Blind identification of sparse dynamic networks and applications
Blind identification of sparse dynamic networks and applications
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稀疏动态网络的盲识别及应用
DOI：
10.1109/cdc.2011.6161088
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
N. Ozay
中科院分区：
文献类型：
--
作者：
Mustafa Ayazoglu;M. Sznaier;N. Ozay
本文研究了从实验噪声数据中识别稀疏互连动力系统网络拓扑结构的问题。具体来说，我们假设观察到的数据是由底层未知的图拓扑生成的，其中每个节点对应于给定的时间序列，每个链接都指向映射这些时间序列的未知自回归模型。目标是恢复与一些先验信息兼容并能够解释观察到的数据的最稀疏（在具有最少数量的链接的意义上）结构。与相关的现有工作相反，我们的框架允许（不可测量的）外生输入，旨在模拟相对不常见的事件，如底层过程中的环境或设定点变化。本文的主要结果表明，网络拓扑和未知输入都可以通过求解一个凸优化问题来识别，该问题是通过将Group-Lasso类型参数与重新加权的启发式方法相结合而得到的。如图所示，这种组合比使用组Lasso或基于正交分解的算法产生更稀疏的拓扑。这些结果是用学术实例和几个重要的问题来说明的，这些问题来自多个应用领域，包括金融、生物学和计算机视觉。
This paper considers the problem of identifying the topology of a sparsely interconnected network of dynamical systems from experimental noisy data. Specifically, we assume that the observed data was generated by an underlying, unknown graph topology where each node corresponds to a given time-series and each link to an unknown autoregressive model that maps those time series. The goal is to recover the sparsest (in the sense of having the fewest number of links) structure compatible with some a-priori information and capable of explaining the observed data. Contrary to related existing work, our framework allows for (unmeasurable) exogenous inputs, intended to model relatively infrequent events such as environmental or set-point changes in the underlying processes. The main result of the paper shows that both the network topology and the unknown inputs can be identified by solving a convex optimization problem, obtained by combining Group-Lasso type arguments with a re-weighted heuristics. As shown here, this combination leads to substantially sparser topologies than using either group Lasso or orthogonal decomposition based algorithms. These results are illustrated using both academic examples and several non-trivial problems drawn from multiple application domains that include finances, biology and computer vision.