$k$ NNVWC: An Efficient $k$ -Nearest Neighbors Approach Based on Various-Widths Clustering

The
$k$
-nearest neighbor approach (
$k$
-NN) has been extensively used as a powerful non-parametric technique in many scientific and engineering applications. However, this approach incurs a large computational cost. Hence, this issue has become an active research field. In this work, a novel
$k$
-NN approach based on various-widths clustering, named
$k$
NNVWC, to efficiently find
$k$
-NNs for a query object from a given data set, is presented.
$k$
NNVWC does clustering using various widths, where a data set is clustered with a global width first and each produced cluster that meets the predefined criteria is recursively clustered with its own local width that suits its distribution. This reduces the clustering time, in addition to balancing the number of produced clusters and their respective sizes. Maximum efficiency is achieved by using triangle inequality to prune unlikely clusters. Experimental results demonstrate that
$k$
NNVWC performs well in finding
$k$
-NNs for query objects compared to a number of
$k$
-NN search algorithms, especially for a data set with high dimensions, various distributions and large size.