Linear convergence of the subspace constrained mean shift algorithm: from Euclidean to directional data
Linear convergence of the subspace constrained mean shift algorithm: from Euclidean to directional data
复制标题
子空间约束均值平移算法的线性收敛：从欧几里德到方向数据
DOI：
10.1093/imaiai/iaac005
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Chen, Yen-Chi
中科院分区：
文献类型：
--
作者：
Zhang, Yikun;Chen, Yen-Chi
本文研究了子空间约束均值漂移（SCMS）算法的线性收敛性，SCMS算法是一种著名的识别由核密度估计定义的密度岭的算法。通过论证SCMS算法是具有自适应步长的子空间约束梯度上升（SCGA）算法的一个特殊变体，我们得到了这种SCGA算法的线性收敛性。虽然现有的研究主要集中在密度脊在欧氏空间，我们推广的密度脊和SCMS算法的方向数据。特别地，我们建立了方向数据密度脊的稳定性定理，并证明了我们提出的方向SCMS算法的线性收敛性。
This paper studies the linear convergence of the subspace constrained mean shift (SCMS) algorithm, a well-known algorithm for identifying a density ridge defined by a kernel density estimator. By arguing that the SCMS algorithm is a special variant of a subspace constrained gradient ascent (SCGA) algorithm with an adaptive step size, we derive the linear convergence of such SCGA algorithm. While the existing research focuses mainly on density ridges in the Euclidean space, we generalize density ridges and the SCMS algorithm to directional data. In particular, we establish the stability theorem of density ridges with directional data and prove the linear convergence of our proposed directional SCMS algorithm.