Dimensionality Reduction for Function Fitting method using Kernels

I have a set of continuous noisy measurements $x_i in R^n$ with $i=1,…,N$ for which I know the value range, i.e. $x_{min} leq x_i leq x_{max}$. Corresponding to the measurements, I have a set of outputs $y_i in R^m$. To give you some numbers: $n=10$, $N=100000$ and $m=2$.
I would like to find a continuous nonlinear function such that $y approx F(x)$. Before running any interpolation method however, I realized to have a lot of redundant samples (very close to each other). I’m currently applying a binning of the samples and keeping one random sample per bin (after normalizing the data in [0,1]). The number of samples goes from 100000 to 10000 approximatively.
Question: Can someone suggest an alternative approach for removing redundant data maybe based on the distance between samples?