Improve GRNN by Weighting

In the post (https://statcompute.wordpress.com/2019/07/14/yet-another-r-package-for-general-regression-neural-network), several advantages of General Regression Neural Network (GRNN) have been discussed. However, as pointed out by Specht, a major weakness of GRNN is the high computational cost required for a GRNN to generate predicted values based on a new input matrix due to its unique network structure, e.g. the number of neurons equal to the number of training samples.

For practical purposes, there is however no need to assign a neuron to each training sample, given the data duplication in real-world model development samples. Instead, a weighting scheme can be employed to reflect the frequency count of each unique training sample. A major benefit of the weight assignment is the ability to improve the efficiency of calculating predicted values, which depends on the extent of data duplicates. More attractively, the weighting application can bring up the possibility of using clustering or binning techniques to preprocess the training data so as to overcome the aforementioned weakness to a large degree.

Below is a demonstration showing the efficiency gain by using the weighting scheme in GRNN.

1. First of all, I constructed a sample data with duplicates to double the size of the original Boston dataset. Based on the constructed data, a GRNN named “N1” was trained.
2. Secondly, I generated another sample data by aggregating the above constructed data based on unique samples and calculating the weight of each unique data point based on its frequency. Based on the aggregated data, another GRNN named “N2” was also trained.

As shown in the output, predicted vectors from both “N1” and “N2” are identical. However, the computing time can be reduced to half by applying the weighting. All R functions used in the example can be found in https://github.com/statcompute/GRnnet/blob/master/code/grnnet.R.

For people interested in the SAS implementation of GRNN, two SAS macros are also available in https://github.com/statcompute/GRnnet/blob/master/code/grnn_learn.SAS and https://github.com/statcompute/GRnnet/blob/master/code/grnn_pred.SAS.