A Comparative Study of Dimension-Reduction Based on Data Distribution

The notions of explanation-radius and the local information based on the data distribution are proposed. The former measures the injective degree and the latter depicts the difference between the original data and the reduction data. Thereafter, through the experiments, the linear and nonlinear dimension-reduction is analyzed, included PCA (Principal Component Analysis), PP (Projection Pursuit) and LLE (Locally Linear Embedding), Laplacion Eigenmap. The experiments show the effectiveness and advantages of the researches.