Isomap Algorithm Based On Multi-basis Point Positioning Improvement

As an unsupervised learning technique, manifold learning has become a hot research direction in recent decades. With the avalanche of information, people will have to deal with large volumes of high-dimensional data. However, it is especially difficult for people to directly interpret the complex high-dimensional data. Manifold learning is an effective tool to find intrinsic low-dimensional structures hidden in the high dimensional data, which will help people to easily capture the intrinsic law among the high-dimensional data.This paper surveys the development of the manifold learning techniques and their applications. Several classic manifold learning algorithms are also carefully analyzed and compared. Based on these analysis and comparison, advantages and disadvantages of the current manifold leaning algorithms are discussed and the potential improvements are also pointed out.By deeply investigating the classic ISOMAP algorithm, this paper proposes a modified ISOMAP algorithm based on multi-point positioning technique. Firstly, we analyze the feasibility of multi-point positioning technique by testing a few of special sample spaces; Secondly, the principles of point selection and the number of selection points are investigated; Finally, we presents the general steps of the proposed algorithm. By comparing the proposed algorithm with several classic manifold learning methods on the representative benchmark datasets, we analyze the advantages and disadvantages of the proposed algorithm, and further point out the direction of our future research.