Describe the movement of gaze positions obtained from visual search experiments in network engineering terms

  

Assuming that the movement of the gaze position during visual search is restricted to move on a certain network, we design the network.

We place 65,536 (256 times 256) nodes on the search-array board and connect each neighbor node with an edge.

This reproduces the motion of the fixational movement of the gaze position.

Then, a shortcut is designed by reconnecting some of the edges with distant nodes with probability q. This reproduces the motion of the saccade at the gaze position.

By varying the ratio q of shortcuts to the total number of edges (the ratio of saccades to fixational movements), we can design various types of networks, from those in which only fixational movements appear to those in which only saccades appear.

The file "C(q).csv" represents the cluster coefficients, which are local attributes that connect neighboring nodes to each other, and "L(q).csv" is the global attribute that connects distant nodes to each other. "L(q).csv" represents the distance between nodes.

The file "h(q).csv" calculates the difference between C(q) and L(q).

"C(q)_and_L(q).jpg" shows a graph of median cluster coefficients and median distances between nodes with q on the horizontal axis. 

This is created from "C(q).csv" and L(q).csv".

"h(q).jpg" is a graph of the difference between C(q) and L(q) with q on the horizontal axis.

This is created from "h(q).csv".

In "h(q).jpg", the network that maximizes the value of h(q) is the small-world network.

The ratio q_{exp} of the saccade to the fixational movement for the 16 participants in the experiment who performed visual search is estimated.

The value of q_{exp} (marked with an X in the first line of the file "h(q).csv") is close to the value of q when the value of h(q) is maximum (marked with a square in the first line of the file "h(q).csv"). 

From the statistical test, it was determined that the network designed with the ratio estimated from the experiment is a small-world network.

The five q values marked with circles and an X in the first line of the file "h(q).csv" are not significantly different from the q value marked with a square.