clm dist(1)                     USER COMMANDS                      clm dist(1)



  NAME
      clm dist - compute the distance between two or more partitions
      (clusterings).

      The distance that is computed can be any of split/join distance,
      variance of information, or Mirkin metric.

      clmdist is not in actual fact a program. This manual page documents the
      behaviour and options of the clm program when invoked in mode dist. The
      options -h, --apropos, --version, -set, --nop are accessible in all clm
      modes. They are described in the clm manual page.

  SYNOPSIS
      clm dist [options] <file name> <file name>+

      clm dist [-mode <sj|vi|mk|sc> (distance type)] [-o fname (output file)]
      [--chain (only compare consecutive clusterings)] [--sort (sort
      clusterings based on coarseness)] [-digits k (output decimals)] [-h
      (print synopsis, exit)] [--apropos (print synopsis, exit)] [--version
      (print version, exit)] <file name> <file name>+

  DESCRIPTION
      clm dist computes distances between clusterings. It can compute the
      split/join distance (described below), the variance of information
      measure, and the Mirkin metric. By default it computes the chosen
      distance for all pairs of distances in the clusterings provided.
      Clusterings must be in the mcl matrix format (cf. mcxio(5)), and are
      supplied on the command line as the names of the files in which they are
      stored.  It is possible to compare only consecutive clusterings by using
      the --chain option.

      Currently, clm dist cannot compute different distance types
      simultaneously.

      The output is linewise, each line giving information about the distance
      between a pair of clusterings. A line has the following format:

      d  d1  d2  N  v  name1  name2  [v50,v75,v90,v95,v99]

      where dT is the distance between the two clusterings, d1 is the distance
      from the first clustering to the greatest common subclustering
      (alternatively called GCS, intersection, or meet) of the two
      clusterings, d2 is similarly the distance from the second clustering to
      the GCS, N is the number of nodes in the set over which the clusterings
      are defined, name1 is the name of the file containing the first
      clustering, name2 is the name of the file containing the second
      clustering, and vXX is the number of volatile nodes at stringency factor
      0.XX (i.e. 0.5 for v50). Refer to clm vol for a definition of volatile
      node.

  OPTIONS
      -mode <sj|vi|mk> (distance type)
        Use sj for the split/join distance (described below), vi for the
        variance of information measure and mk for the Mirkin metric.

      --chain (only compare consecutive clusterings)
        This option can be used if you know that the clusterings are nested
        clusterings (or appoximately so) and ordered from coarse to fine-
        grained or vice versa. An example of this is the set of clusterings
        resulting from applying mcl with a range of inflation parameters.

      --sort (sort clusterings based on coarseness)
        This option can be useful in conjunction with the --chain option, in
        case the list of clusterings supplied is not necessarily ordered by
        granularity.

      -o fname (output file)

      -digits k (output decimals)
        The number of decimals printed when using the variance of information
        measure.

  SPLIT/JOIN DISTANCE
      For each pair of clusterings C1, C2, two numbers are given, say d1 and
      d2. Then d1 + d2 equals the number of nodes that have to be exchanged in
      order to transform any of the two clusterings into the other, and you
      can think of (d1+d2)/2N as the percentage that the two clusterings
      differ. The split/join distance has a linearity property with respect to
      the meet of C1 and C2, see below.

      The split/join distance sjd is very handy in computing the consistency
      of two or more clusterings of the same graph, or comparing clusterings
      made with different resource (but otherwise identical) parameters. The
      latter is for finding out whether you can settle for cheaper mcl
      settings, or whether you need to switch to more expensive settings. The
      former is for finding out whether clusterings are identical,
      conflicting, or whether one is (almost) a subclustering of the other -
      mostly for comparing a set of clusterings of different granularity, made
      by letting the mcl parameter -I vary.  The EXAMPLES section contains
      examples of all these clm dist uses, and the use of clm info and clm
      meet is also discussed there.

      sjd is a metric distance on the space of partitions of a set of a given
      fixed cardinality. It has the following linearity property. Let P1 and
      P2 be partitions, then

      sjd(P1, P2) = sjd(P1, D) + sjd(P2, D)

      where D (for Dutch Doorsnede) is the intersection of P1 and P2, i.e. the
      unique clustering that is both a subclustering of P1 and P2 and a
      superclustering of all other subclusterings of P1 and P2. Sloppily
      worded, D is the largest subclustering of both P1 and P2. See the
      REFERENCES section for a pointer to the technical report in which sjd
      was first defined (and in which the non-trivial triangle inequality is
      proven).

      Because it is useful to know whether one partition (or clustering) is
      almost a subclustering of the other, clm dist returns the two
      constituents sjd(P1,D) and sjd(P2,D).

      Let P1 and P2 be two clusterings of a graph of cardinality N, and
      suppose clm dist returns the integers d1 and d2. You can think of 100 *
      (d1 + d2) / N as the percentage that P1 and P2 differ.  This
      interpretation is in fact slightly conservative.  The numerator is the
      number of nodes that need to be exchanged in order to transform one into
      the other. This number may grow as large as 2*N - 2*sqrt(N), so it would
      be justified to take 50 as a scaling factor rather than 100.

      For example, if A and B are both clusterings of a graph on a set of 9058
      nodes and clm dist returns [38, 2096], this conveys that A is almost a
      subclustering of B (by splitting 38 nodes in A we obtain a clustering D
      that is a subclustering of B), and that B is much less granular than A.
      The latter is because we can obtain B from D by joining 2096 nodes in
      some way.

  EXAMPLES
      The following is an example of several mcl validation tools applied to a
      set of clusterings on a protein graph of 9058 nodes.  In the first
      experiment, six different clusterings were generated for different
      values of the inflation parameter, which was respectively set to 1.2,
      1.6, 2.0, 2.4, 2.8, and 3.2.  It should be noted that protein graphs
      seem somewhat special in that an inflation parameter setting as low as
      1.2 still produces a very acceptable clustering. The six clusterings are
      scrutinized using clm dist, clm info, and clm meet.  In the second
      experiment, four different clusterings were generated with identical
      flow (i.e. inflation) parameter, but with different resource parameters.
      clm dist is used to choose a sufficient resource level.

      High -P/-S/-R values make mcl more accurate but also more time and
      memory consuming. Run mcl with different settings for these parameters,
      holding other parameters fixed. If the expensive and supposedly more
      accurate clusterings are very similar to the clusterings resulting from
      cheaper settings, the cheaper setting is sufficient. If the distances
      between cheaper clusterings and more expensive clusterings are large,
      this is an indication that you need the expensive settings. In that
      case, you may want to increase the -P/-S/-R parameters (or simply the
      -scheme parameter) until associated clusterings at nearby resource
      levels are very similar.

      In this particular example, the validation tools do not reveal that one
      clustering in particular can be chosen as 'best', because all
      clusterings seem at least acceptable. They do aid however in showing the
      relative merits of each clusterings. The most important issue in this
      respect is cluster granularity. The table below shows the output of clm
      info.


           Efficiency  Mass frac  Area frac  Cl weight  Mx link weight
      1.2   0.42364     0.98690    0.02616    52.06002    50.82800
      1.6   0.58297     0.95441    0.01353    55.40282    50.82800
      2.0   0.63279     0.92386    0.01171    58.09409    50.82800
      2.4   0.65532     0.90702    0.01091    59.58283    50.82800
      2.8   0.66854     0.84954    0.00940    63.19183    50.82800
      3.2   0.67674     0.82275    0.00845    66.10831    50.82800

      This data shows that there is exceptionally strong cluster structure
      present in the input graph. The 1.2 clustering captures almost all edge
      mass using only 2.5 percent of 'area'. The 3.2 clustering still captures
      82 percent of the mass using less than 1 percent of area. We continue
      with looking at the mutual consistency of the six clusterings. Below is
      a table that shows all pairwise distances between the clusterings.


          |   1.6  |   2.0  |   2.4  |   2.8  |   3.2  |   3.6
      -----------------------------------------------------------.
      1.2 |2096,38 |2728,41 |3045,48 |3404,45 |3621,43 |3800, 42 |
      -----------------------------------------------------------|
      1.6 |        | 797,72 |1204,76 |1638,78 |1919,70 |2167, 69 |
      -----------------------------------------------------------|
      2.0 |        |        | 477,68 | 936,78 |1235,85 |1504, 88 |
      -----------------------------------------------------------|
      2.4 |        |        |        | 498,64 | 836,91 |1124,103 |
      -----------------------------------------------------------|
      2.8 |        |        |        |        | 384,95 | 688,119 |
      -----------------------------------------------------------|
      3.2 |        |        |        |        |        | 350,110 |
      -----------------------------------------------------------.

      The table shows that the different clusterings are pretty consistent
      with each other, because for two different clusterings it is generally
      true that one is almost a subclustering of the other. The interpretation
      for the distance between the 1.6 and the 3.2 clustering for example, is
      that by rearranging 43 nodes in the 3.2 clustering, we obtain a
      subclustering of the 1.6 clustering. The table shows that for any pair
      of clusterings, at most 119 entries need to be rearranged in order to
      make one a subclustering of the other.

      The overall consistency becomes all the more clear by looking at the
      meet of all the clusterings:


      clm meet -o meet out12 out16 out20 out24 out28 out32
      clm dist meet out12 out16 out20 out24 out28 out32

      results in the following distances between the respective clusterings
      and their meet.


          |   1.2  |    1.6 |  2.0   |   2.4  |  2.8   |  3.2    |
      -------------- --------------------------------------------.
      meet|  0,3663|  0,1972| 0,1321 |  0,958 | 0,559  | 0,283   |
      -------------- --------------------------------------------.

      This shows that by rearranging only 283 nodes in the 3.2 clustering, one
      obtains a subclustering of all other clusterings.

      In the last experiment, mcl was run with inflation parameter 1.4, for
      each of the four different preset pruning schemes k=1,2,3,4.  The clm
      dist distances between the different clusterings are shown below.


          |  k=2   |   k=3  |   k=4  |
      -------------------------------.
      k=1 |  17,17 |  16,16 |  16,16 |
      -------------------------------.
      k=2 |        |   3,3  |   5,5  |
      -------------------------------.
      k=3 |        |        |   4,4  |
      -------------------------------.

      This example is a little boring in that the cheapest scheme seems
      adequate.  If anything, the gaps between the k=1 scheme and the rest are
      a little larger than the three gaps between the k=2, k=3, and k=4
      clusterings. Had all distances been much larger, then such an
      observation would be reason to choose the k=2 setting.

      Note that you need not feel uncomfortable with the clusterings still
      being different at high resource levels, if ever so slightly.  In all
      likelihood, there are anyway nodes which are not in any core of
      attraction, and that are on the boundary between two or more
      clusterings.  They may go one way or another, and these are the nodes
      which will go different ways even at high resource levels.  Such nodes
      may be stable in clusterings obtained for lower inflation values (i.e.
      coarser clusterings), in which the different clusters to which they are
      attracted are merged.

  AUTHOR
      Stijn van Dongen.

  SEE ALSO
      mclfamily(7) for an overview of all the documentation and the utilities
      in the mcl family.

  REFERENCES
      Stijn van Dongen. Performance criteria for graph clustering and Markov
      cluster experiments. Technical Report INS-R0012, National Research
      Institute for Mathematics and Computer Science in the Netherlands,
      Amsterdam, May 2000.
      http://www.cwi.nl/ftp/CWIreports/INS/INS-R0012.ps.Z

      Marina Meila. Comparing Clusterings - An Axiomatic View.  In Proceedings
      of the 22nd International Conference on Machine Learning, Bonn, Germany,
      2005.

      Marina Meila. Comparing Clusterings, UW Statistics Technical Report 418.
      http://www.stat.washington.edu/www/research/reports/2002/tr418.ps



  clm dist 1.008, 09-308            4 Nov 2009                       clm dist(1)
