Research on high dimension, low sample size (HDLSS) data has revealed their neighborless nature. This paper addresses the classification of HDLSS image or video data for human activity recognition. Existing approaches often use off-the-shelf classifiers such as nearest neighbor techniques or support vector machines and tend to ignore the geometry of underlying feature distributions. Addressing this issue, we investigate different geometric classifiers and affirm the lack of neighborhoods within HDLSS data. As this undermines proximity based methods and may cause over-fitting for discriminant methods, we propose a QR factorization approach to Nearest Affine Hull (NAH) classification which remedies the HDLSS dilemma and noticeably reduces time and memory requirements of existing methods. We show that the resulting non-parametric models provide smooth decision surfaces and yield efficient and accurate solutions in multiclass HDLSS scenarios. On several action recognition benchmarks, the proposed NAH classifier outperforms other instance based methods and shows competitive or superior performance than SVMs. In addition, for online settings, the proposed NAH method is faster than online SVMs. high dimension low sample size linear discriminant analysis k nearest neighbor nearest affine hull nearest convex hull nearest hyperdisk one-against-all SVM one-against-one SVM support vector machine SVM with stochastic gradient descent singular value decomposition 
High dimensional low sample size activity recognition using geometric classifiers