A Model of Selecting the Parameters Based on the Variance of Distance Ratios for Manifold Learning Algorithms

ISOMAP, LLE, Laplacian eigenmaps and LTSA are several representative manifold learning algorithms. In most of manifold learning methods, there are two free parameters: the neighborhood size and the intrinsic dimension of the high dimensional data set. In this paper, we analyze and compare the stress function, the residual variance and the dy-dx representation. On the basis of the dy-dx representation, a quantitative measure based on the variance of distance ratios is used to determine these two parameters, which overcomes faults of the stress function and the residual variance. Experiments show that the model can be utilized not only to choose an appropriate neighborhood size but also to estimate the intrinsic dimension of the high dimensional complex data for different manifold learning techniques.