Characterizing datasets using sampling, weighting, and approximation of an eigendecomposition

Abstract

A method, a system, and a computer-readable medium are provided for characterizing a dataset. A representative dataset is defined from a dataset by a computing device. The representative dataset includes a first plurality of data points and the dataset includes a second plurality of data points. The number of the first plurality of data points is less than the number of the second plurality of data points. The data point is added to the representative dataset if a minimum distance between the data point and each data point of the representative dataset is greater than a sampling parameter. The data point is added to a refinement dataset if the minimum distance between the data point and each data point of the representative dataset is less than the sampling parameter and greater than half the sampling parameter. A weighting matrix is defined by the computing device that includes a weight value calculated for each of the first plurality of data points based on a determined number of the second plurality of data points associated with a respective data point of the first plurality of data points. The weight value for a closest data point of the representative dataset is updated if the minimum distance between the data point and each data point of the representative dataset is less than half the sampling parameter. A machine learning algorithm is executed by the computing device using the defined representative dataset and the defined weighting matrix applied in an approximation for a computation of a full kernel matrix of the dataset to generate a parameter characterizing the dataset.