the Map-to-Map (MM) correlation method and the k-means (KM) clustering method, this method does not force a pattern to get classified into only one cluster but assigns varying membership to every cluster. Thus marginal patterns get classified into all clusters with different memberships.

Market definition and segmentation using fuzzy clustering methods

The main theme of this paper is the use of so-called fuzzy clustering methods for market definition and segmentation. Market boundaries are formed according to substitutive relations between brands as seen by homogeneous segments of potential or actual customers. The classification types partition, overlapping classification and fuzzy partition are explained. Segmentation of customers is conceived as a pre-processing step of market definition. Segments are aggregates of customers homogeneous with respect to the substitutive relations between brands. Several fuzzy clustering methods are presented. Evaluation procedures specialized in fuzzy classifications or suited for fuzzy and non-fuzzy classifications are dealt with. One of these procedures is an enlargement of the ADCLUS-model for fuzzy membership values of objects. An empirical pilot study demonstrates and compares the methods discussed. Diverse hard and fuzzy clustering methods are used to form homogeneous segments of customers and sets of competitive brands. External and internal validity of this classifications are determined.