Abstract
In this thesis, we propose RANSAC [6] (RANdom SAmple Consensus) based approaches to achieve robust PCA [1] (Principal Component Analysis) for data containing outliers. This problem is related to a variety of vision applications that require data analysis or subspace learning, especially for the case that outliers are unavoidable. Overall, our algorithms consist of the following steps. We randomly select a subset of data to compute a PCA model, evaluate the model by other unselected data, and repeat the hypothesize-and-test procedure until a good model is found. To deal with different types of outliers, we apply different sampling strategies, one-dimensional sampling for sample outliers, and two-dimensional sampling for intra-sample outliers. In addition, problems resulted from traditional RANSAC, i.e. a prior error scale and the stopping criteria, are solved by the developed extended MSSE [2] (Modified Selective Statistical Estimator) framework. Experiments on simulated and real data demonstrate superior performance of the proposed RANSAC-like algorithms compared to standard PCA and the robust PCA technique [5] based on M-estimation. The results also verify that the proposed algorithms are robust against up to 80% sample outliers or 30% randomly distributed intra-sample outliers.