Research On Robust Manifold Learning Algorithm And Its Application

Many data in the real world are often of high dimension, the direct application of traditional data mining technology will face the problem of "curse of dimensionality". Therefore, the research on effective dimension reduction algorithm for data analysis on a low-dimensional space becomes a hotspot. However, many traditional dimensionality reduction algorithms focus only on the linear distributed data, which can not meet the analysis needs of massive nonlinear distributed data in real world. As a nonlinear dimensionality reduction tool, manifold learning algorithms perform well in the domain of visualization and classification for nonlinear data, and have been widely used in many areas of society. However, the existing manifold learning algorithms still have some shortcomings, particularly the sensitivity to noise, which becomes a bottleneck of manifold learning algorithms that may block it from been widely used. Therefore, the research on robust manifold learning algorithms becomes an immediate need.This paper firstly summarizes many existing excellent manifold learning algorithm, and analyzes the shortcomings of the algorithm in detail. Then, based on the idea of removing and inhibiting the noise, we propose a noisy manifold learning algorithm based on the local correlation dimension, a manifold learning algorithm based on kernel functions and supervised learning, and a nonlinear dimensionality reduction algorithm based on shared nearest neighbors, respectively. We attempt to learn the robust manifold learning algorithm for different applications by three approaches of de-noising, supervised learning, and unsupervised learning. The experiment on artificial data and UCI data show that the proposed algorithms have greatly improved in accuracy comparing to the original ones, and is an effective tool for nonlinear dimensionality reduction. Finally, we applied the algorithm on classification of the spectral data of leukemia cell for supporting clinical research; meanwhile, the algorithm is also applied in the field of hospital performance evaluation.Experimental results show that our algorithm can be successfully applied in the real world with feasibility and reference.