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Dimension reduction is a research hotspot in recent years, especially manifold learning for high-dimensional data. Cause high-dimensional data have complex nonlinear structures there are many researchers focus on nonlinear me- thods. The memory cost and running time are too large and difficult to operate when the scales of data are tremendously large. In order to solve this problem, we utilized the gradient descent to search the low-dimensional embedding. It replaced the eigenvalue decomposition of a large sparse matrix of LLE (Linear Locally Embedding) algorithm. The time complexity is lower than before and storage memory is declined obviously. Experimental results demonstrated our approach performed well than the original algorithm. Furthermore, our approach can be ap- plied to other manifold method or other research fields such as information re- trieval and feature extraction.

Manifold Learning Method for Large Scale Dataset Based on Gradient Descent