Introduction

Large-scale and critical infrastructure monitoring data is usually high dimensional. The structure of this high dimensional data in most cases and conditions can be characterized by a relatively small number of parameters. Reducing the data dimension presents the engineer with different opportunities, including visualization of the intrinsic structure of the data and more efficient data to develop appropriate models, such as prediction. The “flat-world view” of two-way matrix application may be insufficient in making inferences in interdependent infrastructures. In current literature in infrastructure data analysis, most high dimensional data are inappropriately represented, making it very difficult to develop the correct models for further analysis. In some situations, there is a need to analyze simultaneous effects of many features on interdependent infrastructure. The features can also be nonscalar features.

For example, the use of image analysis in infrastructure monitoring requires a new form of data representation in the large-scale civil infrastructure systems. In general, the resilience of an interdependent network once presented as multiple graphs and the adjacency tensor can provide the framework for addressing the resilience of interdependent networks (Figure 8.1).

The multiple networks (graphs) G(V, E(1)E(2) · · ·E(N)) with a vertex set V and an edge sets ﹛E(1), E(2), · · ·E(n)﹜ and, for example, A(n)i j = 1 indicate situations of the presence of a link from vertex i to j with respect to an infrastructure n. Tensors appear to be an appropriate way to represent high dimensional data in large-scale infrastructure and their interdependences. Tensor factorization and decomposition are becoming major tools for large multidimensional data analysis. Factorizing tensors have better advantages than traditional matrix factorization such as uniqueness of the optimal solution, and the decomposition can explicitly take account of the multiway structure of the data. The application of the tensor, apart from addressing the previous shortcomings, will provide a platform for performing data mining applications. Sun et al. (2006) noted that the tensor approach is capable of detecting anomalies in data. The anomaly detection can proceed from the broadest level to a more specific level. Sun et al. (2006) discusses the process of using tensors in computer network modeling, which have some similarities with large civil network infrastructure.