
$$W(b_{i}|D)\equiv\frac{1}{|c|}\sum_{j=0}^{|c|-1}\operatorname*{min}_{(n_{k}\in c_{j})\land(n_{k}\in b_{i})}F(n_{k}).$$
$$(11)$$

The predictor function method ranks the baskets by the largeness of the value of W(bi|D).

More highly ranked baskets are retrieved when the number of baskets to retrieve is given.

## 5 Evaluation

We study how precisely the heuristic predictor function method extracts information on the empty spots from the test data set generated as the observed communication records. Communication is a typical social interaction. The homogeneous social network in Figure 3 is employed as a model for the communication patterns among 995 persons. We use precision as a measure of the performance. In information retrieval, precision **has been used as evaluation** criteria, which is the fraction of the amount of relevant data to the **amount of the all data** returned by search (the data ranked highly by the heuristic predictor function).

## 5.1 Test Data Set

The test data set is generated in the two steps below. Note that the input communication records bi (representing the observation including the empty spot) are different from the communication patterns βi **(representing the original communication). The difference, however,**
does not affect the communication patterns. This difference between bi and βi**is the target to**
predict by our method.

- **Communication patterns are simulated and formatted into basket-shaped observation**
records. A basket βi**includes the nodes which are close to each other. For example,**
we can imagine a situation where a person starts talking and a conversation takes place among neighboring persons. The area of such influence is specified approximately with the distance from a node. The distance can be measured in the number of hop count.

One hop is as long as one link on the network. An example basket is β0 = {n954, n**1930**, n3261, n5093, n5223, n7743, n7808, . . .}, representing communication around the node n954 in Figure 3.

- Test data set representing observation records (with a hidden node) bi **are generated by**
deleting the nodes of interest nx from the baskets βi**. The deleted nodes and the links** connecting them to other nodes become the hidden structure. The baskets bi **are the** input to the predictor function W(bi|D**) in Equation (10). The hidden nodes may exist** in multiple baskets. The predictor function ranks and tries to retrieve all of bi**, which are** different from the βi**, as candidates including the hidden nodes and indicating the empty**
spot. The example basket β0 results in b0 = {n954, n1930, n3261, n5093, n7743, n7808, **. . .**} when the node n5223 is configured to be the hidden node to predict. The baskets bi are like records of email senders and receivers which lacks in persons expressing their opinions in the oral communication, or like records of persons of on-line chat **meetings which lacks** in persons using a satellite telephone.
In the simulation, we made up 995 baskets (β0 to β994**) consisting of nodes within a few**
hops from the initiator node in the 1st step. The number of nodes within 5 hops is about 20% of the whole nodes on average. This is a relatively long-distance communication.