Dimensionality reduction via compressive sensing

Compressive sensing is an emerging field predicated upon the fact that, if a signal has a sparse representation in some basis, then it can be almost exactly reconstructed from very few random measurements. Many signals and natural images, for example under the wavelet basis, have very sparse representations, thus those signals and images can be recovered from a small amount of measurements with very high accuracy. This paper is concerned with the dimensionality reduction problem based on the compressive assumptions. We propose novel unsupervised and semi-supervised dimensionality reduction algorithms by exploiting sparse data representations. The experiments show that the proposed approaches outperform state-of-the-art dimensionality reduction methods.

► We build new dimensionality reduction algorithms based on the compressive sensing. ► We investigate both unsupervised and semi-supervised compressive sensing dimensionality reduction algorithms. ► We provide theoretical results on the error bound of the feature reduction for the algorithms. ► We conduct numerical performance testing of the new algorithms against existing techniques over practical datasets.