"Perhaps the biggest limitation of the support vector approach lies in choice of the kernel."
"A second limitation is speed and size, both in training and testing."
"Discete data presents another problem..."
"...the optimal design for multiclass SVM classifiers is a further area for research."
"Although SVMs have good generalization performance, they can be abysmally slow in test phase, a problem addressed in (Burges, 1996; Osuna and Girosi, 1998)."
"Besides the advantages of SVMs - from a practical point of view - they have some drawbacks. An important practical question that is not entirely solved, is the selection of the kernel function parameters - for Gaussian kernels the width parameter [sigma] - and the value of [epsilon] in the [epsilon]-insensitive loss function...[more]"
Horváth (2003) in Suykens et al.
"However, from a practical point of view perhaps the most serious problem with SVMs is the high algorithmic complexity and extensive memory requirements of the required quadratic programming in large-scale tasks."
Horváth (2003) in Suykens et al. p 392