# Reducing Multiclass to Binary: A Unifying Approach for Margin Classifiers

@article{Allwein2000ReducingMT, title={Reducing Multiclass to Binary: A Unifying Approach for Margin Classifiers}, author={Erin Allwein and Robert E. Schapire and Yoram Singer}, journal={J. Mach. Learn. Res.}, year={2000}, volume={1}, pages={113-141} }

We present a unifying framework for studying the solution of multiclass categorization problems by reducing them to multiple binary problems that are then solved using a margin-based binary learning algorithm. The proposed framework unifies some of the most popular approaches in which each class is compared against all others, or in which all pairs of classes are compared to each other, or in which output codes with error-correcting properties are used. We propose a general method for combining…

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## References

SHOWING 1-10 OF 79 REFERENCES

### A comparison of methods for multiclass support vector machines

- Computer ScienceIEEE Trans. Neural Networks
- 2002

Decomposition implementations for two "all-together" multiclass SVM methods are given and it is shown that for large problems methods by considering all data at once in general need fewer support vectors.

### Solving Multiclass Learning Problems via Error-Correcting Output Codes

- Computer ScienceJ. Artif. Intell. Res.
- 1995

It is demonstrated that error-correcting output codes provide a general-purpose method for improving the performance of inductive learning programs on multiclass problems.

### Multiclass learning, boosting, and error-correcting codes

- Computer ScienceCOLT '99
- 1999

ECC, that, by using a different weighting of the votes of the weak hypotheses, is able to improve on the performance of ADABOOST.OC, is arguably a more direct reduction of multiclass learning to binary learning problems than previous multiclass boosting algorithms.

### Improved Boosting Algorithms Using Confidence-rated Predictions

- Computer ScienceCOLT' 98
- 1998

We describe several improvements to Freund and Schapire's AdaBoost boosting algorithm, particularly in a setting in which hypotheses may assign confidences to each of their predictions. We give a…

### Special Invited Paper-Additive logistic regression: A statistical view of boosting

- Computer Science
- 2000

This work shows that this seemingly mysterious phenomenon of boosting can be understood in terms of well-known statistical principles, namely additive modeling and maximum likelihood, and develops more direct approximations and shows that they exhibit nearly identical results to boosting.

### Arcing the edge

- Computer Science
- 1997

A framework for understanding arcing algorithms is defined and a relation is derived between the optimal reduction in the maximum value of the edge and the PAC concept of weak learner.

### Boosting the margin: A new explanation for the effectiveness of voting methods

- Computer ScienceICML
- 1997

It is shown that techniques used in the analysis of Vapnik's support vector classifiers and of neural networks with small weights can be applied to voting methods to relate the margin distribution to the test error.

### SSVM: A Smooth Support Vector Machine for Classification

- Computer ScienceComput. Optim. Appl.
- 2001

Smoothing methods are applied here to generate and solve an unconstrained smooth reformulation of the support vector machine for pattern classification using a completely arbitrary kernel, which converges globally and quadratically.

### Training support vector machines: an application to face detection

- Computer ScienceProceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition
- 1997

A decomposition algorithm that guarantees global optimality, and can be used to train SVM's over very large data sets is presented, and the feasibility of the approach on a face detection problem that involves a data set of 50,000 data points is demonstrated.

### Additive Logistic Regression : a Statistical View ofBoostingJerome

- Computer Science
- 1998

This work develops more direct approximations of boosting that exhibit performance comparable to other recently proposed multi-class generalizations of boosting, and suggests a minor modiication to boosting that can reduce computation, often by factors of 10 to 50.