The Strength of Weak Learnability
Machine Learning
C4.5: programs for machine learning
C4.5: programs for machine learning
Machine Learning
Error reduction through learning multiple descriptions
Machine Learning
The Random Subspace Method for Constructing Decision Forests
IEEE Transactions on Pattern Analysis and Machine Intelligence
An approach to the automatic design of multiple classifier systems
Pattern Recognition Letters - Special issue on machine learning and data mining in pattern recognition
On Comparing Classifiers: Pitfalls toAvoid and a Recommended Approach
Data Mining and Knowledge Discovery
Combining Nearest Neighbor Classifiers Through Multiple Feature Subsets
ICML '98 Proceedings of the Fifteenth International Conference on Machine Learning
MCS '00 Proceedings of the First International Workshop on Multiple Classifier Systems
Option Decision Trees with Majority Votes
ICML '97 Proceedings of the Fourteenth International Conference on Machine Learning
Generating Classifier Commitees by Stochastically Selecting both Attributes and Training Examples
PRICAI '98 Proceedings of the 5th Pacific Rim International Conference on Artificial Intelligence: Topics in Artificial Intelligence
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Combinations of weak classifiers
IEEE Transactions on Neural Networks
Forest-RK: A New Random Forest Induction Method
ICIC '08 Proceedings of the 4th international conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications - with Aspects of Artificial Intelligence
A Study of Random Linear Oracle Ensembles
MCS '09 Proceedings of the 8th International Workshop on Multiple Classifier Systems
Thinned-ECOC ensemble based on sequential code shrinking
Expert Systems with Applications: An International Journal
Dynamics of variance reduction in bagging and other techniques based on randomisation
MCS'05 Proceedings of the 6th international conference on Multiple Classifier Systems
A double pruning algorithm for classification ensembles
MCS'10 Proceedings of the 9th international conference on Multiple Classifier Systems
Pattern Recognition Letters
How many trees in a random forest?
MLDM'12 Proceedings of the 8th international conference on Machine Learning and Data Mining in Pattern Recognition
How large should ensembles of classifiers be?
Pattern Recognition
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The aim of this paper is to propose a simple procedure that a priori determines a minimum number of classifiers to combine in order to obtain a prediction accuracy level similar to the one obtained with the combination of larger ensembles. The procedure is based on the McNemar non-parametric test of significance. Knowing a priori the minimum size of the classifier ensemble giving the best prediction accuracy, constitutes a gain for time and memory costs especially for huge data bases and real-time applications. Here we applied this procedure to four multiple classifier systems with C4.5 decision tree (Breiman's Bagging, Ho's Random subspaces, their combination we labeled 'Bagfs', and Breiman's Random forests) and five large benchmark data bases. It is worth noticing that the proposed procedure may easily be extended to other base learning algorithms than a decision tree as well. The experimental results showed that it is possible to limit significantly the number of trees. We also showed that the minimum number of trees required for obtaining the best prediction accuracy may vary from one classifier combination method to another.