Isometric projection with reconstruction.

Isometric Projection (IsoP) is a linear dimensionality reduction method, which provides the best linear approximation to the true isometric embedding of data. However, IsoP and all its variants only consider the one-way mapping from high-dimensional space to low-dimensional space. The projected low-dimensional data may not "represent" the original sample accurately and effectively. In this paper, based on the "encoding-decoding" mechanism, a new IsoP method called IsoP-R (Isometric Projection with Reconstruction) has been proposed. In this method, the conventional projection of IsoP is viewed as the encoding stage, and the decoder is used to reconstruct the original high-dimensional data from the projected low-dimensional data. In this way, our algorithm makes the low-dimensional embedding data "represent" the original data more accurately and effectively. Experiment results on Handwritten Alphadigits, COIL-100, Olivetti Research Laboratory and Georgia Tech face datasets show that the proposed IsoP-R approach better represents the data and achieves much higher recognition accuracy. [ABSTRACT FROM AUTHOR]