摘要： 利用基于Ritz加速的逆幂迭代算法，在经典的Hessian LLE算法基础上提出一种增量LLE算法，能够高效地处理新增的一个或多个样本。该算法的核心思想是将增量流形学习问题转化为一个增量特征值问题，利用数值线性代数的工具进行求解，并分析算法的收敛性。在合成数据集和图像数据集上，验证该增量算法的效率和精确度。

关键词: 维数约简, 流形学习, 增量学习, Hessian LLE算法

Abstract: This paper provides an incremental Hessian LLE algorithm, using the inverse iteration with Ritz acceleration, which is capable of dealing with one or more new samples efficiently. The core idea of the algorithm is to translate an incremental manifold problem into an incremental eigen-value problem, and to solve it by the tools of numerical linear algebra. The analysis of its convergence is given. Experiments on both artificial and image datasets confirm the efficiency and accuracy of the proposed method.

Key words: dimensionality reduction, manifold learning, incremental learning, Hessian LLE algorithm

中图分类号: 

• TP301.6