Symbol definition：
is n linear subspace of 
.
is the dimension of 
.
is N noise-free data points.
is a rank-
matrix, represent 
(>) points that lie in .
is a unknown permutation matrix.
SSC Algorithm:
Step 1: Solve the sparse optimization program
① Uncorrupted data
② Corrupted data
ps: E corresponds to a matrix of sparse outlying entries, and Z is a noise matrix.
Step 2: Normalize the columns of C as 
.
ps: max norm : 
.
Step 3: Form a similarity grahp with N nodes wegiths on the edges between the nodes by
.
ps:
Step: Use spectral clustering to the similarity graph.
Output: 
.
Subspace-Sparse Recovery Theory
Definition:
① 
ps: is said to be independent.
② 
③ Principle angle between 
and 
Independent Subspace Model：
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其實，這篇paper主要是講了SSC算法，在求稀疏解時的限定條件原本應該是0-范數最小，求最稀疏解，可是0-范數根本沒法求，只具有實際意義，求解是個NP-hard問題，所以利用凸規划松弛方法，退而且其次，選擇1-范數，使1-范數最小，得到稀疏解。Paper的后面證明了，利用1-范數最小解求解稀疏解，也可以得到理想的稀疏表示，可以使屬於不同空間的點沒有關聯。也就是說Paper的精髓就在於證明1-范數最小值得到的稀疏解，和0-范數最小值得到的稀疏解的效果差不多。