Analysis On The Advantages And Disadvantages Of Isomap And LLE In Dimension Reduction

With the development of society, more and more people are exposed to high dimensional data in the fields of biology, image, finance and so on. In dealing with these high dimensional data we are faced with three aspects of the problem. The first is the "Curse of dimensionality" problem. The amount of sample data of high dimension will make the analysis of the data required to reach the us far beyond the affordability of the US, for analysis of high-dimensional data processing has brought great challenges. The second is the "empty space" problem. Some high dimensional data is sparse. This leads to a lot of data in the low dimensional space in which the original nature is no longer established in high dimensional space. This phenomenon leads to the decrease of correlation dimension algorithm efficiency. Finally is to increase the complexity of the calculation of the problem. With the increase of the data dimension, the complexity of the data computation will be promoted. This will lead to a decline in the performance of algorithms for many processing tasks in real time, which can not meet the requirements of online payment and other real-time issues.Under this condition, descending gradually by the scholars all over the world, manifold learning has become a hot issue. The principle of manifold learning is to maintain a relationship between the topological invariance of high dimensional data and low dimensional data. Isomap and LLE published on 2000 science are two kinds of representative algorithms for manifold learning.In this paper, we will study and analyze the two important manifold learning algorithms based on Isomap and LLE. The specific content includes the following three points.Firstly, the background and manifold learning algorithms are studied and summarized. This paper gives a brief overview of the current development trends, prospects and some problems(such as "Curse of dimensionality") in this field. This paper introduces some basic concepts of dimension reduction. At the same time, a simple algorithm is introduced to reduce the dimension of linear dimension and the dimension of manifold learning in order to understand the advantage of manifold learning dimensionality reduction algorithm.Second, Analysis the advantages and disadvantages of Isomap and LLE algorithm. Through artificial data and real image recognition problem encountered in high dimensional data to the Isometric Feature Mapping(Isomap and locally linear embedding two manifold learning dimension algorithm is tested, the income results analysis between the pros and cons, analysis data structure for ways to make the influence, and further analysis of influence of data structure of Isomap and LLE method, deepen the Isomap and LLE representative manifold learning algorithm of knowledge and understanding.Third, combined with the practical application problems, the use of LLE and Isomap is given. The use of manifold learning algorithms is considered by solving the practical problem.