Research On Dimensionality Reduction Algorithms Based Locally Linear Analysis

As rapid development of information, multimedia and digital technology, high dimensional data approach has become a powerful tool to describe the objective world, such as gene expression, video tracking, medical image processing, high-dimensional time series analysis and so on. Meanwhile, traditional classification, clustering algorithms could not be efficiently applied to high-dimensional data, so it is urgent to seek an approach for dimensionality reduction. The emergence of manifold learning provides an appropriate way for dimensionality reduction of high-dimensional data.Manifold learning has become mature under the efforts of many domestic and foreign scholars in the course of more than a decade, and many efficient learning methods are proposed. Such as Isomap, locally linear embedding and local tangent space alignment algorithm, etc.With the assumption that local data are approximately linearized, LLE and LTSA can get better results in the real world of high dimensional data, which are non-linear learning methods. However, the data is often with high local curvature distribution or noise in many applications, while the local algorithms are very sensitive to that. At this point, LLE and LTSA can not obtain the correct low-dimensional embedding, that problem is an important branch of manifold learning.In this paper, the corresponding methods are proposed for the problems above in manifold learning.(1) Proposed an adaptive neighborhood selection algorithm by analyzing the geometric properties of the local tangent space, and modified LTSA.(2) Analyzed the influence of noise and high curvature to low-dimensional space and classified the noises, then proposed an angle global embedding algorithm with powerful noise immunity.(3) Discussed the linearization of local data based on the LLE algorithm, and provided a standard of approximately linearization. Addressing the situation that sparse distribution in the source data, an embedding dimension reduction algorithm based on sparse analysis is proposed.Finally, the experiments have proved that the proposed methods are effective.