Proposing a Dimensionality Reduction Technique With an Inequality for Unsupervised Learning from High-Dimensional Big Data

task can be considered as the most important unsupervised learning algorithms. For about all clustering algorithms, finding the Nearest Neighbors of a point within a certain radius r (NN -r), is a critical task. For a high-dimensional dataset, this task becomes too time consuming. This article proposes a simple dimensionality reduction (DR) technique. For point p in d-dimensional space, it produces point p' in d'-dimensional space, where d' << d. In addition, for any pair of points p and q, and their maps p' and q' in the target space, it is proved that |p, q| > |p', q'| is preserved, where |, | used to denote the Euclidean distance between a pair of points. This property can speed up finding NN -r. For a certain radius r, and a pair of points p and q, whenever |p', q'| > r, then q can not be in NN -r of p. Using this trick, the task of finding the NN -r is speeded up. Then, as a case study, it is applied to accelerate the k-means, one of the most famous unsupervised learning algorithms, where it can automatically determine the d'. The proposed NN -r method and the accelerated k-means are compared with recent state-of-the-arts, and both yield favorable results.