摘要
数据降维问题存在于包括机器学习、模式识别、数据挖掘等多个信息处理领域。局部线性嵌入(LLE)是一种用于数据降维的无监督非线性流行学习算法,因其优良的性能,LLE得以广泛应用。针对传统的LLE对离群(或噪声)敏感的问题,提出一种鲁棒的基于L1范数最小化的LLE算法(L1-LLE)。通过L1范数最小化来求取局部重构矩阵,减小了重构矩阵能量,能有效克服离群(或噪声)干扰。利用现有优化技术,L1-LLE算法简单且易实现。证明了L1-LLE算法的收敛性。分别对人造和实际数据集进行应用测试,通过与传统LLE方法进行性能比较,结果显示L1-LLE方法是稳定、有效的。
The problem of dimensionality reduction arises in many fields of information processing, including machine learning, pattern recognition, data mining etc. Locally linear embedding （LLE） is an unsupervised and nonlinear learning algorithm for dimensionality reduction, well-known for its outperformance. Unlike classical LLE, which is based on the L2- norm, a novel L1-norm based LLE （L1-LLE） algorithm is proposed in this article, which is robust to outliers because it utilizes the L1-norm, which is less sensitive to outliers. The proposed L1-norm optimization technique is intuitive, simple, and easy to implement. It is also proven to find a globally minimal solution. The proposed method is applied to several data sets and the performance is compared to those of other conventional methods.
出处
《中国图象图形学报》
CSCD
北大核心
2011年第10期1802-1811,共10页
Journal of Image and Graphics
基金
国家自然科学基金项目(60975027
60903100)
宁波市自然科学基金项目(2009A610080)
关键词
降维
L1-范数
流形学习
局部线性嵌入
鲁棒性
dimensionality reduction
L1-norm
manifold learning
locally linear embedding
robust
