Metric

A metric $ d(\mathbf{x,y})$, needs to satisfy the following conditions:

  1. Symmetric: $ d(\mathbf{x,y})=d(\mathbf{y,x})$
  2. Non-negative: $ d(\mathbf{x,y})\geq 0$ with equality iff $ \mathbf{x=y}$
  3. Triangle inequality: $ d(\mathbf{x,y}) \leq d(\mathbf{x,z})
+d(\mathbf{z,y})$

In SciCraft you can choose between $ 9$ different metrices, and you also have the choice of using your own metric. This requires that the input data matrix $ \mathbf{X} \in \mathbb{R}^{n \times p}$ can give rise to a distance matrix, i.e a matrix $ \mathbf{D}$ with dimensions $ n \times n$ if you are clustering over the rows of the matrix, or $ p
\times p$ if you are clustering over the columns.



Bjørn Kåre Alsberg 2006-04-06