关键词: 流形学习, 邻域大小, 主成分分析（PCA）重建误差, 贝叶斯信息准则

Abstract: The success of manifold learning algorithms depends greatly upon selecting a suitable neighborhood size，however，it is an open problem how to do this efficiently.To solve this problem，this paper proposes an efficient method to judge the suitability of a given neighborhood size，by which a suitable neighborhood size can be selected efficiently.Based on the locally Euclidean property of the manifold，this method uses the PCA（Principal Component Analysis） reconstruction error to measure the linearity of each neighborhood in the neighborhood graph，and then judges the suitability of the corresponding neighborhood size according to the number of clusters of all the PCA reconstruction errors in the neighborhood graph，which is detected by BIC（Bayesian Information Criterion） in this paper.This method can judge the suitability of a given neighborhood size while not running the time-consuming manifold learning algorithm，so it is much more efficient than those methods based on residual variance.Finally，the effectivity of this method can be verified by experimental results well.

Key words: manifold learning, neighborhood size, Principal Component Analysis（PCA） reconstruction error, Bayesian Information Criterion（BIC）