Research On Dimensionality Reduction Algorithms Based On Locally Linear Embedding

As the rapid development and wide application of information technology, multimedia and digital technology, high dimensional data have emerged, such as medical image processing, computational biology, global climate models and so on. Existing machine learning and data mining algorithms is difficult to effectively deal with high dimensional data. Data dimensionality reduction algorithm is a very important tool and methods to deal with these high-dimensional data. And manifold learning is a high-dimensional data dimensionality reduction technique and obtains a wide range of applications.LLE is a classic manifold learning method that based on the assumption of local approximation of linearization. It has many advantages, such as less parameters, faster calculation and earier to find the global optimal solution. But LLE losses the density of the original data in the Low-dimensional data, make the dimensionality reduction effect distorted, and unable to obtain the correct low-dimensional embedding. Multi-manifold data does not meet the continuity of the manifold under the locally linear embedding, so makes it difficult to dimensionality reduction. These two issues become the bottleneck of the locally linear embedding.In this paper, local linear embedding based on manifold learning is carried out a thorough research and improvement, and makes a detailed analysis of the LLE’s shortcomings.(1) Addressing the situation that uneven distribution and density changes largely in the source data. so, on the one hand, close neighbors are improved from the geometric properties of the local neighbors; on the other hand, carried out a detailed analysis of the nature of the LLE weight vector, and learned that the dimensionality reduction data does not reflect the density of the original high-dimensional data. Dimension reduction algorithm based on density was proposed, which is based on the basis above.(2) In order to improve the correctness of locally linear embedding caused by multi-manifold data, a novel multi-manifold learning algorithm based on locally linear embedding is proposed in this paper, which is from two independent optimization problems of locally linear embedding algorithm.