Level: MSci, MSc
Title: Image classification and face recognition using 2D visibility graphs
Supervisor:

Dr Lucas Lacasa
Research Area: Complex Systems and Networks
Description:

The so called visibility algorithms [1,2] are a family of simple algorithms that map a time series {x1,x2,…,xn} into a graph of n vertices where each two vertices share an edge if a concrete "visibility criterion" holds. One can then associate a graph / network to a given time series, i.e. one can link graph theory /network theory with dynamics. This project is about extending this concept to the two dimensional setting, and both developing and implementing a 2D visibility algorithm to extract a network from a 2D image h(x,y). The ultimate aim of the project is to extract features from this graph and use standard statistical learning algorithms to classify images.

Note: this is mainly a research project (i.e. exciting but hard). The student is expected to implement numerical routines in the computer, to learn some theory and to make data analysis.

  1. L. Lacasa, B. Luque, F. Ballesteros, J. Luque and J. C. Nuño, From time series to complex networks: the visibility graph, Proc. Natl. Acad. Sci. USA 105 13 (2008) 4972–4975.
  2. B. Luque, L. Lacasa, J. Luque and F. J. Ballesteros, Horizontal visibility graphs: exact results for random time series, Physical Review E80, 046103 (2009).

 
Further Reading:

 
Key Modules:

MTH739U/MTH739P Topics in Scientific Computing
Other Information:

Good management of some programming language and knowledge of machine learning is required.
Current Availability: Yes