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Incremental Manifold Learning Algorithm Using PCA on Overlapping Local Neighborhoods for Dimensionality Reduction

机译：使用PCA的增量流形学习算法在重叠局部邻域上进行降维

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A novel manifold learning algorithm called LPcaML is proposed in this paper. Based on the geometric intuition that d-dimensional manifold locally lies on or close to d-dimensional linear space, LPcaML first finds an a-TSLN of the whole high-dimensional input data set and then obtains the low-dimensional local coordinates of each neighborhood in the a-TSLN using classical PCA technique while preserving the local geometric and topological property of each neighborhood. At last LPcaML transforms each local coordinates to a unified global low-dimensional representation by processing each neighborhood in their order appeared in a-TSLN. And the transformation function of each neighborhood is obtained by solving a least square problem via the overlapped examples. By using the divide and conquer strategy, LPcaML can learn from incremental data and discover the underlying manifold efficiently even if the data set is large scale. Experiments on both synthetic data sets and real face data sets demonstrate the effectiveness of our LPcaML algorithm. Moreover the proposed LPcaML can discover the manifold from sparsely sampled data sets where other manifold learning algorithms can't.

机译：提出了一种新颖的流形学习算法LPcaML。基于d维流形局部位于d维线性空间上或接近d维线性空间的几何直觉，LPcaML首先找到整个高维输入数据集的a-TSLN，然后获得每个邻域的低维局部坐标在使用传统PCA技术的a-TSLN中，同时保留每个邻域的局部几何和拓扑属性。最后，LPcaML通过按a-TSLN中出现的顺序处理每个邻域，将每个局部坐标转换为统一的全局低维表示。并且通过重叠的例子通过求解最小二乘问题来获得每个邻域的变换函数。通过使用分而治之的策略，即使数据集规模很大，LPcaML仍可以从增量数据中学习并有效地发现底层流形。在合成数据集和真实面部数据集上进行的实验证明了我们的LPcaML算法的有效性。此外，提出的LPcaML可以从稀疏采样的数据集中发现流形，而其他流形学习算法则不能。

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来源
《Advances in Computation and Intelligence》|2008年|406-415|共10页
会议地点 Wuhan(CN);Wuhan(CN)
作者
Yubin Zhan; Jianping Yin; Guomin Zhang; En Zhu;
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作者单位

School of Computer, National University of Defense Technology, Changsha, Hunan, China;

School of Computer, National University of Defense Technology, Changsha, Hunan, China;

School of Computer, National University of Defense Technology, Changsha, Hunan, China;

School of Computer, National University of Defense Technology, Changsha, Hunan, China;

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会议组织
原文格式 PDF
正文语种 eng
中图分类计算机网络;
关键词
dimensionality reduction; incremental learning; least squares fit; local PCA;

机译：降维；增量学习；最小二乘方拟合；本地PCA;

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1. Research of Adaptive Neighborhood Incremental Principal Component Analysis and Locality Preserving Projection Manifold Learning Algorithm [J] . DENG Shijie, TANG Liwei, ZHANG Xiaotao 上海交通大学学报（英文版） . 2018,第002期
2. Learning a local manifold representation based on improved neighborhood rough set and LLE for hyperspectral dimensionality reduction [J] . Yu Wenbo, Zhang Miao, Shen Yi Signal processing . 2019,第NOVa期

机译：基于改进的邻域粗糙集和LLE学习局部流形表示以减少高光谱维数
3. Learning a local manifold representation based on improved neighborhood rough set and LLE for hyperspectral dimensionality reduction [J] . Yu Wenbo, Zhang Miao, Shen Yi Signal processing . 2019,第Nova期

机译：基于改进的邻域粗糙集和LLE学习局部流形表示以减少高光谱维数
4. Incremental Manifold Learning Algorithm Using PCA on Overlapping Local Neighborhoods for Dimensionality Reduction [C] . Yubin Zhan, Jianping Yin, Guomin Zhang, International Symposium on Intelligence Computation and Applications . 2008

机译：使用PCA在重叠局部附近的增量歧管学习算法减少
5. Gaussian Process Modeling and Supervised Dimensionality Reduction Algorithms via Stiefel Manifold Learning [D] . Palaci-Olgun, Marc. 2018

机译：通过Stieafel流形学习的高斯工艺建模和监督维度减少算法
6. Puzzle Imaging: Using Large-Scale Dimensionality Reduction Algorithms for Localization [O] . Joshua I. Glaser, Bradley M. Zamft, George M. Church, -1

机译：拼图成像：使用大规模降维算法进行定位
7. Learning a Robust Local Manifold Representation for Hyperspectral Dimensionality Reduction [O] . Hong, Danfeng, Yokoya, Naoto, Zhu, Xiao Xiang 2017

机译：学习用于高光谱降维的鲁棒局部流形表示

Incremental Manifold Learning Algorithm Using PCA on Overlapping Local Neighborhoods for Dimensionality Reduction

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