Density Scaling Factor Based ISOMAP Dimensionality Reduction Algorithm And Its Application

The dimensionality reduction technology is an important method that can alleviate the curse of dimensionality and is so significant.In recent years,manifold learning has become an important research direction for studying dimensionality reduction methods,which main goal is to obtain low-dimensional compact representations and find the essential information of high-dimensional data.Isometric mapping(ISOMAP)is one of representatives of manifold learning algorithms.It has attracted extensive attention due to its good dimensionality reduction result by preserving the global structure of nonlinear data.This paper mainly focuses on two problems.One is that ISOMAP algorithm is sensitive to noise.Another is that it is difficult for ISOMAP to deal multi-manifold datasets.According to the idea of density information,we proposed density scaling factors based ISOMAP algorithm,called D-ISOMAP,and density-based multi-manifold ISOMAP algorithm,called DMM-ISOMAP,respectively.The massive experimental results show that our proposed methods compared with other dimensionality reduction methods are effective and practical.The main work can be summarized as follows:(1)Analysis and comparison of some classical dimensionality reduction algorithms.Linear dimensionality reduction algorithms such as PCA,LDA and nonlinear dimensionality reduction algorithms such as ISOMAP,LLE,and LE are introducted.Then,summarize these algorithms.Finally,propose two improving methods for the shortcomings of ISOMAP.(2)For the shortcoming of noise-sensitive,according to the idea of local density,a density scaling factor-based ISOMAP algorithm,called D-ISOMAP,was proposed.This method can reduce the influence of noise,enhance robustness and make the data beneficial to clustering task after dimension reduction.The experimental results dataset show that the D-ISOMAP algorithm is better than the classical unsupervised dimensionality reduction algorithms for the clustering task.(3)ISOMAP algorithm is an unsupervised dimensionality-reduction method.Moreover,if the data are sampled from multi-manifold,several disconnected neighborhood graphs may be formed,which can lead to the failure of ISOMAP algorithm.In this paper,a novel supervised ISOMAP based on density is proposed,dubbed density-based multi-manifold ISOMAP(DMM-ISOMAP),which can deal with the problem of appearing several disconnected neighborhood graphs.The experimental results for classification tasks on synthetic and real-world data confirm the effectiveness of the proposed method compared with other dimensionality reduction algorithms.