# Solving Multiclass Learning Problems via Error-Correcting Output Codes

@article{Dietterich1994SolvingML, title={Solving Multiclass Learning Problems via Error-Correcting Output Codes}, author={Thomas G. Dietterich and Ghulum Bakiri}, journal={J. Artif. Intell. Res.}, year={1994}, volume={2}, pages={263-286} }

Multiclass learning problems involve finding a definition for an unknown function f(x) whose range is a discrete set containing k > 2 values (i.e., k "classes"). The definition is acquired by studying collections of training examples of the form (xi, f(xi)). Existing approaches to multiclass learning problems include direct application of multiclass algorithms such as the decision-tree algorithms C4.5 and CART, application of binary concept learning algorithms to learn individual binary…

## 2,960 Citations

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

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## References

SHOWING 1-10 OF 33 REFERENCES

### FUNCTION MODELING EXPERIMENTS.

- Computer Science
- 1963

The results of an experimental investigation of the capabilities and the limitations of trainable machines for use in function modeling have been presented, finding that for more difficult applications, the machine performance was sufficiently good to make the speed advantages of a training machine a significant consideration.

### Why Error Correcting Output Coding Works

- Computer Science
- 1994

An empirical investigation of why the ECOC technique works particularly when employed with decision tree learning methods concludes that an important factor in the success of the method is the nearly random behavior of decision tree algorithms near the root of the decision tree when applied to learn decision boundaries.

### An improved boosting algorithm and its implications on learning complexity

- Computer ScienceCOLT '92
- 1992

The main result is an improvement of the boosting-by-majority algorithm, which shows that the majority rule is the optimal rule for combining general weak learners and extends the boosting algorithm to concept classes that give multi-valued labels and real-valuedlabel.

### Training Stochastic Model Recognition Algorithms as Networks can Lead to Maximum Mutual Information Estimation of Parameters

- Computer ScienceNIPS
- 1989

It is shown that once the output layer of a multilayer perceptron is modified to provide mathematically correct probability distributions, and the usual squared error criterion is replaced with a probability-based score, the result is equivalent to Maximum Mutual Information training.

### When Networks Disagree: Ensemble Methods for Hybrid Neural Networks

- Computer Science
- 1992

Experimental results show that the ensemble method dramatically improves neural network performance on difficult real-world optical character recognition tasks.

### Neural Network Classifiers Estimate Bayesian a posteriori Probabilities

- Computer ScienceNeural Computation
- 1991

Results of Monte Carlo simulations performed using multilayer perceptron (MLP) networks trained with backpropagation, radial basis function (RBF) networks, and high-order polynomial networks graphically demonstrate that network outputs provide good estimates of Bayesian probabilities.

### Classiﬁcation and regression trees

- Computer Science

An introduction to classiﬁcation and regression trees is given by reviewing some widely available algorithms and comparing their capabilities, strengths, and weakness in two examples.

### Backpropagation Applied to Handwritten Zip Code Recognition

- Computer ScienceNeural Computation
- 1989

This paper demonstrates how constraints from the task domain can be integrated into a backpropagation network through the architecture of the network, successfully applied to the recognition of handwritten zip code digits provided by the U.S. Postal Service.