AGNSA: Adaptive graph learning-based unsupervised feature selection with non-convex sparse autoencoder

Some unsupervised feature selection methodologies cannot consider the two local structures for samples and features, and there are unreasonable local structures that cannot control the feature redundancy well. So, we study an adaptive graph learning-based unsupervised feature selection with a non-convex sparse autoencoder. Firstly, a single-layer autoencoder is used to construct a reconstruction loss function to reconstruct the original features, and a new Mish activation function is studied to optimize the autoencoder structure. In the autoencoder, a feature similarity matrix is established by integrating Gaussian kernel function and Euclidean distance for reflecting the similarity of features to learn the local structure of feature graph. Particularly, a non-convex regularization term is applied into a weight matrix between the input layer and hidden layer of autoencoder, and then a feature weight matrix with sparser rows can be obtained to realize feature selection. Secondly, the Gaussian kernel function and Euclidean distance are combined to establish a sample similarity matrix. In the process of auto-encoder optimization, this sample local structure is learned by updating the sample similarity matrix adaptively, and the learned local structure is constrained near the original sample similarity matrix to avoid unreasonable local structure. Then, cosine similarity is employed to consider the feature correlation and learn redundancy matrix to control the redundancy of selected features. Finally, a new objective function is constructed, and an alternating iteration scheme is designed to optimize and compute the objective function to obtain an optimal solution for parameters, where the importance of features is judged according to the obtained feature weight matrix, and the representative feature subset is selected. Experimental results illustrate this developed methodology will be better than other comparative schemes on eight high-dimensional datasets for benchmark classification.