Cascading classifiers

Cascading is a particular case of ensemble learning based on the concatenation of several classifiers, using all information collected from the output from a given classifier as additional information for the next classifier in the cascade. Unlike voting or stacking ensembles, which are multiexpert systems, cascading is a multistage one.

The first cascading classifier is the face detector of Viola and Jones (2001). The requirement was that the classifier be fast in order to be implemented on low CPU systems, such as cameras and phones.

The algorithm can be summed up as follows: for all rectangles in the image:

• stage 1: is there a face in the current rectangle according to classifier 1 ? if yes stage2, if no rectangle does not contain a face
• stage 2: is there a face in the current rectangle according to classifier 2 ? if yes stage3, if no rectangle does not contain a face

...

• stage n: is there a face in the current rectangle according to classifier n ? if yes there is a face in current rectangle

The question is there a face in the current rectangle according to classifier i, for the stage number i ranging from 1 to n is answered by a collection of weak learners. For example, the 'face in current rectangle' score of stage 1 might be 0.3*(centerpixels-sidepixels)+0.5*(-pixel 1/3 from the top + rest of pixels) > 0.8. The first condition expresses the fact that the nose catches the light and the second one the fact that eyebrows are darker than the rest of the face.

To have good overall performance, the following criteria must be met:

• each stage must validate all faces, and produce many false positives. For example, if stage 1 were to mark as 'does not contain a face' 20% of rectangles containing a face (false negative rate=20%), then the total performance of the chain cannot be higher than 80% true positive, whatever the next stages are, since 20% of faces have already been rejected.
• this suggests that a good stage must have 100% true positive and for example 40% false positive, that is accept all rectangles containing faces and erroneously mark many rectangles as potentially containing a face, to be eliminated by later stages.
• if the first stage is very fast (a few operations), we have eliminated 60% of rectangles not containing a face very quickly.

The training procedure for one stage is therefore to have many weak learners (simple pixel difference operators), train them as a group (raise their weight if they give correct result), but be mindful of having only a few active weak learners so the computation time remains low, this is usually done through cost-aware ADAboost. The sensitivity threshold (0.8 in our example) is then adjusted so that there is close to 100% true positives and some false positives. The procedure can then be started again for stage 2, until the desired accuracy/computation time is desired.

After this initial algorithm, it was understood that training the cascade a whole can be optimized, to achieve a desired accuracy goal with minimal complexity. Examples of such algorithms are RCBoost, ECBoost or RCECBoost, in their most basic versions, they can be understood as choosing, at each step, between adding a stage or adding a weak learner to a previous stage, whichever is less costly, until the desired accuracy has been reached.

See also

• Boosting (meta-algorithm)
• Bootstrap aggregating

References

• J. Gama and P. Brazdil. Cascade Generalization. Machine Learning, 41(3):315--343, 2000. [1]
• J. Minguillón. On Cascading Small Decision Trees. PhD dissertation. Universitat Autònoma de Barcelona, 2002. [2]
• H. Zhao and S. Ram. Constrained Cascade Generalization of Decision Trees. IEEE Transactions on Knowledge and Data Engineering, 16(6):727--739, 2004.