Least-Squares Log-Density Gradient Clustering for Riemannian Manifolds
Least-Squares Log-Density Gradient Clustering for Riemannian Manifolds
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发表时间：
2016-03
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通讯作者：
Mina Ashizawa;Hiroaki Sasaki;Tomoya Sakai;Masashi Sugiyama
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作者：
Mina Ashizawa;Hiroaki Sasaki;Tomoya Sakai;Masashi Sugiyama
均值漂移是一种模式搜索聚类算法，已成功地用于图像分割和目标跟踪等广泛的应用。为了进一步提高聚类性能，均值漂移已经扩展到各个方向，包括推广到处理黎曼流形上的数据和扩展到直接估计对数密度梯度而无需密度估计。在本文中，我们联合收割机这些想法，并提出了一种新的模式搜索算法的黎曼流形与直接的对数密度梯度估计。虽然结合这两种扩展的想法相当简单，但直接估计黎曼流形上的对数密度梯度在数学上是具有挑战性的。我们将提供一个数学上合理的算法，并通过实验证明其实用性。
Mean shift is a mode-seeking clustering algorithm that has been successfully used in a wide range of applications such as image segmentation and object tracking. To further improve the clustering performance, mean shift has been extended to various directions, including generalization to handle data on Riemannian manifolds and extension to directly estimating the log-density gradient without density estimation. In this paper, we combine these ideas and propose a novel mode-seeking algorithm for Riemannian manifolds with direct log-density gradient estimation. Although the idea of combining the two extensions is rather straightforward, directly estimating the log-density gradient on Riemannian manifolds is mathematically challenging. We will provide a mathematically sound algorithm and demonstrate its usefulness through experiments.