A parameterized fuzzy adaptive K-SVD approach for the multi-classes study of pursuit algorithms

• A parameterized reformative fuzzy LDA is proposed to achieve the distribution information of each sample.
• Apply Hopfield neural network model to parameter estimation of reformative fuzzy LDA.
• Incorporate the proposed fuzzy mechanism into dictionary-update stage of K-SVD.
• Utilize the study of pursuit algorithm combined with fuzzy discriminatory measure for the pattern classification.

Sparse representations using over complete dictionaries has concentrated mainly on the study of pursuit algorithms that decompose signals with respect to a given dictionary. Designing dictionaries to better fit the above model can be done by either selecting one from a pre-specified set of linear transforms or adapting the dictionary to a set of training signals. The K-SVD algorithm is an iterative method that alternates between sparse coding of the examples based on the current dictionary and a process of updating the dictionary atoms to better fit the data. However, the existing K-SVD algorithm is employed to dwell on the concept of a binary class assignment, which means that the multi-classes samples are assigned to the given classes definitely. The work proposed in this paper provides a novel parameterized fuzzy adaptive way to adapting dictionaries. In order to achieve the fuzzy sparse signal representations, the update of the dictionary columns is combined with an update of the sparse representations by embedding a new mechanism of fuzzy set, which is called parameterized fuzzy K-SVD. Experimental results conducted on the ORL, Yale and FERET face databases demonstrate the effectiveness of the proposed method.