the feature $X_{.j}$ in classification. Using this, a weight $\lambda_j$ is assigned to each feature $X_{.j}$ in Mutual Information based KNNI (MI-KNN) [@garcia2009k], such that $$\label{30}
    \lambda_j = \frac{I(X_{.j};Y)}{\sum_{j'=1}^{p}{I(X_{.j'};Y)}} \;,$$ and then the distance between instances is calculated similar to : $$\label{31}
     d_I (X_a,X_b) = \sqrt{\sum_{j=1}^p \lambda_j d_j(X_{aj},X_{bj})^2},$$ where $d_j(X_{aj},X_{bj})$ is as defined in . Using this feature relevance weighted distance, replacing $d$ with $d_I$ (from ) in -, and following Algorithm \[iknni\], we obtain the MI-KNN imputation algorithm [@garcia2009k].

Grey Relational Analysis (GRA) based KNNI
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Grey System Theory (GST) has been developed to tackle systems with partially known and partially missing information [@ju1982control]. The system was named grey since missing data is represented by black whereas known data is white, and this system contains both missing and known data. To obtain Grey-based $k$-nearest neighbors, we used Grey Relational Analysis (GRA) in our algorithm which is calculating Grey Distance between two instances. Grey distance measures similarity of two random instances, which involves the Grey Relational Coefficient (GRC) and the Grey Relational Grade (GRG).

Consider the setup in where the training dataset has $n$ observations and $p$ features. The Grey Relational Coefficient (GRC) between two instances/observation $X_a$ and $X_b$, when 