Department of Bio and Brain Engineering and Brain Science Research Center, KAIST, Daejeon 305-701, Republic of Korea.
Neural Comput. 2010 Jun;22(6):1615-45. doi: 10.1162/neco.2010.01-09-941.
This letter looks at the physics behind sensory data by identifying the parameters that govern the physical system and estimating them from sensory observations. We extend Takens's delay-embedding theorem to the dynamical systems controlled by parameters. An embedding of the product space of the phase and the parameter spaces of the dynamical system can be obtained by the delay-embedding map, provided that the parameter of the dynamical system changes slowly. The reconstruction error is bounded for slowly varying parameters. A manifold learning technique is applied to the embedding obtained to extract a low-dimensional global coordinate system representing the product space. The phase space of the deterministic dynamics can be contracted by using the adjacency relationship in time, which enables recovery of only the parameter space. As examples, the manifolds of synthetic and real-world vowels with time-varying fundamental frequency (F(0)) are analyzed, and the F(0) contours are extracted by an unsupervised algorithm. Experimental results show that the proposed method leads to robust performance under various noise conditions and rapid changes of F(0) compared with the current state-of-the-art F(0) estimation algorithms.
这封信通过确定控制物理系统的参数并从传感器观测中估计这些参数，研究了感觉数据背后的物理。我们将 Takens 的延迟嵌入定理扩展到由参数控制的动力系统。如果动力系统的参数变化缓慢，则可以通过延迟嵌入映射获得相空间和动力系统参数空间的乘积空间的嵌入。对于缓慢变化的参数，重建误差是有界的。应用流形学习技术对获得的嵌入进行处理，以提取表示乘积空间的低维全局坐标系。通过在时间上使用邻接关系，可以收缩确定性动力学的相空间，从而仅恢复参数空间。作为示例，分析了具有时变基频（F(0)）的合成和真实世界元音的流形，并通过无监督算法提取了 F(0)轮廓。实验结果表明，与当前最先进的 F(0)估计算法相比，该方法在各种噪声条件和 F(0)快速变化下具有稳健的性能。
