What is the impact of data dimensionality on computation complexity of SVM? I found on the literature that the complexity of SVM is $O(N^3)$, where $N$ is the number of training examples. If the number of dimension (e.g., $D$) does not impact the training time why it s better to reduce the dimensionality for training high-dimension dataset? Is it just to avoid overfitting?
BTW, I m using SVDD (support vector data description) from RRTools.