A better scaled local tangent space alignment algorithm

We propose a nonlinear dimensionality reduction algorithm called partitional local tangent space alignment (PLTSA), which is based on VQPCA and LTSA. In the algorithm, the sample space is first divided into overlapped blocks by the X-means algorithm. Then each point is projected to the local tangent space of the block to which the point belongs, to get its local low-dimensional coordinate. The global low-dimensional embedded manifold is obtained from local coordinates via local affine transformations. PLTSA is a better-scaled algorithm than LTSA, in that it provides a means of mapping newcome data with much smaller time and space requirements, and works on a much smaller optimization matrix. Since it gives the global coordinates of the data, it is better than VQPCA. The performance of PLTSA is illustrated by results on surfaces in 3D Euclidean spaces and MNIST database.