K-means with centres outside the data? Say we want to split a cube in $\mathbb{R}^{64}$ into 10 pieces.
NN, nearest-neighbor or Voronoi splits,
take 10 cluster centres $c_0, \ldots, c_9$ in the cube,
e.g. from K-means,
then classify a new data point $x$ by finding its nearest centre:
$$\text{NN}( x, c_0, \ldots, c_9 ) \equiv \text{argmin}_j\ \| x - c_j \| \text.$$

Kmeans centres are averages of data points, so fall near the data.
Could allowing centres outside the data give better splits ?
Is there a variant of Kmeans which converges e.g. to SVM weights,
viewed as points in the data space ?

As Suresh Venkat points out, "better" splitting,
better classification, is hard to define.
Since k-means minimizes the within-cluster sum of squares, the cluster centers will always be the mean of the points within that cluster. If you use a different criterion, you are basically using a different method than k-means.