Definition: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
Input: <lb>We consider the problem of subspace clustering: given points that lie on or near the union of<lb>many low-dimensional linear subspaces, recover the subspaces. To this end, one first identifies<lb>sets of points close to the same subspace and uses the sets to estimate the subspaces. As the<lb>geometric structure of the clusters (linear subspaces) forbids proper performance of general<lb>distance based approaches such as K-means, many model-specific methods have been proposed.<lb>In this paper, we provide new simple and efficient algorithms for this problem. Our statistical<lb>analysis shows that the algorithms are guaranteed exact (perfect) clustering performance under<lb>certain conditions on the number of points and the affinity between subspaces. These conditions<lb>are weaker than those considered in the standard statistical literature. Experimental results on<lb>synthetic data generated from the standard unions of subspaces model demonstrate our theory.<lb>We also show that our algorithm performs competitively against state-of-the-art algorithms on<lb>real-world applications such as motion segmentation and face clustering, with much simpler<lb>implementation and lower computational cost.

Greedy Subspace Clustering