鲁棒半监督局部线性嵌入算法

Robust Semi-supervised Locally Linear Embedding

主要研究半监督局部线性嵌入算法(Semi-Supervised Locally Linear Embedding,简称SSLLE)对于噪声的敏感性,提出一种具有鲁棒性的半监督局部线性嵌入算法(Robust Semi-Supervised Locally Linear Embedding,简称RSSLLE).RSSLLE在对数据进行离群点检测的基础上,从两方面增加算法对离群点的鲁棒性.对于光滑点集,直接对其采用SSLLE算法进行降维,以避免离群点对光滑点的影响;对于离群点集,利用其局部投影坐标计算局部重构权,从而真正反映离群点的局部线性关系.再将光滑点集作为训练点集,结合SSLLE方法计算离群点集的低维坐标.模拟实验和实际例子表明RSSLLE对噪声有很好的鲁棒性.

The paper focuses on the sensitivity of Semi-Supervised Locally Linear Embedding （ SSLLE） to outliers, and presents a robust Semi-Supervised Locally Linear Embedding （RSSLLE）. RSSLLE bases on the outlier detection and improves the robustness against outliers in two ways. On the clean data set, SSLLE is applied to obtain the low-dimensional results, to avoid the influence caused by the outliers. On the outlier set, the local reconstruction weights of the outliers are computed by using the local projection coordinates, which can reflect the intrinsic local geometry of the manifold. And then it regards the clean data points as training data points to compute the low-dimensional coordinates of the outliers by SSLLE. Simulation and real examples show that RSSLLE is robust against outliers.