Adaptive Graph Embedded Preserving Projection Learning for Feature Extraction and Selection

Abstract

Preserving projection learning has been widely used in feature extraction and selection for unsupervised image classification. Generally, some related methods constructed a graph to represent the nearest neighbor relationships of the data based on the Euclidean distances among different samples, which used 0 or 1 to predefine whether two samples are from the same class. Since a simple Euclidean distance is sensitive to noise, the predefined graph cannot produce exact correlations between the two samples. What is more, the predefined graph cannot reflect the structure of the projected data on a latent subspace when the projection matrix is learned. To solve these problems, in this article a novel adaptive graph embedded preserving projection learning (AGE_PPL) method is proposed, first combining the sparsity-based graph learning and the projection learning as an integral framework for feature extraction and feature selection. In particular, a sparse representation term with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> -norm is exploited in AGE_PPL to achieve the adaptive graph of the data to preserve the local structures among different samples while the projection matrix is learned. Meanwhile, a global-scale constraint is imposed to preserve the global structure of the data on a latent subspace. Therefore, the transformed samples will be more discriminative, allowing margins of the same class to be reduced, and margins among different classes to be enlarged. Experimental results proved the effectiveness of the proposed algorithm by obtaining competitive performances over other baseline and state-of-the-art methods. In addition, the proposed method is very flexible for feature selection and dimensionality reduction.