# How to ensure smoothness in support vector regression

Let's say I have a set $$I$$ of input parameters, a set $$J$$ of output parameters, and a set $$N$$ of experiments that relates $$I$$ to $$J$$ for each $$n\in N$$.

When I train the algorithm how can I ensure that there is a certain smoothness in the solution given? Let me explain what I mean by that with an example: if for $$i_1,i_2 \in I$$, I have the corresponding output $$f(i_1)$$ and $$f(i_2)$$, and if I join $$i_1$$ and $$i_2$$ by a straight line in my multi-dimensional domain I need the function $$f(i)$$ to behave smoothly or 'nicely' between these values, for instance monotonically.

What I want to avoid in my function is having a 'spiked' surface that for a certain element $$j\in J$$ has several $$i^* \in I$$ such that $$f(i^*)=j$$ and these $$i^*$$ are distributed randomly on the domain I.

I think that my options are imposing that the training algorithm takes this into account as it reads the sample data, or creating first my predictive function $$f$$ and then use a second algorithm to smooth it, trying to maintain its predictive capabilities.

Any opinion on how to approach or rethink this is welcomed.