Trimmed fuzzy clustering for interval-valued data

Abstract

In this paper, following a partitioning around medoids approach, a fuzzy\ud clustering model for interval-valued data, i.e., FCMd-ID, is introduced. Successively,\ud for avoiding the disruptive effects of possible outlier interval-valued data in the clustering\ud process, a robust fuzzy clustering model with a trimming rule, called Trimmed\ud Fuzzy C-medoids for interval-valued data (TrFCMd-ID), is proposed. In order to\ud show the good performances of the robust clustering model, a simulation study and\ud two applications are provided

Informational Paradigm, management of uncertainty and theoretical formalisms in the clustering framework: A review

“…The rationale for it lies in the recognition of the vague nature of the cluster assignment task. In the literature, several fuzzy clustering methods have been proposed and applied in many different fields [78] .…”

“…For this reason, the Bezdek's method represents the best-known and used clustering technique in the body of literature. Several fuzzy approach-based clustering methods have been developed by extending suitably the original Bezdek's method proposed in the 1981 [78] .…”

“…In particular, by considering the case in which the imprecision of the data are formalized in a fuzzy manner (fuzzy data) we point out the following contributes on fuzzy clustering of fuzzy data: Sato and Sato [266] , Hathaway et al [124] , Yang and Ko [320] , Yang and Liu [321] , Takata et al [282] , Auephanwiriyakul and Keller [26] , Butkiewicz [41] , Hung and Yang [128] , D'Urso and Giordani [80] , Zarandi and Razaee [334] , Coppi et al [63] . Suggestive applications of fuzzy clustering methods for fuzzy data in e-health and tourism have been suggested, respectively, by D'Urso et al [74] and D'Urso et al [76,78] . Recently, robust fuzzy clustering methods for fuzzy data have been suggested by D'Urso and De Giovanni [77] .…”

Fuzzy data analysis and classification

“…It should be remarked that, in contrast to the Kruse and Meyer's approach, statistical conclusions with Puri and Ralescu random fuzzy sets always concern the fuzzy-valued random element and the parameters associated with its induced distribution. An interesting distinctive feature of the statistical methodology based on this approach to generate fuzzy data is that most of the classical ideas in data analysis can be immediately preserved without needing to either define or adapt Huang and Ng (1999) and Lee and Pedrycz (2009) Functional data Tokushige et al (2007) and Tan et al (2013) Textual data (text data) Runkler and Bezdek (2003) Time data Coppi and D'Urso (2002, 2003, D'Urso (2005), Maharaj and D'Urso (2011, 2016, 2017b Spatial data Pham (2001) Spatial-time data Coppi et al (2010) and Disegna et al (2017) Three-way data Giordani (2010) and Rocci and Vichi (2005) Sequence data D'Urso and Massari (2013) Network data Liu (2010) Directional data Yang and Pan (1997) and Kesemen et al (2016) Distributional data Irpino et al (2017) Mixed data Yang et al (2004) Outlier data Davé (1991), Krishnapuram and Keller (1993), Frigui and Krishnapuram (1996), Wu and Yang (2002), D'Urso and Giordani (2006), Fritz et al (2013), Ferraro and Vichi (2015), Ferraro and Giordani (2017), D'Urso et al (2015aD'Urso et al ( , b, 2016D'Urso et al ( , 2017a, D'Urso and Leski (2016) and Yang and Nataliani (2017) Incomplete data …”

The sign test and the signed‐rank test for interval‐valued data

“…3,4 Interval-valued data that appear in different contexts drew the attention of many researchers. Various problems concerning interval-valued data in regression analysis, [5][6][7][8][9] time series, 10 principal component analysis, 11,12 correlation analysis, 13,14 classification, 9,[15][16][17][18][19][20][21] clustering, 22,23 analysis of variance, 24 and hypothesis testing [25][26][27][28][29][30][31][32][33] have been deeply studied in the literature.…”