基于流形结构的原数据恢复与重构

项目名称： 基于流形结构的原数据恢复与重构

项目编号： No.61272338

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 自动化技术、计算机技术

项目作者： 冯国灿

作者单位： 中山大学

项目金额： 82万元

中文摘要： 多数流形学习算法只是给出了如何将高维数据嵌入到低维空间中的方法，没有解决将嵌入数据映射回高维空间中的问题 ，即不能基于流形结构对原始数据进行恢复重建。如果能找到低维空间到高维空间的重构映射，那么有助于对非线性维数约简算法的嵌入质量评价，同时通过流形学习算法，我们发现数据潜在的结构，然后根据低维空间中点与点之间关系以及低维数据与高维数据点之间的对应关系来重构一些新的高维观测数据。重构新的高维观测数据是很有意义。它可以广泛应用在数据融合如图像插值、语音恢复与识别、数据压缩和数据的可视化等领域。鉴于问题的理论意义和应用价值，本项拟研究的问题是维数约简中的逆问题: 基于流形结构的数据恢复，即在给定约束条件，根据局部混合高斯模型，找出低维空间的流形结构倒高维空间的映射关系，从而实现从降维空间到高维数据空间的重构。

中文关键词： 流形重构；降维；流形学习；字典学习；

英文摘要： With the development of information technology, the processing of the large high dimensional datasets becomes more and more popular, such as text, images, sounds,videoes and even gene data. To better handle these high dimensional datasets, their dimensionality usually needed to be reduced for compression storage, classification, clustering, and visualization etc. Recently, many dimensionality reduction (DR) algorithms have been developed, including linear methods such as PCA, MDS and nonlinear methods such as Isomap, LLE, LTSA, LLC etc., which are successfully applied for the feature extraction and representation in pattern classification. Many applications need re-projecting the features to the original space. Unfortunately, most of them cannot perform the reconstruction task.Though a few algorithms, such as LTSA, LLC, and deep learning can perform reconstruction.However , most of them, such Isomap, LLE, Laplacian Eigenmap cannot do this.In order to carry out the construction task, this proposal tries to investigate an approach for performing the manifold reconstruction based on the manifold assumption of the high dimensionality. We believe the algorithm could be widely applied in image recovery, information compression, patten recognition.

英文关键词： manifold reconstruction；dimensionality reduction；manifold learning；dictionary learning；