| Nowadays the fast increasing dimensionality of data sets has brought unprecedented difficulties in data processing. How to learn from these high-dimensional data has been the problem immediately to be solved. Dimensionality reduction is an important preprocessing step to cope with high-dimensional data sets. The purpose is to project high-dimensional data to a lower dimensional space while discovering compact representations of high-dimensional data.In real world, Most of the high-dimensional data sets are nonlinear. At this time, linear methods fail to find the correlations and distributions of high-dimensional data. To solve this problem, manifold learning approaches have been proposed, which break the traditional linear dimensionality reduction frame mostly constituted by principal component analysis, and gain extensive attention soon. This paper deeply studies the manifold learning method called locally linear embedding (LLE) and improves it. The main achievements in this paper are as follows:1. It summarizes the development of manifold learning currently, analyzes the characteristic of nonlinear dimensionality reduction methods, compares the virtues and drawbacks, and makes correlative computer experiments.2. Introducing diffusing and growing self-organizing maps (DGSOM), we propose a new algorithm called self-organized LLE and give some theoretical analysis. The new algorithm can determine the nearest neighbors of LLE automatically, estimate the intrinsic dimensionality, save lots of operation, and eliminate noises. These validities can be confirmed through experiments.3. We expatiate on the theoretical analysis on noise manifold learning. Based on that, we propose local neighborhood smoothing method, and make some comparisons with other noise manifold learning methods.4. Through the experiments on three different datasets, we illuminate the effective applications of LLE and its improvements in the fields of high-dimensional data reduction, visualization and face recognition. |
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