Classification with sparse grids
Jochen Garcke (Uni Bonn)
We present a new approach to the classification problem arising in data
mining. It is based on the regularization network approach and uses basis
functions coming from a grid in the usually high-dimensional feature space
for the minimization process.
To cope with the curse of dimensionality, we employ sparse grids.
To be precise, we suggest to use the sparse grid combination technique
where the classification problem is discretized and solved on a certain
sequence of conventional grids with uniform mesh sizes in each coordinate
direction. The sparse grid solution is then obtained from the solutions on
these different grids by linear combination.
The method computes a nonlinear classifier but scales only linearly
with the number of instances, i.e. the amount of data to be classified.
It is therefore well suited for data mining applications where the amount
of data is very large, but where the dimension of the feature space is