## 1 Introduction
On the other hand, wrapper approaches generally, construct a set of candidate feature subsets that are evaluated on a classifier [19]. Embedded techniques are implicitly used by some of the classifiers, such as decision trees, while constructing a model. A number of studies demonstrated that ensemble-based feature selection techniques generally perform better than non-ensemble techniques [8; 16; 17; 20; 21]. Ensemble feature selection approaches are composed of multiple evaluation functions for quantifying the worth of a feature or a subset of features. In this regard, multiple types of feature evaluation functions can be used such as univariate techniques, classification models, or a set of mixed techniques from the aforementioned categories [8]. Ensembles can be comprised of both homogenous and heterogeneous configurations. In this regard, for a homogenous configuration, a dataset is horizontally partitioned into multiple subsets where a single type of the feature evaluation function is executed on each partition [16; 21]. On the other hand, for a heterogeneous configuration, multiple evaluation functions are executed on the dataset in parallel, and later their results are combined [16; 17; 21]. Similarly, ensemble feature ranking approaches can be arranged in either a homogenous configuration or a heterogeneous manner. In both cases, a global ranked list of features is obtained based on multiple feature lists produced by the individual feature ranking functions. One key challenge in this regard is to select a threshold value which divides the global ranked list into a set of retained and removed features [20]. Most of the studies in the CKD domain assume that the cost of data acquisition is symmetric i.e., having the same cost albeit not necessarily zero; therefore, the cost factor associated with each feature is generally ignored [6; 12; 13]. However, this assumption may not hold in many real-worldmedical applications where a patient is required to undergo multiple tests such as urine analysis, electrocardiogram, blood culture, etc., and the tests may vary in terms of incurred cost. Therefore, feature selection methods for CKD diagnosis applications may take into account the cost factor as well. In Figure 1a,b a scenario is depicted in which features are listed in descending order of their importance. In Figure 1a, a feature merit calculation is performed based on the weightage of a feature and feature's associated cost. Both these terms are combined using a trade-off constant factor, \(\alpha\), pre-specified by the user. As it can be seen in the implicit case that although different '\(\alpha\)' values may have the same overall trend, it is still not clear which value of a threshold to select among a set of candidate values. Furthermore, after feature number 13, the feature ranking is not consistent with different '\(\alpha\)' values. Therefore, the implicit case is not only sensitive to the pre-specified '\(\alpha\)', but it also makes it subjective to select a threshold value to retain a set of features. On the other hand, in Figure 1b the blue line denotes feature weightage (FW) while the orange line represents an accumulated cost of selecting a set of features. In the explicit case, a set of features can be easily distinguished at the point of intersection which is comparatively cost-effective and useful than those which are below the intersection point. Hence, in this study, the main question under investigation is this that can the point of feature-cost intersection be used for selecting a subset of features that are both accurate and cost-effective in the CKD diagnosis problem? Recent studies reported significant scholarly work on developing chronic kidney disease diagnosis and management systems [6; 8; 9; 11; 15; 18; 22; 23; 24; 25; 26; 27; 28]. In this regard, this study is continuation of research performed on the CKD diagnosis problem. The study addresses the problem of cost-sensitive feature selection for building decision tree models for the CKD diagnosis problem.