  As a representation learning method, nearest regularized subspace(NRS)
algorithm is an effective tool to obtain both accuracy and speed for PolSAR
image classification. However, existing NRS methods use the polarimetric
feature vector but the PolSAR original covariance matrix(known as Hermitian
positive definite(HPD)matrix) as the input. Without considering the matrix
structure, existing NRS-based methods cannot learn correlation among channels.
How to utilize the original covariance matrix to NRS method is a key problem.
To address this limit, a Riemannian NRS method is proposed, which consider the
HPD matrices endow in the Riemannian space. Firstly, to utilize the PolSAR
original data, a Riemannian NRS method(RNRS) is proposed by constructing HPD
dictionary and HPD distance metric. Secondly, a new Tikhonov regularization
term is designed to reduce the differences within the same class. Finally, the
optimal method is developed and the first-order derivation is inferred. During
the experimental test, only T matrix is used in the proposed method, while
multiple of features are utilized for compared methods. Experimental results
demonstrate the proposed method can outperform the state-of-art algorithms even
using less features.
