In this paper, we propose a new framework for segmenting feature-based multiple moving objects with subspace models in affine views. Since the feature data is high-dimensional and complex in the real video sequences, most traditional approaches for motion segmentation use the conventional PCA to obtain a low-dimensional representation, while our proposed framework applies the sparse PCA (SPCA) to obtain a projected subspace, which is a low-dimensional global subspace on a Stiefel manifold with sparse entries. Then, the local subspace separation is achieved via automatically selecting the sparse nearest neighbours. By combining two sparse techniques, the proposed framework segments different motions through a simple spectral clustering on an affinity matrix built with the principal angles. To the best of our knowledge, our framework is the first one to apply the sparse optimization for optimizing the global and local subspace simultaneously.We test our method extensively and compare its performance to several state-of-art motion segmentation methods with experiments on the Hopkins 155 dataset. Our results are comparable with these results, and in many cases exceed them both in terms of segmentation accuracy and computational speed.