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AbstractClustering of data with incomplete information is a difficult task, which is being researched extensively. Several researchers used fuzzy clustering methods for clustering of such data. Since conventional fuzzy clustering uses Euclidean distance metric to derive the information between a cluster center and a data point, it suffers badly when the clusters are divergent in nature. This paper proposes a new iterative Mahalanobis distance based fuzzy clustering to capture the essence of non-spherical shape of data along with incorporation of an imputation technique. The proposed methodology is compared with several imputation based FCM approaches as well as various clustering approaches as suggested by Hathway and Bezdek for incomplete data. Numerical analysis on one synthetic data set and various real life data sets show that the proposed clustering method is significantly better than other imputation as well as non-imputation techniques for these data sets.

Introduction: Incomplete data sets containing some missing attributes is a prevailing problem in many research areas. The reasons for the lack of missing attributes may be several; human error in tabulating/recording the data, machine failure, errors in data acquisition or refusal of a patient/customer to answer few questions in a questionnaire or survey. Further, clustering of such data sets becomes a challenge. Objective: In this paper, we presented a critical review of various methodologies proposed for handling missing data in clustering. The focus of this paper is the comparison of various imputation techniques based FCM clustering and the four clustering strategies proposed by Hathway and Bezdek. Methods: In this paper, we imputed the missing values in incomplete datasets by various imputation/ non-imputation techniques to complete the data set and then conventional fuzzy clustering algorithm is applied to get the clustering results. Results: Experiments on various synthetic data sets and real data sets from UCI repository are carried out. To evaluate the performance of the various imputation/ non-imputation based FCM clustering algorithm, several performance criteria and statistical tests are considered. Experimental results on various data sets show that the linear interpolation based FCM clustering performs significantly better than other imputation as well as non-imputation techniques. Conclusion: It is concluded that the clustering algorithm is data specific, no clustering technique can give good results on all data sets. It depends upon both the data type and the percentage of missing attributes in the dataset. Through this study, we have shown that the linear interpolation based FCM clustering algorithm can be used effectively for clustering of incomplete data set.

Fuzzy c-means and its derivatives such as possibilistic c-means and possibilistic fuzzy c-means are the most widely used clustering algorithms in the literature. Though efficient, these clustering algorithms do not achieve high cluster quality on real-world datasets, which are not linearly separable. Kernel-based clustering algorithms employ nonlinear similarity measures to define the inter-point similarities. As a result, they are able to identify clusters of arbitrary shapes and densities. Comparative analysis over standard datasets has established the superiority of kernel methods over its corresponding standard algorithms. In this paper, we propose a kernel-based Atanassov's possibilistic intuitionistic fuzzy clustering for data clustering and image segmentation. The paper explores the performance of the proposed methodology with respect to various internal and external indices for various real datasets and it is found to perform better than other clustering techniques in the sequel, i.e., normal as well as kernel-based algorithms. Experimental results on noisy image datasets also show the competence of the proposed approach.

In the past few years, the kernel-based clustering methods have overpowered the conventional clustering techniques in the field of unsupervised learning due to its strength and effectiveness to deal with nonlinearly separable data and mapping it into higher dimensional feature space by preserving the inner structure of the data. Many kernel functions exist in the literature which works effectively depending on the type of dataset to be used. In this paper, we have proposed a new log kernel function which is embedded in the unsupervised possibilistic clustering and this kernel function is not explored much in research. We have done extensive comparison of the proposed algorithm with few clustering techniques over a test suite of several synthetic and real life datasets. Based on the experimental results, we have proved that our algorithm gives better performance than the previous methods on various comparative parameters like ideal centroids, error rate, misclassification, accuracy and elapsed time.

Kernel methods are ones that, by replacing the inner product with positive definite function, implicitly perform a non-linear mapping of input data into a high dimensional feature space. Kernel functions are used to make this mapping in higher dimension redundant. These kernel functions play an important role in classification. The kernel-based clustering methods are found to be superior in accuracy to the conventional ones. The choice of kernel function is neither easy nor trivial. Various types of kernel based clustering methods have been studied so far by many researchers, where Gaussian kernel, in particular, has been found to be useful. In this study, we present a comprehensive comparative analysis of kernel based hybrid c-means clustering using different kernel functions. We have incorporated Mercer kernel functions (positive definite kernels) as well as conditionally positive definite kernel functions. Various synthetic datasets and real-life datasets are used for analysis. Experiments results show that there exist other robust kernel functions which hold like Gaussian kernel.