Optimal sparse L1-norm principal-component analysis
نویسندگان
چکیده
We present an algorithm that computes exactly (optimally) the S-sparse (1≤S<D) maximum-L1-norm-projection principal component of a real-valued data matrix X ∈ RD×N that contains N samples of dimension D. For fixed sample support N , the optimal L1-sparse algorithm has linear complexity in data dimension, O (D). For fixed dimension D (thus, fixed sparsity S), the optimal L1-sparse algorithm has polynomial complexity in sample support, O(N). Numerical studies included in this paper illustrate the theoretical developments and demonstrate the remarkable robustness to faulty data/measurements of the calculated sparse-L1 principal components.
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