Authenticating Banknotes Based on Images

Simple and accurate solution with hyperplane classification trees

Automating the authentication procedure for banknotes

With image data on genuine and forged banknotes, we aimed to develop an automated procedure to differentiate the forged ones as part of the authentication process.

The features from the images were extracted using wavelet transform tools, yielding information on the variance, skewness, curtosis, and entropy of the image. We used Optimal Classification Trees to learn which feature combinations help distinguish between genuine and forged banknotes. The learned decision tree achieved an Area-Under-the-Curve (AUC) of 99.3%, indicating near-perfect performance.

Optimal Classification Tree predicting the banknote authenticity

Optimal Classification Trees offer unparalleled flexibility with hyperplanes

This tree is very accurate, but we would like to reduce the size to make it more understandable and easier to inspect. The original tree uses the traditional approach of splitting on one variable at a time with so-called parallel splits, which are limited in power and often require large trees to achieve high performance. We can improve the power of the splits by considering more than one variable at a time, yielding hyperplane splits and hopefully smaller trees as a result.

In the past, decision trees with hyperplane splits were impractical to fit on even moderately-sized datasets. However, it is straightforward to extend the global optimization model that powers Optimal Trees to incorporate hyperplane splits. This means that Optimal Trees are unique in offering a practical way to train these hyperplane split trees at scale, allowing us to revisit the problem with more modeling power.

Example hyperplane splits into three classes using two variables

Shallower and simpler trees with hyperplanes

We fit an Optimal Classification Tree with hyperplanes on the same data, resulting in a tree with only two splits, and the same near-perfect performance. We can see that the simple addition of a single split involving multiple variables is able to eliminate most of the complexity of the earlier tree with parallel splits and segment the data in a more efficient manner.

This simple solution not only automates the banknote authentication process with near-perfect accuracy, but also permits much easier verification of the decision process by experts as a result of the reduced size of the tree.

Optimal Classification Tree with hyperplanes predicting the banknote authenticity

Unique Advantage

Why is the Interpretable AI solution unique?

  • More modeling flexibility

    The ability to incorporate hyperplanes at scale unlocks unprecedented modeling power for decision trees.

  • Simpler models for inspection

    Introducing hyperplane splits into the tree reduced the size significantly, making it easier to inspect and verify the model.

Want to try Interpretable AI software?
We provide free academic licenses and evaluation licenses for commercial use.
We also offer consulting services to develop interpretable solutions to your key problems.

© 2020 Interpretable AI, LLC. All rights reserved.