<filename>Report/topo.tex
\subsection{Method Selection}

Before establishing models for prediction, we have to choose what algorithms to use in analyses.

Besides common considerations, what we especially take into account is the global topology of the attribute space: because of the attributes WDF2 and WDF5, the space is in fact homeomorphic to $\mathbb R^{p-2}\times \mathbb S^1\times\mathbb S^1$ instead of $\mathbb R^p$. In this case, a hyperplane (or, more generally, an \emph{open} hypersurface) may not be able to seperate it into two \emph{disconnected} subspace.

As the result, we exclude LDA, QDA and several other well-developed classification methods because an open hypersurface is always needed for these. Instead, we tend to apply methods that do not heavily depend on global topology (random forest, $k$-NN) or that classify with a \emph{closed} hypersurface (kernel SVM).