Application of ideas from graph theory in machine learning

4

1

I work with neural networks (ConvNNs, DeepNNs, RNNs/LSTMs) for image segmentation and recognition and Genetic Algorithms for some optimization problems. Recently I started to learn some deep graph theory ideas (random graphs, chromatic numbers, graph coloring). I'm familiar with combinatorics at undergrad level. Are there any existing interesting applications and areas of research of graph theory and combinatorics in ML?

Alex

Posted 2016-03-17T10:38:41.777

Reputation: 692

Question was closed 2017-01-06T17:56:28.890

Answers

1

Graphs are a very flexible form of data representation, and therefore have been applied to machine learning in many different ways in the past. You can take a look to the papers that are submitted to specialized conferences like S+SSPR (The joint IAPR International Workshops on Structural and Syntactic Pattern Recognition and Statistical Techniques in Pattern Recognition) and GBR (Workshop on Graph-based Representations in Pattern Recognition) to start getting a good idea of potential applications. Some examples:

  • Within the Computer Vision field, graphs have been used to extract structure information that can later on be used on several applications, like for instance object recognition and detection, image segmentation and so on.
  • Spectral clustering is an example of clustering method based on graph theory. It makes use of the eigenvalues of the similarity matrix to combine clustering and dimensionality reduction.
  • Random walks may be used to predict and recommend links in social networks or to rank webpages by relevance.

Pablo Suau

Posted 2016-03-17T10:38:41.777

Reputation: 1 507

thanks Pablo. Could you give me some links to publications for the 1st and 3rd examples. – Alex – 2016-03-19T12:10:32.913

Take a look to the following slides. There you will see more details about spectral theory and very brief examples of application to shape recognition and webpage ranking (PageRank):

https://www.cs.york.ac.uk/cvpr/talks/PRGraphsFinal.pdf

– Pablo Suau – 2016-03-21T09:31:32.497