Clustering and classification of fuzzy data using the fuzzy EM algorithm

Abstract

In this article, we address the problem of clustering imprecise data using a finite mixture of Gaussians. We propose to estimate the parameters of the model using the fuzzy EM algorithm. This extension of the EM algorithm allows us to handle imprecise data represented by fuzzy numbers. First, we briefly recall the principle of the fuzzy EM algorithm. Then, we provide closed-forms for the parameter estimates in the case of Gaussian fuzzy data. We also describe a Monte-Carlo procedure for estimating the parameter updates in the general case. Experiments carried out on synthetic and real data demonstrate the interest of our approach for taking into account attribute and label uncertainty.

Data Distribution Aware Classification Algorithm based on K-Means

“…In Table III, the results of the proposed K-Means-Mod algorithm is compared against three other recent classification studies which are [11]- [13]. The three compared studies contain the accuracy performances achieved from fuzzy expectation maximisation and several modified KNN approaches, respectively.…”

“…The study presented in [11] investigates the efficiency of Gaussian Mixture Models (GMM) and fuzzy Expectation Maximisation (EM). The technique proposed in [11] mainly focuses on clustering and classification of fuzzy data.…”

“…The technique proposed in [11] mainly focuses on clustering and classification of fuzzy data. The results presented in [11] illustrate that the proposed technique is a contribution which helps estimating the distribution of imprecisely known data. The authors also claim to improve the classification accuracy of noisy data, which they present in their results.…”

Classification of unlabeled observations in Species Distribution Modelling using Point Process Models

“…They showed varying performance depending on the aspects of the model and the performance measure considered. The novelty of these tools, makes it difficult to compare to other existing tools that either do not consider point pattern process (Frame & Jammalamadaka, 2007; Frühwirth-Schnatter, 2006; Hui, 2016; Martinez, 2015; Melnykov & Maitra, 2010; Quost & Denœux, 2016), Poisson distributions (Figueirido & Jain, 2002; Hui et al , 2015; Scrucca et al , 2016; Woillez et al , 2012), count data (Benaglia et al , 2009; Iovleff, 2018; Leisch, 2004) or implementation of mixture (Witten, 2011; Wendel et al , 2015) or semi-supervised learning frameworks (Di Zio et al , 2007; Fraley & Raftery, 1998; Jeffries & Pfeiffer, 2001; Taddy & Kottas, 2012).…”

Exploratory multivariate analysis for empirical information affected by uncertainty and modeled in a fuzzy manner: a review

“…In conclusion, when using a hybrid approach (statistical modeling based on simultaneously exploratory and inferential tools), it could be particularly interesting to study exploratory multivariate methods for imprecise data in which inferential tools-such as likelihood function defined in a fuzzy framework, fuzzy extension of the EM algorithm or statistical test procedures-are considered (see, e.g., Colubi et al 2009;Quost and Denoeux 2016).…”