Feature selection by joint graph sparse coding

This paper takes manifold learning and regression simultaneously into account to perform unsupervised spectral feature selection. We first extract the bases of the data, and then represent the data sparsely using the extracted bases by proposing a novel joint graph sparse coding model, JGSC for short. We design a new algorithm TOSC to compute the resulting objective function of JGSC, and then theoretically prove that the proposed objective function converges to its global optimum via the proposed TOSC algorithm. We repeat the extraction and the TOSC calculation until the value of the objective function of JGSC satisfies pre-defined conditions. Eventually the derived new representation of the data may only have a few non-zero rows, and we delete the zero rows (a.k.a. zero-valued features) to conduct feature selection on the new representation of the data. Our empirical studies demonstrate that the proposed method outperforms several state-of-the-art algorithms on real datasets in term of the kNN classification performance.