A-Optimal Projection for Image Representation

• Published in: IEEE transactions on pattern analysis and machine intelligence Vol. 38; no. 5; pp. 1009 - 1015
• Main Authors: He, Xiaofei, Zhang, Chiyuan, Zhang, Lijun, Li, Xuelong
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.05.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Covariance matrices; Dimensionality reduction; image representation; Image retrieval; Laplace equations; Linear programming; Manifolds; optimal design; Optimization; Principal component analysis; Regression analysis; Symmetric matrices; Dimensionality reduction; optimal design; image representation
• ISSN: 0162-8828; 1939-3539; 2160-9292
• DOI: 10.1109/TPAMI.2015.2439252

We consider the problem of image representation from the perspective of statistical design. Recent studies have shown that images are possibly sampled from a low dimensional manifold despite of the fact that the ambient space is usually very high dimensional. Learning low dimensional image representations is crucial for many image processing tasks such as recognition and retrieval. Most of the existing approaches for learning low dimensional representations, such as principal component analysis (PCA) and locality preserving projections (LPP), aim at discovering the geometrical or discriminant structures in the data. In this paper, we take a different perspective from statistical experimental design, and propose a novel dimensionality reduction algorithm called A-Optimal Projection (AOP). AOP is based on a linear regression model. Specifically, AOP finds the optimal basis functions so that the expected prediction error of the regression model can be minimized if the new representations are used for training the model. Experimental results suggest that the proposed approach provides a better representation and achieves higher accuracy in image retrieval.