Basic Cell

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Definition (Basic cell)

The set $R_{0}=\{ \mathbf{x}\in\mathbb{R}^{k}:\lVert \mathbf{x} \rVert \le \lVert \mathbf{x}-\mathbf{y} \rVert, \mathbf{y}\in\Lambda \}$ is the basic cell of the lattice $\Lambda$ .

Proposition

Let $Q_{\Lambda}$ be a LVQ. The cell $R_{i}$ is the $R_{0}$ shifted by $\mathbf{y}_{i}$ : $R_{i}=R_{0}+\mathbf{y}_{i}=\{ \mathbf{x}+\mathbf{y}_{i}:\mathbf{x}\in R_{0}\}$

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High-Resolution Conditions LVQ