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.
K-means with centres outside the data?
machine learning;clustering;svm