A RANSAC-Based ISOMAP for Filiform Manifolds in Nonlinear Dynamical Systems-An Application to Chaos in a Dripping Faucet
A RANSAC-Based ISOMAP for Filiform Manifolds in Nonlinear Dynamical Systems-An Application to Chaos in a Dripping Faucet
复制标题
非线性动力系统中基于RANSAC的丝状流形ISOMAP——在滴水水龙头混沌中的应用
DOI：
10.1007/978-3-642-21738-8_36
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Hiromichi Suetani and Shotaro Akaho
中科院分区：
文献类型：
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作者：
S Munejiri;F Shimojo and K Hoshino;Hiromichi Suetani and Shotaro Akaho
混沌动力系统产生的轨迹位于状态空间的非线性流形上。即使这样一个流形的维数比全状态空间的维数低得多，只要我们仍然使用原始坐标，我们就需要许多状态变量来跟踪它上的运动，因此所得的动力学表达式变得多余。在本研究中，我们采用流形学习算法之一，ISOMAP，构建一个新的非线性坐标，全局覆盖的流形，这使我们能够描述它作为一个低维动力系统的动力学。在这里，为了改善传统的ISOMAP，我们提出了一种方法的基础上结合RANSAC修剪相邻图中的错误连接的边缘。我们表明，一个明确的确定性关系提取的质量弹簧模型的时间序列的混沌滴水龙头使用所提出的方法。
Trajectories generated from a chaotic dynamical system are lying on a nonlinear manifold in the state space. Even if the dimensionality of such a manifold is much lower than that of the full state space, we need many state variables to trace a motion on it as far as we remain to employ the original coordinate, so the resulting expression of the dynamics becomes redundant. In the present study, we employ one of the manifold learning algorithms, ISOMAP, to construct a new nonlinear coordinate that globally covers the manifold, which enables us to describe the dynamics on it as a low-dimensional dynamical system. Here, in order to improve the conventional ISOMAP, we propose an approach based on a combination with RANSAC for pruning the misconnected edges in the neighboring graph. We show that a clear deterministic relationship is extracted from time series of a mass-spring model for the chaotic dripping faucet using the proposed method.