Robust GPCA Algorithm with Applications in Video Segmentation Via Hybrid System Identification

In this paper, we introduce the robust recursive GPCA algorithm that can segment a set of data points into multiple unknown linear models with different dimensions in the presence of noise and outliers. The algorithm is designed based on a robust model selection criterion for mixtures of subspaces called minimum effective dimension (MED). We apply the robust GPCA algorithm in a video segmentation problem via hybrid linear system identification, which has been successfully solved by the GPCA algorithm. Specifically, we model the hidden dynamics contained in the video sequence as a hybrid linear system without any input and develop two video segmentation schemes based on hybrid linear system identification, namely the direct segmentation and the segmentation for the embedded output data. Using the robust GPCA algorithms, both schemes generate satisfactory video segmentation results in a series of experiments. The direct segmentation requires less computational cost and the segmentation for the embedded output data captures the change in the hidden dynamics more faithfully.