Abstract
Relational fuzzy clustering has been developed for extracting intrinsic cluster structures of relational data and was extended to a linear fuzzy clustering model based on Fuzzyc-Medoids (FCMdd) concept, in which Fuzzyc-Means-(FCM-) like iterative algorithm was performed by defining linear cluster prototypes using two representative medoids for each line prototype. In this paper, the FCMdd-type linear clustering model is further modified in order to handle incomplete data including missing values, and the applicability of several imputation methods is compared. In several numerical experiments, it is demonstrated that some pre-imputation strategies contribute to properly selecting representative medoids of each cluster.
Highlights
Relational fuzzy clustering is a relational extension of fuzzy clustering for revealing cluster structures buried in relational data
Fuzzy c-Means (FCM) and other variants of k-Means [3] use the clustering criterion of the distance between a data point and a cluster prototype, Relational Fuzzy c-Means (RFCM) defines the clustering criterion by using mutual dissimilarities only
This paper studies the Fuzzy c-Medoids (FCMdd)-based linear clustering model [10], which can reveal local linear substructures buried in relational data
Summary
Relational fuzzy clustering is a relational extension of fuzzy clustering for revealing cluster structures buried in relational data. Relational Fuzzy c-Means (RFCM) [1] extended the Fuzzy c-Means (FCM) [2] clustering criterion with mutual dissimilarity measures instead of object-type observation in FCM. The FCMdd-type linear clustering model was further modified for dealing with non-Euclidean relational data [11, 12], in which data transformation, called β-spread transformation, was performed before applying the clustering algorithm in a similar manner to Non-Euclideantype Relational Fuzzy (NERF) c-Means [13]. A comparative study on the applicability of β-spread transformation is performed in FCMdd-based linear clustering of incomplete relational data. This paper demonstrates that the performance of FCMdd-type linear fuzzy clustering for incomplete relational data can .
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