## 3 Demonstration of Filter-Wrapper Approach in Evaluating Chronic Disease Datasets
### Description of the Proposed Hybrid Classification Model  
In this section, a new hybrid classification model for chronic disease datasets is presented. Figure 12 illustrates the proposed machine learning model using the integrated 3-step attribute evaluator method and an improved decision tree classifier. A chronic disease dataset collected from a suitable and reliable source is the input to the model. Many times, these raw datasets are in unstructured form and thus it needs to be filtered and pre-processed to get it in proper format. The pre-processing of chronic disease data samples is the next step. The data records are scanned and the presence of unintended delimiters, commas or any other symbols is identified and removed. Inconsistencies like missing values or repetitive instances are detected and are replaced with the mean value in the corresponding column. Once the dataset is made free from any ambiguity and thoroughly pre-processed, it is pushed into the skewed data minimizer. The pre-processed data samples are usually unbalanced and uneven. Due to this uneven distribution of data instances the data visualization does not follow a normal distribution thereby its classification performance gets hampered. In this model this skewed data is effectively handled by using box cox transformation. It is a transformation that transforms a random dependent features into normal forms. It enables the predictors to execute the datasets with a wide range of use cases. The core part of box cox transformation is an exponential value which ranges in between \(-5\) to \(5\). values within the specified range are taken into consideration and its optimum value is chosen. The optimum value denotes the value that creates the best normal distribution curve. It can be represented as in Equation (1). \[ \begin{array}{l}\mathrm{Y},\lambda=(y+\lambda_{2})^{\lambda_{1}}-y/\lambda_ {1},\;\lambda_{1}\
eq 0\\ \mathrm{Y},\lambda=\log(y+\lambda_{2}),\lambda_{1}=0\end{array}  \tag{1}\]  
The normalized data obtained is made input to Attribute Evaluator Module. It takes advantage of a clustering approach, which helps it obtain a more accurate selection of attributes form a chronic disease dataset. This 'Attribute Evaluator' module integrates K-Means clustering with the CFS method used as a filter method and the BFS method as a wrapper. Clustering with K-Means is the first step in this module. The attribute set is the input and multiple clusters are formed on the basis of similarity among attributes. K-Means clustering selects 'K' attributes as its cluster centers from the initial disease dataset. On the basis of the similarity measure, distances between the cluster mean and the attributes are computed. Updated mean value is calculated for every cluster. The most similar attribute is allotted to the corresponding cluster. Euclidean distance is used in our proposed model to determine the attributes that exhibit similarity, as shown in Equation (2). The squared distance between two vectors p = (p1, p2) and q = (q1, q2) is denoted as the sum of squared differences in their coordinates in Equation (3). \[\mathrm{d}^{2}_{\mathrm{pq}}=(\mathrm{p}1-\mathrm{q}1)^{2}+(\mathrm{p}2- \mathrm{q}2)^{2} \tag{2}\]  
Figure 12: Illustration of the Hybrid Classification Model based on 3-Step Attribute Evaluator. \[\mathrm{d}_{\mathrm{pq}}=\sqrt{\left(\mathrm{p1-q1}\right)^{2}+\left(\mathrm{p2-q2} \right)^{2}} \tag{3}\]  
A new variation of K-Means algorithm referred to as 'Integrated Supervised K-Means' is presented and implemented. The main idea behind this new variant is to perform logistic regression in every iteration. Since regression approach is combined with unsupervised clustering hence it is named as Integrated Supervised K-Means. Regression generates a cluster member probability and it is used to eliminate appropriate samples from participating in finding cluster mean process. It is useful in dealing with real time datasets which comprises of heterogeneous instances with overlapping samples.