Fast Training Set Size Reduction Using Simple Space Partitioning Algorithms

The Reduction by Space Partitioning (RSP3) algorithm is a well-known data reduction technique. It summarizes the training data and generates representative prototypes. Its goal is to reduce the computational cost of an instance-based classifier without penalty in accuracy. The algorithm keeps on dividing the initial training data into subsets until all of them become homogeneous, i.e., they contain instances of the same class. To divide a non-homogeneous subset, the algorithm computes its two furthest instances and assigns all instances to their closest furthest instance. This is a very expensive computational task, since all distances among the instances of a non-homogeneous subset must be calculated. Moreover, noise in the training data leads to a large number of small homogeneous subsets, many of which have only one instance. These instances are probably noise, but the algorithm mistakenly generates prototypes for these subsets. This paper proposes simple and fast variations of RSP3 that avoid the computationally costly partitioning tasks and remove the noisy training instances. The experimental study conducted on sixteen datasets and the corresponding statistical tests show that the proposed variations of the algorithm are much faster and achieve higher reduction rates than the conventional RSP3 without negatively affecting the accuracy.