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Basic Cell

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Definition
InfoTheory

The set R0={x∈Rk:∄xāˆ„ā‰¤āˆ„xāˆ’y∄,yāˆˆĪ›}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 Ī›\Lambda.

Let QĪ›Q_{\Lambda} be a LVQ. The cell RiR_{i} is the R0R_{0} shifted by yi\mathbf{y}_{i}: Ri=R0+yi={x+yi:x∈R0}R_{i}=R_{0}+\mathbf{y}_{i}=\{ \mathbf{x}+\mathbf{y}_{i}:\mathbf{x}\in R_{0}\}

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