Abstract: This paper presents a method of localized linear manifold self-organizing map, which is able to learn a set of ordered low-dimensional linear manifolds in the high-dimensional vector space. Compared to state-of-the-art methods based on Kohonen's adaptive-subspace self-organizing map (ASSOM), our method avoids confusion of data in the manifold representation. Each neuron in the network approximately learns the mean vector and principal subspace of the data in its local region. The data representation is therefore more discernable. Experiments show that the proposed method performs much better than other three methods in separating clusters. In terms of handwritten digit recognition, the proposed method achieves an accuracy of 98.26\% on the training set of the MNIST database and 97.46\% on the test set.