The alignment distance on Spaces of Linear Dynamical Systems
The alignment distance on Spaces of Linear Dynamical Systems
复制标题
线性动力系统空间上的对齐距离
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
R. Vidal
中科院分区：
文献类型：
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作者：
B. Afsari;R. Vidal
在固定大小和阶的线性动力系统空间上引入了一族群作用诱导距离。两个LDS之间的距离是通过找到最佳对齐两个LDS的状态空间实现的基的变化来计算的，因此称为对齐距离。该距离可以被有效地计算，因此它特别适合于现代动态数据分析中的应用（例如，视频序列分类和聚类），其中可能需要比较大量的高维LDS。基于对齐距离，我们还定义了相同大小和顺序的LDS之间的平均值的概念，其具有顺序和在某些情况下稳定性自然保留的属性。还提出了对对准距离的基本概念的各种扩展。
We introduce a family of group action induced distances on spaces of Linear Dynamical Systems (LDSs) of fixed size and order. The distance between two LDSs is computed by finding the change of basis that best aligns the state-space realizations of the two LDSs, hence the name alignment distance. This distance can be computed efficiently, hence it is particularly suitable for applications in modern dynamic data analysis (e.g., video sequence classification and clustering), where a large number of high-dimensional LDSs may need to be compared. Based on the alignment distance, we also define a notion of average between LDSs of the same size and order with the property that the order and in some cases stability are naturally preserved. Various extensions to the basic notion of alignment distance are also proposed.