Adaptive Boosting vs. SVM I am working on a binary classification case and comparing the performance of different classifiers.Testing the performance of adaboost algorithm (with decision tree as its base classifier) against SVM on multiple data sets I found that the boosting algorithm performs better. 
The question I have is why this is happening? Is this because boosting always outperforms SVM? or it has something to do with the characteristics of my data set?  I wonder if anyone can help me with some potential explanations of such finding. 
 A: For me your question is part of a larger one involving classification algorithms in general. This paper Do we Need Hundreds of Classifiers to Solve Real World Classfication Problems?, gets at this more fundamental question in finding that random forests outperforms all other competitors. A link to an ungated copy is here:
http://jmlr.csail.mit.edu/papers/volume15/delgado14a/delgado14a.pdf
There are other flavors of boosting that haven't been mentioned such as GBM, the generalized boosted model, which has an R package:
https://github.com/gbm-developers/gbm
Also worth a mention is XGBoost or extreme gradient boosting, which some have found to out perform everything (and despite the Delgado paper's findings).
https://cran.r-project.org/web/packages/xgboost/xgboost.pdf
A: In short: Regular AdaBoost (decision stumps, not decision trees as weak learners) usually outperform linear SVMs. Of course this is dependent on your data, data normalization, etc, so this is certainly not a general rule. The reasoning should be fairly clear. AdaBoost can learn non-linear decision boundaries, which is almost always helpful, especially if your data can not be linearly separated. If it can, it is all just a question of empircal results and not much can be said about AdaBoost vs. SVM except that the SVM builds upon Statistical Learning Theory (SLT, http://videolectures.net/mlss09uk_shawe_taylor_lt/?q=machine%20learning%20summer%20school). I am not entirely sure that can be said for AdaBoost. Given that the SVM maximizes the margin between the point clouds it should, given linearly separable data, outperform AdaBoost since we would expect better generalization from the SVM than from AdaBoost at this point.
When the SVM uses a proper non-linear kernel that fits the data better and generalizes well, it usually outperforms AdaBoost. 
AdaBoost is commonly used because it is very fast. Viola  & Jones have used it 15 years ago to realize fast object detection, especially face recognition: https://www.cs.cmu.edu/~efros/courses/LBMV07/Papers/viola-cvpr-01.pdf
In addition, please see my comments on your question.
A: It looks like you may have used a linear SVM (i.e. an SVM with a linear kernel). Depending on the base learner, ADABoost can learn a non-linear boundary, so may perform better than the linear SVM if the data is not linearly separable. This of course depends on the characteristics of the dataset. See this page on wikipedia for more information about kernel methods.
