This is a set of Matlab procedures for performing PQSQ-based data approximation.
PQSQ stands for "piece-wise quadratic sub-quadratic" error function which can approximate a large family of error functions in any standard machine learning algorithm and substitute the standard quadratic error function. This is a way to construct very fast and relatively accurate approximators or regressions with non-quadratic error function or with non-quadratic regularizers.
The theory behind PQSQ methods.
In particular,
PQSQmean - computes the mean value with PQSQ approximation error
pcaPQSQ - computes PCA with PQSQ approximation error
kmeansPQSQ - computes k-means clustering using PQSQ potential
Simplest examples of use are provided in the comments to the corresponding functions
'test_data' folder contains real and synthetic data and the code used to benchmark PQSQ algorithms against existing L1-based PCA implementations