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

A non-transitory computer-readable medium having stored thereon computer-readable instructions that when executed by a computing device cause the computing device to:

• define a representative dataset from a dataset by adding a data point of the dataset 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 and adding the data point of the dataset 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, wherein the representative dataset includes a first plurality of data points and the dataset includes a second plurality of data points, and the number of the first plurality of data points is less than the number of the second plurality of data points;
• define a weighting matrix, wherein the weighting matrix 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, and further wherein 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;
• and
• execute a machine learning algorithm 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.

A method of characterizing a dataset, the method comprising:

• defining, by a computing device, a representative dataset from a dataset by adding a data point of the dataset 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 and adding the data point of the dataset 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, wherein the representative dataset includes a first plurality of data points and the dataset includes a second plurality of data points, and the number of the first plurality of data points is less than the number of the second plurality of data points;
• defining, by the computing device, a weighting matrix, wherein the weighting matrix 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, and further wherein 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;
• and
• executing, by the computing device, a machine learning algorithm using the defined representative dataset and the defined weighting matrix applied in a approximation for a computation of a full kernel matrix of the dataset to generate a parameter characterizing the dataset.