Hybrid Wasserstein distance and fast distribution clustering
Hybrid Wasserstein distance and fast distribution clustering
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DOI：
10.1214/19-ejs1639
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发表时间：
2018-12
影响因子：
1.1
通讯作者：
I. Verdinelli;L. Wasserman
中科院分区：
文献类型：
--
作者：
I. Verdinelli;L. Wasserman
我们定义了一个修改后的Wasserstein距离分布聚类，继承了许多属性的Wasserstein距离，但可以很容易地估计和快速计算。修改后的距离是两项之和。第一项-具有封闭形式-测量分布之间的位置-尺度差异。第二项是一个近似值，它测量了考虑位置-尺度差异后的剩余距离。我们考虑几种形式的近似，我们的主要重点是切线空间近似，可以使用非参数回归估计。我们评估的优点和缺点，这种方法的模拟和真实的例子。
We define a modified Wasserstein distance for distribution clustering which inherits many of the properties of the Wasserstein distance but which can be estimated easily and computed quickly. The modified distance is the sum of two terms. The first term --- which has a closed form --- measures the location-scale differences between the distributions. The second term is an approximation that measures the remaining distance after accounting for location-scale differences. We consider several forms of approximation with our main emphasis being a tangent space approximation that can be estimated using nonparametric regression. We evaluate the strengths and weaknesses of this approach on simulated and real examples.