流形表示的层次等距自组织映射

Haiying Guan, M. Turk
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引用次数: 8

摘要

我们提出了一种算法,层次等长自组织映射(H-ISOSOM),用于在低维空间中对复杂、非线性、大规模、高维输入数据进行简洁、有组织的流形表示。我们的算法的主要贡献有三个方面。首先,采用局部线性插值(LLl)技术对ISOSOM算法进行改进,将数据样本从低维空间映射回高维空间,使完全映射伪可逆。改进的isosom (M-ISOSOM)在遵循数据全局几何结构的同时,也保留了局部几何关系,减少了非线性映射失真,使学习更加准确。其次,针对Isomap、SOM和LLI的计算复杂性问题以及高扭曲流形的非线性复杂性问题,提出了H-ISOSOM算法。H-ISOSOM学习非凸、大规模流形的组织结构,并通过一组分层组织映射来表示它。层次结构遵循从粗到精的策略。它根据粗糙的全局结构,在粗糙的层次上“展开”流形,将样本数据分解成小块,然后在更精细的层次上迭代学习每个小块的非线性。该算法同时在低维空间对数据样本进行重组和聚类,以获得简洁的表示。第三,我们将所提出的方法与标准数据集上的类似方法进行了定量比较。最后,我们将H-ISOSOM应用于基于外观的手部姿态估计问题。令人鼓舞的实验结果验证了H-ISOSOM的有效性和效率。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Hierarchical Isometric Self-Organizing Map for Manifold Representation
We present an algorithm, Hierarchical ISOmetric Self-Organizing Map (H-ISOSOM), for a concise, organized manifold representation of complex, non-linear, large scale, high-dimensional input data in a low dimensional space. The main contribution of our algorithm is threefold. First, we modify the previous ISOSOM algorithm by a local linear interpolation (LLl) technique, which maps the data samples from low dimensional space back to high dimensional space and makes the complete mapping pseudo-invertible. The modified-ISOSOM (M-ISOSOM) follows the global geometric structure of the data, and also preserves local geometric relations to reduce the nonlinear mapping distortion and make the learning more accurate. Second, we propose the H-ISOSOM algorithm for the computational complexity problem of Isomap, SOM and LLI and the nonlinear complexity problem of the highly twisted manifold. H-ISOSOM learns an organized structure of a non-convex, large scale manifold and represents it by a set of hierarchical organized maps. The hierarchical structure follows a coarse-to-fine strategy. According to the coarse global structure, it "unfolds " the manifold at the coarse level and decomposes the sample data into small patches, then iteratively learns the nonlinearity of each patch in finer levels. The algorithm simultaneously reorganizes and clusters the data samples in a low dimensional space to obtain the concise representation. Third, we give quantitative comparisons of the proposed method with similar methods on standard data sets. Finally, we apply H-ISOSOM to the problem of appearance-based hand pose estimation. Encouraging experimental results validate the effectiveness and efficiency of H-ISOSOM.
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