Identifying the key genes related to tumors from gene expression data with a large number of features is important for the accurate classification of tumors and to make special treatment decisions. In recent years, unsupervised feature selection algorithms have attracted considerable attention in the field of gene selection as they can find the most discriminating subsets of genes, namely the potential information in biological data. Recent research also shows that maintaining the important structure of data is necessary for gene selection. However, most current feature selection methods merely capture the local structure of the original data while ignoring the importance of the global structure of the original data. We believe that the global structure and local structure of the original data are equally important, and so the selected genes should maintain the essential structure of the original data as far as possible. In this paper, we propose a new, adaptive, unsupervised feature selection scheme which not only reconstructs high-dimensional data into a low-dimensional space with the constraint of feature distance invariance but also employs ℓ2,1-norm to enable a matrix with the ability to perform gene selection embedding into the local manifold structure-learning framework. Moreover, an effective algorithm is developed to solve the optimization problem based on the proposed scheme. Comparative experiments with some classical schemes on real tumor datasets demonstrate the effectiveness of the proposed method.
Estimating a planetary magnetic field with time-dependent global MHD simulations using an adjoint approach