中文摘要：

非线性降维方法是目前对降维研究有着重要影响的方法，但在降维过程中经常会遇到局部邻域信息量不足、短路和噪声干扰等问题，严重影响降维效果，很难广泛应用于真实数据的处理中。对以上问题分析发现，其主要原因在于经典降维算法都是采用全局固定的邻域大小。提出了一种基于压缩感知的邻域优化算法，运用压缩感知技术对高维空间目标点近邻进行压缩采样，构建“收一放”模型，自适应得到最优子空间，同时优化邻域组成元素，使得数据的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。

英文摘要：

The non-linear dimension reduction method is an important aspect in dimension reduction domain. However, for neighbor selection, it＇ s still difficult to deal with problems such as lack of sufficient information, short circuit and noise ete, which seriously affect the effect of dimensionality reduction. Thus, the application of neighbor selection is limited in practice. This paper analyzed the theory of compressive sensing and the mechanism of neighborhood structure in depth and proposed a new optimization algorithm for neighbor selection. Meanwhile, it constructed a model of ＂compression and amplification＂ , which could calculate the optimal subspaee from high dimension data. The new constructed model ensured the scale of the neighborhood of data and the global effect of dimensionality reduction of data was more stable. Experiments with artificial umni- fold and a real-world dataset verify the effectiveness and stability of the proposed algorithm.