Improving the Graph Mincut Approach to Learning from Labeled and Unlabeled

Examples

Avrim Blum, John Lafferty, Raja Reddy, Mugizi Rwebangira

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

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

Construct a Graph

Add sink and source

-+

Obtain s-t mincut

Mincut

-+

Classification

+ -

Mincut

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

Experiments

• Digits data set (each digit is a 16 X 16 integer array)

• 100 labeled examples

• 3900 unlabeled examples

• 100 runs of mincut

Results

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

Questions?