Papers › A new Linear Time Bi-level ℓ_(1,∞) projection ; Application to the sparsification of...
A new Linear Time Bi-level ℓ_(1,∞) projection ; Application to the sparsification of auto-encoders neural networks
Michel Barlaud, Guillaume Perez, Jean-Paul Marmorat
The ℓ_(1,∞) norm is an efficient-structured projection, but the complexity of the best algorithm is, unfortunately, 𝒪(n m log(n m)) for a matrix n×m.\\ In this paper, we propose a new bi-level projection method, for which we show that the time complexity for the ℓ_(1,∞) norm is only 𝒪(n m ) for a matrix n×m. Moreover, we provide a new ℓ_(1,∞) identity with mathematical proof and experimental validation. Experiments show that our bi-level ℓ_(1,∞) projection is $2.5$ times faster than the actual fastest algorithm and provides the best sparsity while keeping the same accuracy in classification applications.
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