!=9@      !"#$%&'()*+,-./0123456789:;<=>?None clustering$O(1) Return the size of a dendrogram  clusteringcompute distance matrix  clustering#compute distance matrix in parallel   (c) 2015 Kai ZhangMITkai@kzhang.org experimentalportableNonej clustering nearest neighbor chain algorithm clustering^all update functions perform destructive updates, and hence should not be called by end userssingle linkage update formula clusteringcomplete linkage update formula clusteringaverage linkage update formula clusteringweighted linkage update formula clusteringward linkage update formula@ clusteringdistance matrix clusteringquery clustering;this would be selected if it achieves the minimal distance(c) 2015 Kai ZhangMITkai@kzhang.org experimentalportableNone> clustering*Different hierarchical clustering schemes. clustering>O(n^2) Single linkage, $d(A,B) = min_{a in A, b in B} d(a,b)$. clustering@O(n^2) Complete linkage, $d(A,B) = max_{a in A, b in B} d(a,b)$. clusteringYO(n^2) Average linkage or UPGMA, $d(A,B) = frac{sum_{a in A}sum_{b in B}d(a,b)}{|A||B|}$. clusteringO(n^2) Weighted linkage. clusteringO(n^2) Ward's method. clustering)O(n^3) Centroid linkage, not implemented. clustering'O(n^3) Median linkage, not implemented.  clustering Perform hierarchical clustering.! clustering4Normalize the tree heights so that the highest is 1." clustering!Cut a dendrogram at given height.# clustering1Return the elements of a dendrogram in pre-order.$ clustering%2-dimensional drawing of a dendrogram% clustering.Compute euclidean distance between two points.& clusteringHamming distance. !"#$%& !"#$%&None>"EA clusteringRGenerate N non-duplicated uniformly distributed random variables in a given range.' clusteringThe number of clusters clustering Input data clusteringFeature extraction function( clusteringThe number of clusters clustering Input data clusteringFeature extraction function'()'()(c) 2015 Kai ZhangMITkai@kzhang.org experimentalportableNone0( * clustering Different initialization methods+ clusteringpThe Forgy method randomly chooses k unique observations from the data set and uses these as the initial means., clusteringK-means++ algorithm.- clusteringProvide a set of k centroids. clusteringResults from running kmeans0 clusteringYA vector of integers (0 ~ k-1) indicating the cluster to which each point is allocated.1 clusteringA matrix of cluster centers.3 clusteringthe sum of squared error (SSE)7 clustering!Seed for random number generation8 clustering/Wether to return clusters, may use a lot memory9 clusteringMaximum iteration: clusteringDefault options. > defaultKMeansOpts = KMeansOpts > { kmeansMethod = KMeansPP > , kmeansSeed = U.fromList [1,2,3,4,5,6,7] > , kmeansClusters = True > , kmeansMaxIter = 10 > }*,+-./1023456789:456789:./1023*,+-None>8i< clusteringPerform K-means clustering= clustering?Perform K-means clustering, using a feature extraction functionB clusteringK-means algorithm> clustering.Assign data to clusters based on KMeans result< clusteringThe number of clusters clustering%Input data stored as rows in a matrix= clusteringThe number of clusters clustering Input dataB clusteringInitial set of k centroids clustering Max inter clustering Input data clusteringFeature extraction function*,+-./1023456789:<=>./1023456789:<=*,+->None>9? clusteringrearrange the rows of a matrix??C      !"#$%&'()*+,-./01234556789::;<=>?@ABCDEFGH'clustering-0.4.1-9VL6Gr3pDvUKFxRVOtqQTo AI.Clustering.Hierarchical.Types#AI.Clustering.Hierarchical.InternalAI.Clustering.HierarchicalAI.Clustering.KMeans.InternalAI.Clustering.KMeans.TypesAI.Clustering.KMeansAI.Clustering.Utils DistanceMat DendrogramLeafBranchSizeDistFnDistancesize!idx computeDists computeDists'$fFunctorDendrogram$fBinaryDendrogram$fShowDendrogram$fEqDendrogram$fShowDistanceMatnnChainsinglecompleteaverageweightedwardLinkageSingleCompleteAverageWeightedWardCentroidMedianhclust normalizecutAtflattendrawDendrogram euclideanhammingforgykmeansPP sumSquaresMethodForgyKMeansPPCentersKMeans membershipcentersclusterssse KMeansOpts kmeansMethod kmeansSeedkmeansClusters kmeansMaxIterdefaultKMeansOpts $fShowKMeanskmeanskmeansBydecodeorderBynearestNeighbor uniformRNkmeans'