INCORPORATING DENSITY IN K-NEAREST NEIGHBORS REGRESSION

The application of the traditional k-nearest neighbours in regression analysis suffers from several difficulties when only a limited number of samples are available. In this paper, two decision models based on density are proposed. In order to reduce testing time, a k-nearest neighbours table (kNN-Table) is maintained to keep the neighbours of each object x along with their weighted Manhattan distance to x and a binary vector representing the increase or the decrease in each dimension compared to x’s values. In the first decision model, if the unseen sample having a distance to one of its neighbours x less than the farthest neighbour of x’s neighbour then its label is estimated using linear interpolation otherwise linear extrapolation is used. In the second decision model, for each neighbour x of the unseen sample, the distance of the unseen sample to x and the binary vector are computed. Also, the set S of nearest neighbours of x are identified from the kNN-Table. For each sample in S, a normalized distance to the unseen sample is computed using the information stored in the kNN-Table and it is used to compute the weight of each neighbor of the neighbors of the unseen object. In