Dictionary learning is important for many pattern recognition and image processing. Some known jobs focus on the sample complexity of dictionary learning on the independent data for characterizing the performance of a learned dictionary. In this pa-per, the sample complexity of dictionary learning on the stationary mixing input sequence is considered because the stationary mixing input sequence appears in many applications. By discussing the sample complexity of learning dictionary on the β-mixing sequence, it has been shown that the better performance of a learned dictionary is a result of controlling the size of a learned dictionary, which means too large size of a learned dictionary will decrease the generalization of the learned dictionary.
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