Or the algorithm which can assess the
"goodness" of the clustering also
based on the distance matrix?
KNN should be useful in assessing the “goodness” of a clustering assignment. Here's how:
Given a distance matrix with each point labeled according to the cluster it belongs to (its “cluster label”):
- Test the cluster label of each point against the cluster labels implied from k-nearest neighbors classification
- If the k-nearest neighbors imply an alternative cluster, that classified point lowers the overall “goodness” rating of the cluster
- Sum up the “goodness rating” contributions from each one of your pixels to get a total “goodness rating” for the whole cluster
Unlike k-means cluster analysis, your algorithm will return information about poorly categorized points. You can use that information to reassign certain points to a new cluster thereby improving the overall "goodness" of your clustering.
Since the algorithm knows nothing about the placement of the centroids of the clusters and hence, nothing about the global cluster density, the only way to insure clusters that are both locally and globally dense would be to run the algorithm for a range of k values and finding an arrangement that maximizes the goodness over the range of k values.
For a significant amount of points, you'll probably need to optimize this algorithm; possibly with a hash-table to keep track of the the nearest points relative to each point. Otherwise this algorithm will take quite awhile to compute.