Feature selections : Still a high dimentionality One of the advantage of using a features reduction/sub feature selection is to avoid a high dimentionality.

The most known method is the Forward selection, where it finds the best combinations of features among others, iteratively. Now please have a look at this picture retrieved from a ppt slide on the internet.



The second row of the table shows that the 11 features are the features selected/reduced from initial 20 features. My question is that, the 11 features are still considered as a high-dimensional features set, indeed one can't just subtitute it over a KNN function. Now I'm confused as to how he/she then adapt it to the KNN classifier for the 11 features?
There seems to be a misconception.  You can use $k$-nearest neighbors with any number of dimensions.  There is no prohibition on using it with a large number of features.  And in some cases $k-NN will work well even in high dimensions (a large number of features); it all depends on the dataset, and to find out whether it will work well, you have to try it.  In general, feature selection might make the algorithm work better, or it might make it work worse -- it all depends.