Quasi-curvature Local Linear Projection and Extreme Learning Machine for nonlinear dimensionality reduction

As one of the classical nonlinear dimensionality reduction algorithms, Locally Linear Embedding (LLE) has shown powerful performance in many research fields. However, there are still two limitations in LLE: (1) traditional LLE is sensitive to high-curvature noise; (2) the computation is too expensive. To solve these problems, we present Quasi-curvature LLE (QLLE) through taking the curvature of local neighborhoods into consideration when mapping local configuration into low-dimensional coordinates. And then a novel learning framework called Quasi-curvature Local Linear Projection (QLLP) is proposed for efficient dimensionality reduction. This framework first selects small landmarks from original data to obtain the low-dimensional coordinates in QLLE, and then adopts Extreme Learning Machine (ELM) to learn the explicit mapping function from original data to low-dimensional coordinates for nonlinear dimensionality reduction. The extensive experiments in synthetic and Frey facial expression datasets demonstrate that this framework can greatly improve the efficiency in nonlinear dimensionality reduction.