Robust Positive semidefinite L-Isomap Ensemble

In this paper, we derive an ensemble method inspired by boosting, a novel Robust Positive semidefinite L-Isomap Ensemble (RPL-IsomapE) approach. Specifically, we first apply a constant-shifting method to yield a symmetric positive semidefinite (SPSD) matrix. For topological stability, we also employ a method for eliminating critical outlier points using the confusion rate of all the data points. Then we align individual Robust Positive semidefinite L-Isomap (RPL-Isomap) solutions in common coordinate system through high dimensional affine transformations. Finally, we combine multiple RPL-Isomap solutions by the weighted averaging procedure according to residual variance to improve the noise-robustness of our method. Our RPL-IsomapE maintains the scalability and the speed of L-Isomap. Experiments on two images data sets and a video data set confirm the promising performance of the proposed RPL-IsomapE.

Research highlights
► We apply a preprocessing method that can automatically remove the critical outliers using the confusion rate of all the data points.
► Resorting to affine registration in computer vision, individual RPL-Isomap solutions are aligned in a common coordinate system through high dimensional affine transformations.
► We propose a novel RPL-IsomapE algorithm that achieves the final solution by combining aligned individual solutions through residual variance weighted averaging. Our RPL-IsomapE maintains the scalability and the speed of L-Isomap.