一种新的全局嵌入降维算法

摘要

目前大多数流形学习算法都以距离来度量数据间的相似度,并取得满意的效果,但都难以处理噪音造成的子空间偏离.针对此间题,提出了一种基于角度优化的全局降维算法.通过给出多样本增量的协方差阵更新方式,从理论上证明了中心化样本长度与其偏离低维空间角度为子空间偏离的主要因素,进而解决了噪音造成的子空间偏离问题.同时,与主成分分析相比,能够更好地与其他算法融合解决小样本问题.实验证实了该算法在手工和真实数据集上的有效性.%Recently, most manifold learning algorithms take advantage of distance to measure similarity of data, and obtain satisfactory results, but most of them can not handle subspace deviation caused by noise. To solve this problem, a global dimensionality reduction algorithm based on angle optimization is proposed in this paper. Theoretically it proves that the main factors of subspace deviation are the length of the center sample and the angle of deviation from the low-dimensional space by providing covaxiance matrix update mode of multi-sample incremental. Consequently, the algorithm solves the subspace deviation problem caused by noise. Compared with the principal component analysis, it can integrate better with other algorithms to solve small sample problems. Experiments carried out on handwork and real data sets show a clear improvement over the results of other linear algorithms.