actions of the perpetrators who have prepared for the terrorist attack in the observable layer. The collective actions are attending an meeting or **event, for**
example.

The intelligence data set consists of the secret agents' records on the collective actions of the perpetrators. The wire-puller, however, does not appear in the intelligence. The wire-puller is referred to by a covert node ncvt**. The**
investigator applies three tools: (1) link inference to infer the communication between the perpetrators, (2) node discovery to discover the position of the wire-puller, and (3) visualization of the result of the inference and discovery into the form of a social network diagram. The social network diagram serves as an intuitive interface to understand the intelligence data set.

Mathematical definition of the intelligence data set is given here. In eq.(1),
δi **represents the participants to single communication in the latent layer. It is** a set of nodes nj .

## Δi = {Nj}. (1)

It is assumed that the individual intelligence data obtained from the observable layer is the pattern in eq.(1) minus the covert node ncvt**. It is denoted by**
eq.(2).

$$d_{i}=\delta_{i}\backslash\{n_{\mathrm{cut}}\}.$$

$$\left(4\right)$$
di = δi\{ncvt}. (2)
The whole intelligence data set is denoted by D **in eq.(3). The number of**
intelligence data is |d|.

$$D=\{d_{i}\}\ (0\leq i\leq|d|-1).$$
D = {di} (0 ≤ i ≤ |d| − 1). (3)
The intelligence data set D **can be expressed by a two dimensional matrix**
of binary variables. The presence, or absence of the node nj **in the intelligence** data di**is represented by eq.(4). The number of node species is given by** |n|.

$$d_{i j}={\left\{\begin{array}{l l}{1}&{{\mathrm{~if~}}n_{j}\in d_{i}}\\ {0}&{{\mathrm{~otherwise~}}}\end{array}\right.}(0\leq j\leq|n|-1).$$

The intelligence data set is the input to the method for link inference, **node**
discovery, and visualization. The nodes in an intelligence data do not necessarily form a clique structure, where there are links between every pair of nodes. Assuming that they formed a clique would result in a very densely connected structure in the latent layer. Such a superficial interpretation of **the intelligence** data set leads to a wrong understanding of the terrorist organization. This is why we need a new computational method. The method is described below.

## 3.2 Link Inference

The communication in the latent layer is modeled by a graph. Strictly speaking, a graph, a diagram, and a map are defined differently. A graph is an abstract mathematical entity, which consists of a set whose elements are nodes, and a