Improving the Graph Mincut Approach to Learning from Labeled and Unlabeled Examples

1. Improving the Graph Mincut Approach to Learning from Labeled and Unlabeled Examples Avrim Blum, John Lafferty, Raja Reddy, Mugizi Rwebangira

2. Outline • Often have little labeled data but lots of unlabeled data • Graph mincuts: based on a belief that most ‘close’ examples have same classification • Problem: -Does not say where it is most confident • Our approach: Add noise to edges to extract confidence scores

3. Learning using Graph Mincuts:Blum and Chawla (ICML 2001)

4. Construct a Graph

5. Add sink and source + -

6. Obtain s-t mincut + - Mincut

7. Classification + - Mincut

8. Goal • To obtain a measure of confidence on each classification Our approach • Add random noise to the edges • Run min cut several times • For each unlabeled example take majority vote

9. Experiments • Digits data set (each digit is a 16 X 16 integer array) • 100 labeled examples • 3900 unlabeled examples • 100 runs of mincut

10. Results

11. Conclusions • 3% error on 80% of the data • Standard mincut only gives us 6% error on all the data • Future Work • Conduct further experiments on other data sets • Compare with similar algorithm of Jerry Zhu • Investigate the properties of the distribution we get by selecting minimum cuts in this way

12. Questions?