Improve local tangent space alignment using various dimensional local coordinates
Improve local tangent space alignment using various dimensional local coordinates
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DOI：
10.1016/j.neucom.2008.02.008
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发表时间：
2008-10
期刊：
影响因子：
6
通讯作者：
J. Wang
中科院分区：
文献类型：
--
作者：
J. Wang
近年来，在信息处理的许多领域都出现了非线性降维问题。局部切空间对齐（LTSA）是一种有效的非线性降维算法。它有许多吸引人的特性：简单的几何直观、直接的实现和全局优化。然而，在噪声分布不均匀或曲率较大的流形上，LTSA可能失效。本文通过引入不同维度的局部坐标来表示每个邻域的局部几何，对LTSA进行了改进。理论分析表明，改进后的LTSA （MLTSA）在噪声流形上具有较好的稳定性。我们还说明了我们的方法在合成和真实数据集上的有效性。
In the past few years, the problem of nonlinear dimensionality reduction arises in many fields of information processing. The local tangent space alignment (LTSA) is one of the effective and efficient algorithms to perform nonlinear dimensionality reduction. It has a number of attractive features: simple geometric intuitions, straightforward implementation, and global optimization. However, LTSA may fail on the manifold with nonuniformly distributed noise or large curvatures. In this paper, LTSA is improved by introducing various dimensional local coordinates to represent the local geometry for each neighborhood. The modified LTSA (MLTSA) is much stable and theoretical analysis is given to show the improvement of MLTSA on noisy manifold. We also illustrate the effectiveness of our method on both synthetic and real-world data sets.