Table 2.

Two-stage variable backward elimination procedure for Random KNN

Stage 1: Geometric Elimination

q ← proportion of the number features to be dropped each time;

p ← number of features in data;

$ni\leftarrow ⌊ln\left(4∕p\right)∕ln\left(1-q\right)⌋$; /* number of iterations, minimum dimension 4*/

initialize rknn_list[m]; /* stores feature supports for each Random KNN */

initialize acc[m]; /* stores accuracy for each Random KNN */

for i from 1 to ni do

if i == 1 then

rknn ← compute supports via Random KNN from all variables of data;

else

$p\leftarrow ⌊p\cdot \left(1-q\right)⌋;$

rknn ← compute supports via Random KNN from p top important variables of rknn;

end if

rknn list[i] ← rknn;

acc[i] ← accuracy of rknn;

end for

$max=\underset{1\le k\le ni}{argmax}\left(acc\left[k\right]\right);$

pre_max = max - 1;

rknn ← knn_list[pre_max]; /* This Random KNN goes to stage 2 */

Stage 2: Linear Reduction

d ← number features to be dropped each time;

p ← number of variables of rknn;

$ni\leftarrow ⌊\left(p-4\right)∕d⌋$; /* number of iterations */

for i from 1 to ni do

if i ≠ 1 then

p ← p - d;

end if

rknn ← compute supports via Random KNN from p top important variables of rknn;

acc[i] ← accuracy of rknn;

rknn_list[i] ←rknn;

end for

$best\leftarrow \underset{1\le k\le ni}{argmax}\left(acc\left[k\right]\right);$

best_rknn ← rknn_list[best]; /* This gives final random KNN model */

return best_rknn;