hopach                package:hopach                R Documentation

_f_u_n_c_t_i_o_n _t_o _p_e_r_f_o_r_m _H_O_P_A_C_H _h_i_e_r_a_r_c_h_i_c_a_l _c_l_u_s_t_e_r_i_n_g

_D_e_s_c_r_i_p_t_i_o_n:

     The Hierarchical Ordered Partitioning and Collapsing Hybrid
     (HOPACH) clustering algorithm builds a hierarchical tree by
     recursively  partitioning a data set (e.g., gene expression
     measurements) with the PAM algorithm, while ordering and possibly
     collapsing clusters at each level. The algorithm uses the
     Mean/Median Split Silhouette (MSS) criteria to identify the level
     of the tree with maximally homogeneous clusters. It also runs the
     tree down to produce a final ordered list of the elements.

_U_s_a_g_e:

     hopach(data, dmat = NULL, d = "cosangle", clusters = "best", K = 15, 
     kmax = 9, khigh = 9, coll = "seq", newmed = "medsil", mss = "med", 
     impr = 0, initord = "co", ord = "own")

_A_r_g_u_m_e_n_t_s:

    data: data matrix, data frame or exprSet of gene expression
          measurements. Typically, each column corresponds to an array,
          and each row corresponds to a gene. For clustering arrays,
          the arrays appear in the rows and the genes in the columns.
          All values must be numeric. Missing values are ignored.

    dmat: matrix of pair wise distances between all genes (arrays). All
          values must be numeric, and missing values are not allowed.
          If NULL, this matrix is computed  using the metric specified
          by 'd'. If a matrix is provided, the user is responsible for
          ensuring that the metric used agrees with 'd'.

       d: character string specifying the metric to be used for
          calculating  dissimilarities between variables. The currently
          available options are  "cosangle" (cosine angle or uncentered
          correlation distance), "abscosangle"  (absolute cosine angle
          or absolute uncentered correlation distance),  "euclid"
          (Euclidean distance), "abseuclid" (absolute Euclidean
          distance), "cor" (correlation distance), and "abscor"
          (absolute correlation distance). Advanced users can write
          their own distance functions and add these to the functions
          'distancematrix()' and 'distancevector()'.

clusters: character string specifying if clusters are to be identified
          as the level of the tree with the minimum mean/median split 
          silhouette (MSS) ("best"), the first level of the tree below
          which MSS  increases ("greedy"), or not at all ("none").

       K: positive integer specifying the maximum number of levels in
          the tree.  Must be 15 or less, due to computational
          limitations (overflow).

    kmax: integer between 1 and 9 specifying the maximum number of
          children at each node in the tree.

   khigh: integer between 1 and 9 specifying the maximum number of
          children at each node in the tree when computing MSS. Can be
          different from kmax,  though typically these are the same
          value.

    coll: character string specifying how collapsing steps are
          performed at each  level. The options are "seq" (begin with
          the closest pair of clusters and collapse pairs sequentially
          as long as MSS decreases) and "all" (consider all pairs of
          clusters and collapse any that decrease MSS).

  newmed: character string specifying how to choose a medoid for the
          new cluster after collapsing a pair of clusters. The options
          are "medsil"  (maximizer of medoid based silhouette, i.e.:
          (a-b)/max(a,b), where  a is distance to medoid and b is
          distance to next closest medoid), "nn" (nearest neighbor of
          mean of two collapsed cluster medoids weighted by cluster
          size), "uwnn" (unweighted version of nearest neighbor, i.e. 
          each cluster - rather than each element - gets equal weight),
          "center"  (minimizer of average distance to the medoid).

     mss: character vector specifying what criteria function to use.
          The options are "med" (median split silhouette) or "mean"
          (mean split silhouette). See details for definition of split
          silhouettes. The MSS criteria is used to determine the number
          of children at each node, to decide what collapsing  should
          be performed at each level, and to determine the main
          clusters.

    impr: number between 0 and 1 specifying the margin of improvement
          in MSS  needed to accept a collapse step. If (MSS.before -
          MSS.after)/MSS.before  is less than 'impr', then the collapse
          is not performed.

 initord: character string specifying how to order the clusters in the
          initial level of the tree. The options are "co" (maximize
          correlation ordering, i.e.  the empirical correlation between
          distance apart in the ordering and distance between the
          cluster medoids) or "clust" (apply hopach with binary splits
          to  the cluster medoids and use the final level of that tree
          as the ordering). In subsequent levels, the clusters are
          ordered relative to the previous level, so this initial
          ordering determines the overall structure of the tree.

     ord: character string specifying how to order the elements within
          clusters. This method is used to create an ordering of all
          elements at the level of the tree  corresponding to the main
          clusters. The options are "own" (order based on distance from
          cluster medoid with medoid first, i.e. leftmost), "neighbor"
          (order based on distance to the medoid of the next cluster to
          the right), or "co" (maximize correlation ordering - can be
          slow for large clusters!).

_D_e_t_a_i_l_s:

     The HOPACH hierarchical clustering algorithm is a hybrid between
     an agglomerative (bottom up) and a divisive (top down) algorithm.
     The HOPACH tree is built from the root node (all  elements) down
     to the leaf nodes, but at each level collapsing steps are used to
     unite similar clusters. In addition, the clusters in each level
     are ordered with a deterministic algorithm based on the same
     distance metric that is used in the clustering. In this way, the
     ordering produced in the final level of the tree does not depend
     on the order of the data in the original data set (as can be the
     case with algorithms that have a random  component in their
     ordering methods). Unlike other hierarchical clustering methods,
     HOPACH  builds a tree of clusters in which the nodes need not be
     binary, i.e. there can be more than two children at each split.
     The divisive steps of the HOPACH algorithm are performed using the
     PAM algorithm described in chapter 2 of Kaufman and Rousseeuw
     (1990) and the R package 'cluster'.

     The Median (or Mean) Split Silhouette (MSS) criteria is used by
     HOPACH to (i) determine  the optimal number of children at each
     node, (ii) decide which pairs of clusters to  collapse at each
     level, and (iii) identify the first level of the tree with
     maximally homogeneous clusters. In each case, the goal is to
     minimize MSS, which is a measure of cluster heterogeneity
     described in http://www.bepress.com/ucbbiostat/paper107/. 

     Note that the correlation and cosine-angle distances (plus their 
     absolute values) used for clustering in hopach are the square
     roots  of the usual distances. Typically, this transformation
     makes the  dissimilarity correspond more closely with the norm.
     Also, the  Euclidean distance is standardized by the sample size,
     so that the values  produced are equal to the values from the
     dist() function divided by  sqrt(n). See ? distancematrix().

_V_a_l_u_e:

     A list with the following components:

clustering: the partitioning or 'main clusters' with the following
          components

          'k' is an integer specifying the number of clusters
          identified by minimizing MSS.

          'medoids' is a vector indicating the rows of 'data' that are
          the 'k' cluster medoids, i.e. profiles (or centroids) for
          each cluster.

          'sizes' is a vector containing the 'k' cluster sizes.

          'labels' is a vector containing the main cluster labels for
          every variable. Each label consists of one digit per level of
          the tree (up to the level identified as the main clusters).
          The digit (1-9) indicates which child cluster the variable
          was in at that level. For example, '124' means the fist
          (leftmost in the tree) cluster in level 1, the second child
          of cluster '1' in level 2, and the fourth  child of cluster
          '12' in level 3. These can be mapped to the numbers 1:k for
          simplicity, though the tree structure and relationship
          amongst the clusters is then lost, e.g. 1211 is closer to
          1212 than to 1221.

          'order' is a vector containing the ordering of variables
          within the main clusters. The clusters are ordered
          deterministically as the tree is built. The elements within
          each of the main clusters are ordered with the method
          determined by the value of 'ord': "own" (relative to own
          medoid), "neighbor" (relative to next medoid to the right),
          or "co" (maximize correlation ordering). 

   final: the final level of the hierarchical tree with the following
          components

          'labels' is a vector containing the final labels for every
          variable. Each label consists of one digit per level of the
          tree (up to the final level), and the  format for the labels
          is the same as for the clustering labels. The final labels
          contain the entire history of the tree. In fact, internal
          level 'n' can be  reproduced by truncating the final labels
          to 'n' digits. Ordering the final  labels produces the final
          ordering (final level of the tree), while ordering internal
          level labels produces an ordering of the clusters at that
          level.

          'order' is a vector containing the ordering of variables at
          the final level of the tree. Essentially, this is the numeric
          ordering of the final labels. Due to the limit on the largest
          possible integer (overflow), the final labels can have  at
          most 16 digits, i.e. the tree can have at most 16 levels. For
          large data sets, this may not be enough partitioning steps to
          result in final nodes (leaves) with only one variable each.
          Furthermore, PAM can not partition a node of size 3 or  less,
          so that leaves may contain 2 or 3 variables regardless of the
          number of levels in the tree. Hence, the final ordering of
          variables is completed by ordering the variables in any leaf
          of size 2 or larger with the method determined by the value
          of 'ord': "own" (relative to own medoid), "neighbor"
          (relative  to next medoid to the right), or "co" (maximize
          correlation ordering).

          'medoids' is a matrix containing the labels and corresponding
          medoids for each internal node and leaf of the tree. The
          number of digits in the label indicates the level for that
          node. The medoid refers to a row of 'data' 

    call: the matched 'call' generating the HOPACH output

  metric: the distance metric

_N_o_t_e:

     Thank you to Karen Vranizan <vranizan@uclink.berkeley.edu> for her
     input

_A_u_t_h_o_r(_s):

     Katherine S. Pollard <kpollard@soe.ucsc.edu> and Mark J. van der
     Laan <laan@stat.berkeley.edu>

_R_e_f_e_r_e_n_c_e_s:

     van der Laan, M.J. and Pollard, K.S. A new algorithm for hybrid
     hierarchical clustering with visualization and the bootstrap.
     Journal of Statistical Planning and Inference, 2003, 117, pp.
     275-303.

     <URL:
     http://www.stat.berkeley.edu/~laan/Research/Research_subpages/Papers/hopach.pdf>

     <URL: http://www.bepress.com/ucbbiostat/paper107/>

     <URL:
     http://www.stat.berkeley.edu/~laan/Research/Research_subpages/Papers/jsmpaper.pdf>

     Kaufman, L. and Rousseeuw, P.J. (1990). Finding Groups in Data: An
     Introduction to Cluster Analysis. Wiley, New York.

_S_e_e _A_l_s_o:

     'distancematrix', 'labelstomss', 'boothopach', 'pam', 'makeoutput'

_E_x_a_m_p_l_e_s:

     #25 variables from two groups with 3 observations per variable
     mydata<-rbind(cbind(rnorm(10,0,0.5),rnorm(10,0,0.5),rnorm(10,0,0.5)),cbind(rnorm(15,5,0.5),rnorm(15,5,0.5),rnorm(15,5,0.5)))
     dimnames(mydata)<-list(paste("Var",1:25,sep=""),paste("Exp",1:3,sep=""))
     mydist<-distancematrix(mydata,d="cosangle") #compute the distance matrix.

     #clusters and final tree
     clustresult<-hopach(mydata,dmat=mydist)
     clustresult$clustering$k #number of clusters.
     dimnames(mydata)[[1]][clustresult$clustering$medoids] #medoids of clusters.
     table(clustresult$clustering$labels) #equal to clustresult$clustering$sizes.

     #faster, sometimes fewer clusters
     greedyresult<-hopach(mydata,clusters="greedy",dmat=mydist) 

     #only get the final ordering (no partitioning into clusters)
     orderonly<-hopach(mydata,clusters="none",dmat=mydist)

     #cluster the columns (rather than rows)
     colresult<-hopach(t(mydata),dmat=distancematrix(t(mydata),d="euclid"))

