This problem illustrates utilization of GFT in sensor malfunction detection. You will first create anomalous data and then validate the anomaly in the data by utilizing GFT. Using GSPBox (see Appendix G for additional information on GSPBox), create a 50-node random sensor network and define a signal f on the graph as

where c is a constant and d (i, j) is the distance between nodes i and j (can be found using

Dijkstra’s shortest path algorithm). This signal can be thought of as temperature values in

a geographical area, since the variations in temperature values are not high if the sensors are

placed densely.

(a) Plot the graph signal and its spectrum for c = 0.1. Now assume that sensors 31 and 42

are anomalous and show temperature values of zero.

(b) Plot the spectrum of this anomalous data. Can we conclude that the data generated by

the sensor network is anomalous?

(c) Can we find the location of anomalous sensors using GFT? Explain why or why not.

This problem is a computer-based exercise. You may use an appropriate software such Matlab
for solving this problem. Some useful code fractions can be found at the support website:
https://complexnetworksbook.github.io