## 3 Materials and Methods
### Proposed MFS  
In the proposed MFS, all merit features that are not similar to other ones are selected. For the input data \(\mathrm{X}=\left\{\mathrm{x}_{\mathrm{i}}\right\}_{\mathrm{i=1}}^{\mathrm{n}}= \left\{\mathrm{x}_{\mathrm{1}},\mathrm{x}_{\mathrm{2}},\cdots,\mathrm{x}_{ \mathrm{n}}\right\}\), where each input has p features (dimensions), \(\mathrm{x}_{\mathrm{i}}=\left[\mathrm{x}_{\mathrm{i},1},\mathrm{x}_{\mathrm{ i},2},\cdots,\mathrm{x}_{\mathrm{i},p}\right]^{\mathrm{T}}\), \(\mathrm{i}=1,2\cdots,\mathrm{n}\), the classification performance of each feature is evaluated separately. This means that when the input data are considered a training set for the classification, each feature (j-th feature) is considered the sole data feature and the classification is performed based on this single feature (classification using \(\left\{\mathrm{x}_{\mathrm{i}}\right\}_{\mathrm{j}}\))\({}_{\mathrm{i=1}}^{\mathrm{n}}\)). This process is performed for all features (j \(=1,2,\cdots,\mathrm{p}\)) and the corresponding classification accuracy of each feature is evaluated as \(\mathrm{CA}_{\mathrm{j}}\), \(\mathrm{j}=1,2,\cdots,\mathrm{p}\). Then, all features are sorted based on classification accuracy. After this descending-based sorting, the features of each input data \(\mathrm{x}_{\mathrm{i}}\) are rearranged to \(\mathrm{x}_{\mathrm{(i)}}=\left[\mathrm{x}_{\mathrm{i},(1)},\mathrm{x}_{ \mathrm{i},(2)},\cdots,\mathrm{x}_{\mathrm{i},(\mathrm{p})}\right]^{\mathrm{T}}\), where \(\mathrm{CA}_{\mathrm{(1)}}\geq\mathrm{CA}_{\mathrm{(2)}}\geq\cdots\geq\mathrm{ CA}_{\mathrm{(p)}}\). Then, as the first selected feature, the feature with the best classification accuracy \(\mathrm{x}_{\mathrm{i},(1)}\) is selected. Therefore, the number of selected features so far (named nsf) is one (nsf = 1) and the selected features and data can be noted by \(\mathrm{X}_{\mathrm{fs}}=\left\{\mathrm{x}_{\mathrm{(i)}}\right\}_{\mathrm{i=1 }}^{\mathrm{n}},\mathrm{x}_{\mathrm{(i)}}=\left[\mathrm{x}_{\mathrm{i},((1))} \right]^{\mathrm{T}}\), where \(\mathrm{x}_{\mathrm{i},((1))}=\mathrm{x}_{\mathrm{i},(1)}\). In the next step and where the \(\mathrm{(m)}\)-th sorted feature is examined for selection or not (m = 2.\(\cdots,\mathrm{p}\)), a threshold value (named T) is defined and used. After a comparison of the \(\mathrm{(m)}\)-th feature with all previously selected nsf features one by one (e.g., let the \(\left((\mathrm{l})\right)\)-th selected feature, where l varies from 1 to nsf), if the \(\mathrm{(m)}\)-th feature has at least T new correctly classified data where they are classified incorrectly using the \(\left((\mathrm{l})\right)\)-th feature, then the \(\mathrm{(m)}\)-th feature has merit and is selected; otherwise, it is not selected. Finally, the proposed MFS for p dimensional input data \(=\left\{\mathrm{x}_{\mathrm{i}}\right\}_{\mathrm{i=1}}^{\mathrm{n}}=\left\{ \mathrm{x}_{\mathrm{1}},\mathrm{x}_{\mathrm{2}},\cdots,\mathrm{x}_{\mathrm{n}}\right\}\), \(\mathrm{x}_{\mathrm{i}}=\left[\mathrm{x}_{\mathrm{i},1},\mathrm{x}_{\mathrm{i}, 2},\cdots,\mathrm{x}_{\mathrm{i},p}\right]^{\mathrm{T}}\) can be summarized to a semi-code as follows:  
1. Set j = 1
2. Perform classification using only the j-th feature (i.e., fulfilling the classification where the input data are \(\left\{\mathrm{x}_{\mathrm{i}}\right\}_{\mathrm{i=1}}^{\mathrm{n}}\)) and get the corresponding classification accuracy \(\mathrm{CA}_{\mathrm{j}}\). 3. If j \(<p\), j \(\rightarrow\mathrm{j+1}\) and go to **Step 2**; else, go to **Step 4**. 4. Sort \(\left\{\mathrm{CA}_{\mathrm{j}}\right\}_{\mathrm{j=1}}^{\mathrm{p}}\) in a descending manner and get the corresponding descended input data \(\mathrm{X}_{\mathrm{d}}=\left\{\mathrm{x}_{\mathrm{(i)}}\right\}_{\mathrm{i=1 }}^{\mathrm{n}}\), \(\mathrm{x}_{\mathrm{(i)}}=\left[\mathrm{x}_{\mathrm{i},(1)},\mathrm{x}_{ \mathrm{i},(2)},\cdots,\mathrm{x}_{\mathrm{i},(\mathrm{p})}\right]^{\mathrm{T}}\), where \(\mathrm{CA}_{\mathrm{(1)}}\geq\mathrm{CA}_{\mathrm{(2)}}\geq\cdots\geq\mathrm{ CA}_{\mathrm{(p)}}\).