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中文摘要：
目前一些经典的降维流形学习方法以距离来度量数据间的相似度，难以处理噪音造成的子空间偏离。针对此问题，文中提出一种基于等角映射的多样本增量流形学习算法，将以样本均值为中心的高维样本数据的协方差矩阵变为以邻域均值为中心的协方差矩阵，消除基于距离度量对子空间带来的误差，并对协方差矩阵进行加权，减少不规则新增样本或噪音对降维造成的影响。实验证明该算法与其他算法相比，具有更好的抗噪能力及降维效果，可更好地应用于图像识别问题。
英文摘要：
In the classical dimension reducing manifold learning algorithms, the distance is used to measure the similarity between data, and the problem of subspace deviation caused by noise can not be solved. A multi-sample incremental manifold learning algorithm based on Isogonal mapping is proposed. The covariance matrix of the high dimensional samples with sample mean as the center is turned into the covariance matrix with neighborhood mean as the center. Thus, the error of the subspace caused by distance measurement is eliminated, the covariance matrix is weighted, and the effect of noise or irregular new samples on dimension reduction is reduced. Experimental results show an improvement of the proposed algorithm compared with other algorithms. Moreover, the proposed algorithm can be well applied to image recognition.
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