A nonnegative sparse representation based fuzzy similar neighbor classifier

This paper presents a new classification technique by combining the well-known Sparse Representation based algorithm with the theory of Fuzzy Set. The basic idea of this work is that samples with the same class-labels should be more similar to each other than those with different class-labels. Based on this similarity rule, we first impose the nonnegative coefficient constraints on the sparse representation based algorithm and obtain the desirable similar neighbors. Then by introducing the theory of Fuzzy Set into our work, we construct the fuzzy class membership matrix and then assign the decision membership of the query sample to each class. The class assigned with the dominant decision membership is wanted. The proposed approach is called the Nonnegative Sparse Representation based Fuzzy Similar Neighbor Classification (FSNC). FSNC has the following properties: (a) the neighbor parameter K is not needed to be set in advance, and K is adaptively set by the algorithm itself; (b) similar neighbors are also generated adaptively and contain much more similar properties of the query sample; (c) the degree of similarity of data is clearly recorded in the sparse nonnegative coefficient vector; (d) the fuzzy decision rule is effective and the proposed classifier FSNC is simple. Experimental results conducted on the Wine database from UCI, the AR face database, the CENPARMI handwritten numeral database, and the PolyU palmprint database show that the new proposed classification technique outperforms some other state-of-the-art classifiers.