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PQSQ-DataApproximators

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

Acknowledgements

Supported by the University of Leicester (UK), Institut Curie (FR), the Ministry of Education and Science of the Russian Federation, project № 14.Y26.31.0022

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Matlab and Java implementations of data analysis methods based on piece-wise quadratic approximation error (PQSQ)

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