基于子空间距离的局部切空间增量学习  

Local tangent space incremental learning based on subspace distance

作　　者：李德宜[1] 曾弦 周勇 Li Deyi;Zeng Xian;Zhou Yong(College of Science,Wuhan University of Science and Technology,Wuhan 430065,China)

机构地区：[1]武汉科技大学理学院

出　　处：《武汉科技大学学报》2019年第5期394-400,共7页Journal of Wuhan University of Science and Technology

基　　金：国家自然科学基金资助项目(61671338)

摘　　要：提出一种基于子空间距离的局部切空间增量学习方法ISLTSA。首先采用基于划分的简化局部切空间排列算法SLTSA,把初始样本集划分为彼此重叠的多个局部最大线性片;然后引入向量到子空间的距离测度描述新数据点与局部最大线性片的接近程度,并将新数据点归入距离其最近的局部最大线性片中;最后,新数据点的全局低维坐标可由局部线性子空间与全局低维流形的仿射变换计算得出。对多个经典数据集的降维结果表明,ISLTSA算法能够保留数据集的局部几何性质,是一种有效的非线性增量学习方法。This paper proposes a novel incremental learning method of local tangent space alignment based on subspace distance,named as ISLTSA.Firstly,a simplified local tangent space alignment(SLTSA)algorithm is used to divide the initial dataset into several overlapped local maximum linear slices.Then a distance metric from vector to subspace is introduced to describe the closeness degree between a new data point and a local maximum linear slice,and the new data point should be included in its nearest local maximum linear slice.Finally,the global low dimensional coordinates of new data points can be computed by the affine transformations from local linear subspaces to global low-dimensional manifolds.ISLTSA is applied to reduce the dimensions of several classical datasets.The results show that it can preserve the local geometrical characteristics of the datasets and is an effective non-linear incremental learning method.

关 键 词：增量学习 流形学习 局部切空间排列 子空间距离 降维 ISLTSA算法 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]