úÎüì     (c) 2015 Kai ZhangMITkai@kzhang.org experimentalportableNone32Lloyd's algorithm, also known as K-means algorithm2Lloyd's algorithm, also known as K-means algorithmnThe Forgy method randomly chooses k unique observations from the data set and uses these as the initial meansnumber of clusterseach row represents a pointmembership vectorinitial set of k centroidseach row represents a pointmembership vector and centroidsNone $O(1) Return the size of a dendrogram       None nearest neighbor chain algorithm ^all update functions perform destructive updates, and hence should not be called by end userssingle linkage update formula!complete linkage update formula"average linkage update formula#weighted linkage update formula$ward linkage update formula %&' !"#$ !"#$ %&' !"#$(c) 2015 Kai ZhangMITkai@kzhang.org experimentalportableNone3 *Different hierarchical clustering schemes.'O(n^3) Median linkage, not implemented.)O(n^3) Centroid linkage, not implemented.O(n^2) Ward's method.O(n^2) Weighted linkage.YO(n^2) Average linkage or UPGMA, $d(A,B) = frac{sum_{a in A}sum_{b in B}d(a,b)}{|A||B|}$.@O(n^2) Complete linkage, $d(A,B) = max_{a in A, b in B} d(a,b)$.>O(n^2) Single linkage, $d(A,B) = min_{a in A, b in B} d(a,b)$. Perform hierarchical clustering.!Cut a dendrogram at given height.1Return the elements of a dendrogram in pre-order.%2-dimensional drawing of a dendrogram-compute euclidean distance between two points  (      !"#$%&'()*+,clustering-0.1.1AI.Clustering.KMeans AI.Clustering.Hierarchical.TypesAI.Clustering.Hierarchical#AI.Clustering.Hierarchical.Internalkmeans kmeansWith forgyMethod DistanceMat DendrogramBranchLeafSizeDistFnDistancesize!idxMetricMedianCentroidWardWeightedAverageCompleteSinglehclustcutAtflattendrawDendrogram computeDists euclideansample$fFunctorDendrogram$fBinaryDendrogramnnChainsinglecompleteaverageweightedward DistUpdateFn ActiveNodeSetnearestNeighbor