数据流形边界及其分布条件的增量式降维算法  

Incremental dimensionality reduction algorithm based on data manifold boundaries and distribution state

作　　者：赵光华 杨焘[1,2] 付冬梅[1,2] ZHAO Guanghua;YANG Tao;FU Dongmei(School of Automation and Electrical Engineering,University of Science and Technology Beijing,Beijing 100083,China;Shunde Innovation School,University of Science and Technology Beijing,Foshan 528300,China)

机构地区：[1]北京科技大学自动化学院,北京100083 [2]北京科技大学顺德创新学院,广东佛山528300

出　　处：《智能系统学报》2023年第5期975-983,共9页CAAI Transactions on Intelligent Systems

基　　金：国家自然科学基金项目(61903029);科技部-科技基础资源调查专项(2019FY101404);佛山市人民政府科技创新专项(BK20AE004)。

摘　　要：为了解决增量流形学习中的噪声干扰,以及对不同分布状态下的新数据进行流形降维问题,本文提出一种数据流形边界及其分布条件的增量式降维算法(incremental dimensionality reduction algorithm based on data manifold boundaries and distribution state,IDR-DMBDS)。该算法首先分析噪声概率分布同时对数据降噪,确定降噪数据的流形形态为主流形,并在主流形上表征出噪声的分布形式,以此获得近似的原数据流形边界,然后基于流形边界判别新数据的分布状态,最后将分布于原流形形态之上以及之外的新数据分别映射至低维空间。实验表明,该算法能够有效实现基于流形的增量式高维含噪数据的低维特征挖掘。To eliminate the impact of noise on incremental manifold learning and conduct manifold dimensionality re-duction on new data under different distribution states,an incremental dimensionality reduction algorithm is proposed based on data manifold boundaries and distribution state.In the algorithm,the probability distribution of noises is ana-lyzed while simultaneously performing data noise reduction.The manifold shape of the data with noise reduction is de-termined as the main manifold,wherein the distribution form of noise is represented to obtain the approximate manifold boundary of the original data.Subsequently,the distribution state of the new data is determined based on the manifold boundary.Finally,the new data distributed inside and outside the original manifold shape are mapped to the low-dimen-sional space.Experiments reveal that the algorithm can effectively achieve the excavation of the low-dimensional fea-tures of incremental high-dimensional noisy data based on manifold learning.

关 键 词：增量式学习 流形降维 噪声 流形边界 概率分布 投影 离群点检测 分类 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]