Papers › Convergence radius and sample complexity of ITKM algorithms for dictionary learning
Convergence radius and sample complexity of ITKM algorithms for dictionary learning
Karin Schnass
In this work we show that iterative thresholding and K-means (ITKM) algorithms can recover a generating dictionary with K atoms from noisy S sparse signals up to an error ε̃ as long as the initialisation is within a convergence radius, that is up to a logK factor inversely proportional to the dynamic range of the signals, and the sample size is proportional to K logK ε̃⁻². The results are valid for arbitrary target errors if the sparsity level is of the order of the square root of the signal dimension d and for target errors down to K^(-ℓ) if S scales as S ≤d/(ℓlogK).
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