基于L_1范数重建的稳健独立成分分析  

Robust independent component analysis based on L_1 norm reconstruction

作　　者：王楠[1] 洪涛[1] 孟德宇[1] 

机构地区：[1]西安交通大学数学与统计学院,西安710049

出　　处：《中国科技论文》2013年第10期1050-1056,共7页China Sciencepaper

基　　金：高等学校博士学科点专项科研基金资助项目(20090201120056)

摘　　要：独立成分分析(independent component analysis,ICA)是一种混合信号处理与分离方法,能够从多维混合观测数据中分离出各个独立成分。目前,ICA已成功应用于特征提取、信号处理、模式识别等诸多领域。然而,由于实际问题的复杂性,可观测到的混合观测中往往含有噪声、异常点与缺失点,而标准ICA算法对这类数据往往不能有效处理。针对该问题,提出了一种基于L1范数重建的新思路。基本思路是将传统ICA模型中加入L1范数项重新建模,利用L1范数误差对噪声与缺失点的本质稳健性,提高模型应用普适性;进一步设计了针对该模型的有效求解算法。在混合人工信号分离、混合图像分离以及混合音频信号分离的实验证明中,所提算法能够显著提升现有ICA方法对于含噪声、异常点与缺失点数据的计算稳健性。Independent component analysis （ICA） is a hybrid method of signal processing and separation. It can isolate separate components from the multidimensional mixed observation data. At present, ICA has been successfully applied to feature extraction, signal processing, pattern recognition, and many other fields. Given the complexity of the actual problem, the mixed obser- vation often contains noise, abnormal points and missing points, whereas the standard ICA algorithms often cannot effectively deal with this kind of data. In order to solve this problem, we propose a new idea based on L1 norm reconstruction. The basic i- dea is to add the L1 norm into the traditional ICA model for re-modeling, and using L1 norm error to improve the nature robust- ness of noise and missing points applied universality. We further design an effective algorithm for this model. Experiments of hy- brid artificial signal separation, mixed image separation and the mixed audio signal separation all show that the proposed algorithm for the existing ICA method is effective to improve robustness of calculating data that contain abnormal and missing points.

关 键 词：独立成分分析 噪声 异常点 缺失点 稳健ICA算法 

分 类 号：TN911.7[电子电信—通信与信息系统]