Fuzzy clustering of distributional data with automatic weighting of variable components

Improving Seeded k-Means Clustering with Deviation- and Entropy-Based Term Weightings

“…Such approaches can be classified into two types: deviation-and entropy-based term weightings [13], [14], [20]. Some weighting methods used deviation-based distributions obtained from a set of labeled data to reflect the importance of a term in a certain class [21]. As a fuzzy approach, Lo et al [22] proposed an objective weighting model based on the maximum deviation, and then integrated the interval number and distance function into the main structure to handle the uncertain information.…”

“…Furthermore, the macro-average is calculated for the performance on all classes, regardless of the size (or length) of the class. r k = T P k T P k + FP k (20) p k = T P k T P k + FN k (21) where r k is recall and p k is precision of the class k, calculated from T P k (true positive of the class k) and FP k (false positive of the class k). While the measure A is used to evaluate all classes as one set,F assess the performance of each class separately and then combine the performances by averaging.…”

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 …”