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The classification rate of the resulting classifier applied to the full data set if
67.91 % and thus almost the same as that obtained by the offline algorithm.
Concerning the total time of 185 s, the adaptive version is even faster than the
offline one. However, when we further reduce the block size, the situation is
changing. For the block size
M ΒΌ
1,000, the run time of the adaptive version
increases to 443 s suffering from the overhead of each update.
7.4 Summary
In this chapter we have studied sparse grid approximation for scoring, i.e., classi-
fication and regression. We first demonstrated how scoring can be efficiently used
for generating recommendations.
We discussed shortcomings of current classification methods. We then intro-
duced sparse grids and demonstrated how they can overcome many of these
problems. Especially, sparse grids scale linearly with the number of data points
and thus can handle huge data sets. Data adaptivity can directly be applied to sparse
grid algorithms. Another advantage is that sparse grid classifiers can be interpreted
and manipulated in a spectral sense as it is known from signal processing. More-
over, sparse grids can in general be applied to wide classes of operator equations. In
summary, sparse grids represent a new quality of data analysis based on hierarchi-
cal decomposition of the attribute space.
On the other hand, sparse grids are very complex in theory and application.
There exist many versions of sparse grid techniques. Much further research is
required to extend the classical concepts of the numerical analysis of PDEs to the
high-dimensional case in order to use them for sparse grids.
