Linear local tangent space alignment with autoencoder

Linear local tangent space alignment (LLTSA) is a classical dimensionality reduction method based on manifold. However, LLTSA 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 accurately and effectively “represent” the original samples. This paper proposes a novel LLTSA method based on the linear autoencoder called LLTSA-AE (LLTSA with Autoencoder). The proposed LLTSA-AE is divided into two stages. The conventional process of LLTSA is viewed as the encoding stage, and the additional and important decoding stage is used to reconstruct the original data. Thus, LLTSA-AE makes the low-dimensional embedding data “represent” the original data more accurately and effectively. LLTSA-AE gets the recognition rates of 85.10, 67.45, 75.40 and 86.67% on handwritten Alphadigits, FERET, Georgia Tech. and Yale datasets, which are 9.4, 14.03, 7.35 and 12.39% higher than that of the original LLTSA respectively. Compared with some improved methods of LLTSA, it also obtains better performance. For example, on Handwritten Alphadigits dataset, compared with ALLTSA, OLLTSA, PLLTSA and WLLTSA, the recognition rates of LLTSA-AE are improved by 4.77, 3.96, 7.8 and 8.6% respectively. It shows that LLTSA-AE is an effective dimensionality reduction method.