Most machine learning methodologies do not directly vote on class membership. That is, when you ask most non-svm machine learning models for a prediction, they do not respond "this observation is an observation of class 0", or "this observation is an observation of class 1." Instead, they report a score, and the user may choose to create a classification rule by applying a threshold to the score.
Some models go a bit further and attempt to produce a score that is also a statistical estimate of the conditional probability:
$$ P(Y = 1 \mid X) $$
what is the actual meaning of 'no direct probabilistic interpretation?
An SVM makes no attempt to estimate the conditional probability $P(Y = 1 \mid X)$. It only attempts to produce class assignments.
and what other method provide the 'probabilistic interpretation'?
Logistic regression, gradient boosted classification, and neural networks have this property, and to a lesser extend so do both classification trees, and random forests.
why this characteristic is disadvantages of svm?
Models that produce an estimate of $P(Y = 1 \mid X)$ are useful in a wider set of circumstances than those that do not. For example, if you have a measurement that depends on $Y$ is some way, say:
$$ \text{Profit} = f(Y) $$
Then knowing the conditional probability $P(Y = 1 \mid X)$ is an important step to computing, say, the expected profit for a given set of circumstances $X$:
$$ E \left[ \text{Profit} \mid X \right] = f(0) P(Y = 0 \mid X) + f(1) P(Y = 1 \mid X) $$
If you only have a model that make as good guess at the class membership, you can't do this.
for my thought this will increase the speed since it does not have to deal with the probabilistic interpretation for the group member.
Maybe, maybe not. Even if that was so, model fitting speed is usually a secondary concern to model suitability. Since there are so many situations where having a handle on some probabilities is important, it very often outweighs any advantages of an SVM.
