Abstract: In order to maintain the local geometric structure of features while learning the deep nonlinear relationship between features, this paper proposes a single-layer autoencoder as a joint framework for feature selection and manifold learning. Firstly, the reconstruction capability of single-layer autoencoder is used to eliminate the single feature with weak contribution to the reconstructed sample, learn the deep nonlinear relationship of the feature, and carry out sparse regularization on the feature weight matrix. Secondly, an optimal feature subset is obtained by improving the local linear embedding algorithm to preserve the local structure among features. Finally, a new target loss function is designed and the L-BFGS algorithm is used for iterative optimization. Compared with other six unsupervised feature selection algorithms on six data sets, the experimental results show that this algorithm is superior to other unsupervised feature selection algorithms in clustering performance and classification performance.

Key words: feature selection, autoencoder, local linear embedding, nonlinear relationship, local geo-metric structure