Subspace Clustering with Missing Data

1 Subspace clustering with missing data can be seen as the combination of subspace clustering and low rank matrix completion, which is essentially equivalent to high-rank matrix completion under the assumption that columns of the matrix X ∈ Rd×N belong to a union of subspaces. It’s a challenging problem, both in terms of computation and inference. In this report, we study two efficient algorithms proposed for solving this problem, the EM-type algorithm [1] and k-means form algorithm – k-GROUSE[2], and implement the two algorithms on both simulated and real dataset. Besides that we will also give a brief description of recently developed theorem [1] on the sampling complexity for subspace clustering, which is a great improvement over the previously existing theoretic analysis [3] that requires impractically sample size, e.g. the number of observed vectors per subspace should be super-polynomial in the dimension d.