Toolbox for Distance Estimation and Cluster Validation on Data With Missing Values

Abstract

Missing data are unavoidable in the real-world application of unsupervised machine learning, and their nonoptimal processing may decrease the quality of data-driven models. Imputation is a common remedy for missing values, but directly estimating expected distances have also emerged. Because treatment of missing values is rarely considered in clustering related tasks and distance metrics have a central role both in clustering and cluster validation, we developed a new toolbox that provides a wide range of algorithms for data preprocessing, distance estimation, clustering, and cluster validation in the presence of missing values. All these are core elements in any comprehensive cluster analysis methodology. We describe the methodological background of the implemented algorithms and present multiple illustrations of their use. The experiments include validating distance estimation methods against selected reference methods and demonstrating the performance of internal cluster validation indices. The experimental results demonstrate the general usability of the toolbox for the straightforward realization of alternate data processing pipelines. Source code, data sets, results, and example macros are available on GitHub a .

A Comprehensive Bibliometric Analysis of Missing Value Imputation

“…CTL with multi-estimation for missing data is based on belief function theory [139]. Niemela et al also developed a toolbox that offers a wide range of algorithms for data preprocessing, distance estimation, clustering, and cluster validation, specifically designed to handle missing values in data analysis [140].…”

Application of a Knowledge Discovery Process to Study Instances of Capacitated Vehicle Routing Problems

“…The proposed analysis process is composed of a novel combination of reliable unsupervised and supervised data mining and machine learning methods, which have been developed in the earlier research [30,33,4,34,31,54,23,21,55,45,22]. The overall process reads as follows:…”

“…The essence behind Step 1 is the availability of robust and reliable clustering method [33,4,21,22] which can tolerate over 30% of missing values [3]. In this unsupervised setting, also the number of clusters is to be estimated, and for this purpose, a set of cluster validation indices, also applicable with missing values, were tested in [27,21,45].…”

Improving Clustering and Cluster Validation with Missing Data Using Distance Estimation Methods

“…As depicted in Hämäläinen et al [7], Niemelä et al [13], the cluster validation indices are composed of a quotient of estimates of Inter and Intra of a clustering result, i.e., the variability of data within clusters divided by the separation of clusters. Both of these measures are computed with a distance measure which is inhereted from the clustering problem formulation (Hämäläinen et al [8]).…”

“…Therefore, a key to reliable cluster validation indices with missing values is how to estimate the distances between the prototypes and the observations. For this purpose, in Niemelä et al [13], the classical partial distance strategy (Gower [6]) was applied with promising results. However, more recently a set of papers have appeared (Eirola et al [3,4], Mesquita et al [12]), which have addressed the distance estimation with missing values for both squared and euclidean (nonsquared) distances with better accuracy than in Gower [6].…”