一种邻域线性竞争的排列降维方法

局部线性嵌入算法以及局部切空间排列算法是目前对降维研究有着重要影响的算法, 但对于稀疏数据及噪声数据, 在使用这些经典算法降维时效果欠佳。一个重要问题就是这些算法在处理局部邻域时存在信息涵盖量不足。对经典算法中全局信息和局部信息的提取机制进行分析后, 提出一种邻域线性竞争的排列方法（neighborhood linear rival alignment algorithm, NLRA）。通过对数据点的近邻作局部结构提取, 有效挖掘稀疏数据内部信息, 使得数据整体降维效果更加稳定。通过手工流形和真实数据集的实验, 验证了算法的有效性和稳定性。

Neighborhood linear rival alignment dimensionality reduction algorithm

LLE and LTSA algorithm are famous canonical dimensionality reduction algorithms. However, the algorithms do not perform well on sparse and noise data. The main reason is insufficient information acquisition in the algorithms. Based on the analysis to the canonical algorithms for the mechanism of global and local information acquisition, this paper presented a new algorithm called a NLRA algorithm. The NLRA used neighborhood linear rival alignment algorithm to extract the local structure of the close neighbors of the data points, and effectively mined the internal information of sparse data. The principle of the algorithm enabled stable global dimensionality reduction effect. The experimental results on the manual manifold and sparse real-world datasets show the efficiency and stability of the algorithm.