1 research outputs found
Adaptive Neighboring Selection Algorithm Based on Curvature Prediction in Manifold Learning
Recently manifold learning algorithm for dimensionality reduction attracts
more and more interests, and various linear and nonlinear, global and local
algorithms are proposed. The key step of manifold learning algorithm is the
neighboring region selection. However, so far for the references we know, few
of which propose a generally accepted algorithm to well select the neighboring
region. So in this paper, we propose an adaptive neighboring selection
algorithm, which successfully applies the LLE and ISOMAP algorithms in the
test. It is an algorithm that can find the optimal K nearest neighbors of the
data points on the manifold. And the theoretical basis of the algorithm is the
approximated curvature of the data point on the manifold. Based on Riemann
Geometry, Jacob matrix is a proper mathematical concept to predict the
approximated curvature. By verifying the proposed algorithm on embedding Swiss
roll from R3 to R2 based on LLE and ISOMAP algorithm, the simulation results
show that the proposed adaptive neighboring selection algorithm is feasible and
able to find the optimal value of K, making the residual variance relatively
small and better visualization of the results. By quantitative analysis, the
embedding quality measured by residual variance is increased 45.45% after using
the proposed algorithm in LLE.Comment: 3 figures, from Journal of Harbin Institute of Technolog