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<title>
The clmformat manual
</title>
</head>
<body>
<p style="text-align:right">
6 Sep 2004
<a class="local" href="clmformat.ps"><b>clmformat</b></a>
1.004, 04-250
</p>
<div style="margin-top:$margintopem">
<table
cellspacing="0" border=0
cellpadding="0" summary="itemize">
<tr>
<td width=48 valign="top" align="left">
2.
</td>
<td width=8> </td>
<td><div style="text-align:justify">
<a class="intern" href="#synopsis">SYNOPSIS</a>
</div></td>
</tr>
<tr>
<td width=48 valign="top" align="left">
3.
</td>
<td width=8> </td>
<td><div style="text-align:justify">
<a class="intern" href="#description">DESCRIPTION</a>
</div></td>
</tr>
<tr>
<td width=48 valign="top" align="left">
4.
</td>
<td width=8> </td>
<td><div style="text-align:justify">
<a class="intern" href="#options">OPTIONS</a>
</div></td>
</tr>
<tr>
<td width=48 valign="top" align="left">
5.
</td>
<td width=8> </td>
<td><div style="text-align:justify">
<a class="intern" href="#xpl">OUTPUT EXPLAINED</a>
</div></td>
</tr>
<tr>
<td width=48 valign="top" align="left">
6.
</td>
<td width=8> </td>
<td><div style="text-align:justify">
<a class="intern" href="#author">AUTHOR</a>
</div></td>
</tr>
<tr>
<td width=48 valign="top" align="left">
7.
</td>
<td width=8> </td>
<td><div style="text-align:justify">
<a class="intern" href="#references">REFERENCES</a>
</div></td>
</tr>
<tr>
<td width=48 valign="top" align="left">
8.
</td>
<td width=8> </td>
<td><div style="text-align:justify">
<a class="intern" href="#seealso">SEE ALSO</a>
</div></td>
</tr>
</table>
</div>
<a name="name"></a>
<h2>NAME</h2>
<p style="text-align:justify">
clmformat - display cluster results in readable form
<p style="text-align:justify">
(optionally with labels and/or cohesion and stickiness measures
attached).
<p style="text-align:justify">
Unless used with the -dump option,
<b>clmformat</b> depends on the presence of the macro processor <b>zoem</b>, as
described further below.
<a name="synopsis"></a>
<h2>SYNOPSIS</h2>
<p style="text-align:justify">
<b>clmformat</b>
<a class="intern" href="#opt-icl"><b>-icl</b> fname (<i>input cluster file</i>)</a>
<a class="intern" href="#opt-dump"><b>-dump</b> fname (<i>write dump to file</i>)</a>
<a class="intern" href="#opt-tab"><b>[-tab</b> fname (<i>read tab file</i>)<b>]</b></a>
<p style="text-align:justify">
The clustering in file <b>fname</b> should be in mcl matrix format - mcl
generates clusters in this format. This will create a dump where each line
contains a cluster in the form of tab-separated indices, or tab-separated
labels in case the <b>-tab</b> option is used. This dump is easy to parse
with a simple or even quick-and-dirty script.
<p style="text-align:justify">
<b>clmformat</b>
<a class="intern" href="#opt-icl"><b>-icl</b> fname (<i>input cluster file</i>)</a>
<a class="intern" href="#opt-imx"><b>-imx</b> fname (<i>input matrix/graph file</i>)</a>
<a class="intern" href="#opt-tab"><b>[-tab</b> fname (<i>read tab file</i>)<b>]</b></a>
<a class="intern" href="#opt-dir"><b>[-dir</b> dirname (<i>write results to directory</i>)<b>]</b></a>
<a class="intern" href="#opt-zmm"><b>[-zmm</b> fname (<i>assume macro definitions are in fname</i>)<b>]</b></a>
<a class="intern" href="#opt-fmt"><b>[-fmt</b> fname (<i>write to encoding file fname</i>)<b>]</b></a>
<p style="text-align:justify">
<b>clmformat</b>
<a class="intern" href="#opt-icl"><b>-icl</b> fname (<i>input cluster file</i>)</a>
<a class="intern" href="#opt-imx"><b>-imx</b> fname (<i>input matrix/graph file</i>)</a>
<a class="intern" href="#opt-tab"><b>[-tab</b> fname (<i>read tab file</i>)<b>]</b></a>
<a class="intern" href="#opt-dir"><b>[-dir</b> dirname (<i>write results to directory</i>)<b>]</b></a>
<a class="intern" href="#opt-zmm"><b>[-zmm</b> fname (<i>assume macro definitions are in fname</i>)<b>]</b></a>
<a class="intern" href="#opt-fmt"><b>[-fmt</b> fname (<i>write to encoding file fname</i>)<b>]</b></a>
<a class="intern" href="#opt-h"><b>[-h</b> (<i>synopsis</i>)<b>]</b></a>
<a class="intern" href="#opt-dump"><b>[-dump</b> fname (<i>write dump to file</i>)<b>]</b></a>
<a class="intern" href="#opt--dump-pairs"><b>[--dump-pairs</b> (<i>write cluster/node pair per line</i>)<b>]</b></a>
<a class="intern" href="#opt-dump-node-sep"><b>[-dump-node-sep</b> str (<i>separate entries with str</i>)<b>]</b></a>
<a class="intern" href="#opt-pi"><b>[-pi</b> num (<i>apply pre-inflation to matrix</i>)<b>]</b></a>
<a class="intern" href="#opt-infix"><b>[-infix</b> str (<i>use after base name/directory</i>)<b>]</b></a>
<a class="intern" href="#opt-lump-count"><b>[-lump-count</b> n (<i>node threshold</i>)<b>]</b></a>
<a class="intern" href="#opt-nsm"><b>[-nsm</b> fname (<i>output node stickiness file</i>)<b>]</b></a>
<a class="intern" href="#opt-ccm"><b>[-ccm</b> fname (<i>output cluster cohesion file</i>)<b>]</b></a>
<a class="intern" href="#opt--split"><b>[--split</b> (<i>prepare output for csplit usage</i>)<b>]</b></a>
<a class="intern" href="#opt--adapt"><b>[--adapt</b> (<i>allow domain mismatch</i>)<b>]</b></a>
<a class="intern" href="#opt--version"><b>[--version</b> (<i>print version</i>)<b>]</b></a>
<a class="intern" href="#opt--subgraph"><b>[--subgraph</b> (<i>take subgraph with --adapt</i>)<b>]</b></a>
<p style="text-align:justify">
<b>clmformat</b> generates a logical description of the to-be-formatted content in
a very small vocabulary of clmformat-specific zoem macros. The appearance
of the output can be easily changed by adapting a zoem macro definition file
(also output by clmformat) that is used by the zoem interpreter to interpret
the logical elements.
<p style="text-align:justify">
The output format is apt to change over subsequent releases, as a result of
user feedback. Such changes will most likely be confined to the zoem macro
definition file.
<p style="text-align:justify">
The OUTPUT EXPLAINED section further below is likely to be of interest.
<a name="description"></a>
<h2>DESCRIPTION</h2>
<p style="text-align:justify">
The primary function of <b>clmformat</b> is to display cluster results and
associated confidence measures in a readable form, by listing clusters in
terms of the labels associated with the indices that are used in the mcl
matrix. The labels must be stored in a so called <i>tab</i> file; see the
<a class="intern" href="#opt-tab"><b>-tab</b></a> option for more information.
<p style="text-align:justify">
<b>NOTE</b>
<br>
<b>clmformat</b> output is in the form of <i>zoem</i> macros.
You need to have zoem installed in your system if you want clmformat
to be of use. Zoem will not be necessary if you are using
the <b>-dump</b> option.
<p style="text-align:justify">
The <a class="intern" href="#opt-imx"><b>-imx</b> <i>mx</i></a> option is required
unless the <b>-dump</b> option is used. The latter option
results in special behaviour described under the
<a class="intern" href="#opt-dump"><b>-dump</b> <i>fname</i></a> entry.
<p style="text-align:justify">
Output is by default written in a directory that
is newly created if it does not yet exist (normally several files
will be created, for which the directory acts as a natural container).
It is possible to simply output to the current directory, for that you need
to specify <b>-dir</b> <b>./</b>. If <b>-dir</b> is not specified, the output
directory <tt>fmt.<clname></tt> will be used, where <tt><clname></tt> is the argument
to the <b>-cl</b> option. In the output directory, clmformat will
normally write two files. One contains zoem macros encoding formatted output
(the encoding file), and the second (the definition file) contains zoem
macro definitions which are used by the former.
<p style="text-align:justify">
The encoding file is by default called <tt>fmt.azm</tt>
(cf. the <a class="intern" href="#opt-fmt"><b>-fmt</b> <i>fname</i></a> option).
It contains <i>zoem</i> macros. It imports the macro definition file
called <tt>clmformat.zmm</tt>
that is normally also written by clmformat. Another macro definition
file can be specified by using the <a class="intern" href="#opt-zmm"><b>-zmm</b> <i><defsname></i></a>
option. In this case clmformat will refrain from writing the definition
file and replace mentions of <tt>clmformat.zmm</tt> in the encoding file
by <tt><defsname></tt>.
<p style="text-align:justify">
The encoding file needs to be processed by issuing one of the following
commands from within the directory where the file is located.
<pre> zoem -i fmt -d html
zoem -i fmt -d txt</pre>
<p style="text-align:justify; margin-top:0em">
The first will result in HTML formatted output, the second in
plain text format. Obviously, you need to have installed zoem
(e.g. from <a class="extern" href="http://micans.org/zoem/src/">http://micans.org/zoem/src/</a>) for this to work.
<p style="text-align:justify">
For each cluster a paragraph is output. First comes a listing of other
clusters (in order of relevance, possibly empty) for which a significant
amount of edges exists between the other and the current cluster. Second
comes a listing of the nodes in the current cluster. For each node a small
sublist is made (in order of relevance, possibly empty) of other clusters in
which the node has neighbours and for which the total sum of corresponding
edge weights is significant.
Several quantities are output for each node/cluster pair that is
deemed relevant. These are explained in the section OUTPUT EXPLAINED.
<p style="text-align:justify">
Clusters will by default be output to file until the total node count has
exceeded a threshold (refer to the <a class="intern" href="#opt-lump-count"><b>-lump-count</b>
option</a>).
<p style="text-align:justify">
<b>clmformat</b> also shows how well each node fits in the cluster it is in and
how cohesive each cluster is, using simple but effective measures
(described in section OUTPUT EXPLAINED).
This enables you to compare the quality of the clusters in a clustering
relative to each other, and may help in identifying both interesting areas
and areas for which cluster structure is hard to find or perhaps absent.
<a name="options"></a>
<h2>OPTIONS</h2>
<div style="margin-top:$margintopem">
<table
cellspacing="0" border=0
cellpadding="0" summary="itemize">
<tr>
<td colspan=3>
<a name="opt-icl"></a><b>-icl</b> fname (<i>input cluster file</i>)
</td>
</tr>
<tr>
<td width=32>
</td><td width=8>
</td>
<td><div style="text-align:justify">
Name of the clustering file.
</div></td>
</tr>
<tr>
<td width=32>
</td>
<td width=8>
</td>
<td>
</td>
</tr>
<tr>
<td colspan=3>
<a name="opt-imx"></a><b>-imx</b> fname (<i>input matrix/graph file</i>)
</td>
</tr>
<tr>
<td width=32>
</td><td width=8>
</td>
<td><div style="text-align:justify">
Name of the graph/matrix file.
</div></td>
</tr>
<tr>
<td width=32>
</td>
<td width=8>
</td>
<td>
</td>
</tr>
<tr>
<td colspan=3>
<a name="opt-tab"></a><b>-tab</b> fname (<i>read tab file</i>)
</td>
</tr>
<tr>
<td width=32>
</td><td width=8>
</td>
<td><div style="text-align:justify">
The file <tt>fname</tt> should be in <i>tab format</i>; each line starts
with a unique number which is an index used in the matrix input
file and the cluster input file. The rest of the line contains a
descriptive string associated with the number. Lines starting with
<tt>#</tt> are considered comment and are disregarded. A single unique
line should be present for each node/index of the cluster row domain
(or the graph/matrix domain optionally specified with the <b>-imx</b>
option). The leading indices should be in ascending order.
</div></td>
</tr>
<tr>
<td width=32>
</td>
<td width=8>
</td>
<td>
</td>
</tr>
<tr>
<td colspan=3>
<a name="opt-dir"></a><b>-dir</b> dirname (<i>write results to directory</i>)
</td>
</tr>
<tr>
<td width=32>
</td><td width=8>
</td>
<td><div style="text-align:justify">
Use <b>dirname</b> as target directory. It will be created
if it does not exist already.
</div></td>
</tr>
<tr>
<td width=32>
</td>
<td width=8>
</td>
<td>
</td>
</tr>
<tr>
<td colspan=3>
<a name="opt-fmt"></a><b>-fmt</b> fname (<i>write to encoding file fname</i>)
</td>
</tr>
<tr>
<td width=32>
</td><td width=8>
</td>
<td><div style="text-align:justify">
Write to encoding file <b>fname</b> rather than the default <tt>fmt.azm</tt>.
It is best to supply fname with the standard zoem suffix <tt>.azm</tt>. Zoem
will process file of any name, but those lacking the <tt>.azm</tt> suffix must be
specified using the zoem <b>-I</b> <i>fname</i> option.
</div></td>
</tr>
<tr>
<td width=32>
</td>
<td width=8>
</td>
<td>
</td>
</tr>
<tr>
<td colspan=3>
<a name="opt-zmm"></a><b>-zmm</b> defsname (<i>assume macro definitions are in fname</i>)
</td>
</tr>
<tr>
<td width=32>
</td><td width=8>
</td>
<td><div style="text-align:justify">
If this option is used, clmformat will not output the definition file,
and mentions of the definition file in the encoding file will use
the file name <tt>defsname</tt>. This option assumes that a valid definition
file by the name of <tt>defsname</tt> does exist.
</div></td>
</tr>
<tr>
<td width=32>
</td>
<td width=8>
</td>
<td>
</td>
</tr>
<tr>
<td colspan=3>
<a name="opt-dump"></a><b>-dump</b> fname (<i>write dump to file</i>)
</td>
</tr>
<tr>
<td width=32>
</td><td width=8>
</td>
<td><div style="text-align:justify">
Clusters are written to file. For each cluster a single line is written
containing all indices of all nodes in that cluster. The indices are
separated by tabs. If a tab file is specified, the indices are replaced by
the corresponding tab file entry. If an input matrix is specified, three
measures of efficiency are prepended, respectively the simple projection
score, efficiency or coverage, and the max-efficiency or max-coverage.
<p style="text-align:justify">
This option can be used e.g. in conjunction with mclgraga to gauge
the granularity (size distribution) of a clustering.
</div></td>
</tr>
<tr>
<td width=32>
</td>
<td width=8>
</td>
<td>
</td>
</tr>
<tr>
<td colspan=3>
<a name="opt--dump-pairs"></a><b>--dump-pairs</b> (<i>write cluster/node pair per line</i>)
</td>
</tr>
<tr>
<td width=32>
</td><td width=8>
</td>
<td><div style="text-align:justify">
Rather than writing a single cluster on each line, write a single
cluster index/node (either tab entry or index) pair per line.
Works in conjunction with the
<a class="intern" href="#opt-tab"><b>-tab</b></a> and <a class="intern" href="#opt-imx"><b>-imx</b></a> options.
</div></td>
</tr>
<tr>
<td width=32>
</td>
<td width=8>
</td>
<td>
</td>
</tr>
<tr>
<td colspan=3>
<a name="opt-dump-node-sep"></a><b>-dump-node-sep</b> str (<i>separate entries with str</i>)
</td>
</tr>
<tr>
<td width=32>
</td><td width=8>
</td>
<td><div style="text-align:justify">
Separate entries in the dump file with <b>str</b>.
</div></td>
</tr>
<tr>
<td width=32>
</td>
<td width=8>
</td>
<td>
</td>
</tr>
<tr>
<td colspan=3>
<a name="opt-pi"></a><b>-pi</b> num (<i>apply pre-inflation to matrix</i>)
</td>
</tr>
<tr>
<td width=32>
</td><td width=8>
</td>
<td><div style="text-align:justify">
Apply pre-inflation to the matrix specified with the <b>-imx</b> option.
This will cause the efficiency scores to place a higher reward on
high-weight edges being covered by a clustering (assuming that
<i>num</i> is larger than one).
<p style="text-align:justify">
This option is also useful when <b>mcl</b> itself was instructed to use
pre-inflation when clustering a graph.
</div></td>
</tr>
<tr>
<td width=32>
</td>
<td width=8>
</td>
<td>
</td>
</tr>
<tr>
<td colspan=3>
<a name="opt-lump-count"></a><b>-lump-count</b> n (<i>node threshold</i>)
</td>
</tr>
<tr>
<td width=32>
</td><td width=8>
</td>
<td><div style="text-align:justify">
The zoem file is created such that during zoem processing clusters are
formatted and output within a single file until the node threshold has been
exceeded. A new file is then opened and the procedure repeats itself.
</div></td>
</tr>
<tr>
<td width=32>
</td>
<td width=8>
</td>
<td>
</td>
</tr>
<tr>
<td colspan=3>
<a name="opt--adapt"></a><b>--adapt</b> (<i>allow domain mismatch</i>)
</td>
</tr>
<tr>
<td width=32>
</td><td width=8>
</td>
<td><div style="text-align:justify">
Allow the cluster domain to differ from the graph domain. Presumably
the clustering is a clustering of a subgraph. The cohesion and stickiness
measures will pertain to the relevant part of the graph only.
</div></td>
</tr>
<tr>
<td width=32>
</td>
<td width=8>
</td>
<td>
</td>
</tr>
<tr>
<td colspan=3>
<a name="opt-nsm"></a><b>-nsm</b> fname (<i>output node stickiness file</i>)
</td>
</tr>
<tr>
<td width=32>
</td><td width=8>
</td>
<td><div style="text-align:justify">
This option specifies the name in which to store (optionally) the <b>node
stickiness matrix</b>. It has the following structure. The columns range over
all elements in the graph as specified by the <b>-imx</b> option.
The rows range over the clusters as specified by the <b>-icl</b> option.
The entries contain the projection value of that particular
node onto that particular clusters, i.e. the sum of the weights of
all arcs going out from the node to some node in that cluster, written
as a fraction relative to the sum of weights of all outgoing arcs.
</div></td>
</tr>
<tr>
<td width=32>
</td>
<td width=8>
</td>
<td>
</td>
</tr>
<tr>
<td colspan=3>
<a name="opt-ccm"></a><b>-ccm</b> fname (<i>output cluster cohesion file</i>)
</td>
</tr>
<tr>
<td width=32>
</td><td width=8>
</td>
<td><div style="text-align:justify">
This option specifies the name of the file in which to store (optionally)
the <b>cluster cohesion matrix</b>. It has the following structure.
Both columns and rows range over all clusters in the clustering as specified
by the <b>-icl</b> option. An entry specifies the projection
of one cluster onto another cluster, which is simply the average
of the projection value onto the second cluster of all nodes in the
first cluster.
</div></td>
</tr>
<tr>
<td width=32>
</td>
<td width=8>
</td>
<td>
</td>
</tr>
<tr>
<td colspan=3>
<a name="opt--subgraph"></a><b>--subgraph</b> (<i>use restriction</i>)
</td>
</tr>
<tr>
<td width=32>
</td><td width=8>
</td>
<td><div style="text-align:justify">
If the cluster domain is a subset of the graph domain, the cohesion and
stickiness measures will by default still pertain to the entire graph. By
setting this option, the measures will pertain to the subgraph induced by
the cluster domain.
</div></td>
</tr>
<tr>
<td width=32>
</td>
<td width=8>
</td>
<td>
</td>
</tr>
<tr>
<td colspan=3>
<a name="opt--version"></a><b>--version</b> (<i>write version</i>)
</td>
</tr>
<tr>
<td width=32>
</td><td width=8>
</td>
<td><div style="text-align:justify">
Write version. Really.
</div></td>
</tr>
</table>
</div>
<a name="xpl"></a>
<h2>OUTPUT EXPLAINED</h2>
<p style="text-align:justify">
What follows is an explanation of the output provided by the
standard zoem macros. The output comes in a pretty terse number-packed
format. The decision was made not to include headers and captions
in the output in order to keep it readable.
You might want to print out the following annotated examples.
At the same side of the equation, the following is probably tough
reading unless you have an actual example of clmformatted output at hand.
<p style="text-align:justify">
Below mention is made of the projection value for a node/cluster pair.
This is simply the total amount of edge weights for that node
in that cluster (corresponding to neighbours of the node in the
cluster) relative to the overall amount of edge weights for that node
(corresponding to all its neighbours).
The coverage measure (refered to as <b>cov</b>)
is also used. This is similar to the projection
value, except that a) the coverage measure rewards the inclusion
of large edge weights (and penalizes the inclusion of insignificant
edge weights) and b) rewards node/cluster pairs for which the neighbour set
of the node is very similar to the cluster.
The maximum coverage measure (refered to as <b>maxcov</b>) is similar
to the normal coverage measure except that it rewards inclusion
of large edge weights even more.
The cov and maxcov performance measures have several nice continuity and
monotonicity properties and are described in <a class="intern" href="#pcfgcmce">[1]</a>.
<p style="text-align:justify">
<b>Example cluster header</b>
<br>
<pre>Cluster 0 sz 15 self 0.82 cov 0.43-0.26
10: 0.11
18: 0.05
12: 0.02</pre>
<p style="text-align:justify">
<b>explanation</b>
<br>
<pre>Cluster 0 sz 15 self 0.82 cov 0.43-0.26
| | | | |
clid count proj cov covmax
10: 0.11
| |
clidx1 projx1
18: 0.05
| |
clidx2 projx2
clid Numeric cluster identifier (arbitrarily) assigned by MCL.
count The size of cluster clid.
proj Projection value for cluster clid [d].
cov Coverage measure for cluster clid [d].
maxcov Max-coverage measure for cluster clid [d].
clidx1 Index of other cluster sharing relatively many edges.
projx1 Projection value for the clid/clidx1 pair of clusters [e].
clidx2 :
projx2 : as clidx1 and projx1</pre>
<p style="text-align:justify">
<b>Example inner node</b>
<br>
An inner node is listed under a cluster, and it is simply a member of that
cluster. The name is as opposed to 'outer node', described below.
<pre>[foo bar zut]
21 7-5 0.73 0.420-0.331 0.282-0.047 0.071-0.035 <3.54>
10 6/3 0.16 0.071-0.047 0.268-0.442
12 4/2 0.11 0.071-0.035 0.296-0.515</pre>
<p style="text-align:justify">
<b>explanation</b>
<br>
<pre>[label]
21 7-5 0.73 0.420-0.331 0.282-0.047 0.071-0.035 <3.54>
| | | | | | | | | | |
idx nbi nbo proj cov covmax max_i min_i max_o-min_o SUM
10 6/3 0.16 0.268-0.442 0.071-0.047
| | | | | | | |
clusid sz nb proj cov covmax max_i min_i
label Optional; with -tab <tabfile> option.
idx Numeric (mcl) identifier.
nbi Count of the neighbours of node idx within its cluster.
nbo Count of the neighbours of node idx outside its cluster.
proj Projection value [a] of nbi edges.
cov Skewed projection [b], rewards inclusion of large edge weights.
covmax As cov above, rewarding large edge weights even more.
max_i Largest edge weight in the nbi set, normalized [c].
min_i Smallest edge weight in the nbi set [c].
max_o Largest edge weight outside the nbi set [c]
min_o Smallest edge weight outside the nbi set [c].
SUM The sum of all edges leaving node idx.
clusid Index of other cluster that is relevant for node idx.
sz Size of that cluster.
nb Count of neighbours of node idx in cluster clusid.
proj Projection value of edges from node idx to cluster clusid.
cov Skewed projection of edges from node idx to cluster clusid.
covmax Maximally skewed projection, as above.
max_o Largest edge weight for node idx to cluster clusid [c].
min_o Smallest edge weight for node idx to cluster clusid [c].</pre>
<p style="text-align:justify">
<b>Example outer node</b>
<br>
An outer node is listed under a cluster. The node is not part of that cluster,
but seems to have substantial connections to that cluster.
<pre>[zoo eek few]
29 18#2 2-5 0.65 0.883-0.815 0.436-0.218 0.073-0.055
/4 0.27 0.070-0.109 0.073-0.055</pre>
<p style="text-align:justify">
<b>explanation</b>
<br>
<pre>[label]
29 18#2 2-5 0.65 0.883-0.815 0.436-0.218 0.073-0.055
| | | | | | | | | | | |
idx cl sz nbi nbo proj cov maxcov max_i min_i max_o min_o
id
/4 0.27 0.070-0.109 0.073-0.055 <2.29>
| | | | | | |
nb proj cov maxcov max_i min_i SUM
label Optional; with -tab <tabfile> option.
idx Numeric (mcl) identifier
clid Index of the cluster that node idx belongs to
sz Size of the cluster that node idx belongs to
proj :
cov : All these entries are the same as described above
covmax : for inner nodes, pertaining to cluster clid,
max_i : i.e. the native cluster for node idx
min_i : (it is a member of that cluster).
max_o :
min_o :
nb The count of neighbours of node idx in the current cluster
proj Projection value for node idx relative to current cluster.
cov Skewed projection (rewards large edge weights), as above.
covmax Maximally skewed projection, as above.
max_o Largest edge weight for node idx in current cluster [c].
min_o smallest edge weight for node idx in current cluster [c].
SUM The sum of *all* edges leaving node idx.</pre>
<div style="margin-top:$margintopem">
<table
cellspacing="0" border=0
cellpadding="0" summary="itemize">
<tr>
<td width=48 valign="top" align="right">
[a]
</td>
<td width=8> </td>
<td><div style="text-align:justify">
The projection value for a node relative to some subset of
its neighbours is the sum of edge weights of all edges to that
subset. The sum is witten as a fraction relative to the sum
of edge weights of all neighbours.
</div></td>
</tr>
<tr>
<td width=48>
</td>
<td width=8>
</td>
<td>
</td>
</tr>
<tr>
<td width=48 valign="top" align="right">
[b]
</td>
<td width=8> </td>
<td><div style="text-align:justify">
cov and covmax stand for coverage and maximal coverage.
The coverage measure of a node/cluster pair is a generalized and skewed
projection value [a] that rewards the presence of large edge weights in the
cluster, relative to the collection of weights of all edges departing from
the node. The maxcov measure is a projection value skewed even further,
correspondingly rewarding the inclusion of large edge weights. The cov and
maxcov performance measures have several nice continuity properties and are
described in <a class="intern" href="#pcfgcmce">[1]</a>.
</div></td>
</tr>
<tr>
<td width=48>
</td>
<td width=8>
</td>
<td>
</td>
</tr>
<tr>
<td width=48 valign="top" align="right">
[c]
</td>
<td width=8> </td>
<td><div style="text-align:justify">
All edge weights are written as the fraction of the sum
SUM of all edge weights of edges leaving node idx.
</div></td>
</tr>
<tr>
<td width=48>
</td>
<td width=8>
</td>
<td>
</td>
</tr>
<tr>
<td width=48 valign="top" align="right">
[d]
</td>
<td width=8> </td>
<td><div style="text-align:justify">
For clusters the projection value and the coverage measures
are simply the averages of all projection values [a], respectively
coverage measures [b], taken over all nodes in the cluster.
The cluster projection value simply measures the sum of edge
weights internal to the cluster, relative to the total sum of
edge weights of all edges where at least one node in the edge
is part of the cluster.
</div></td>
</tr>
<tr>
<td width=48>
</td>
<td width=8>
</td>
<td>
</td>
</tr>
<tr>
<td width=48 valign="top" align="right">
[e]
</td>
<td width=8> </td>
<td><div style="text-align:justify">
The projection value for start cluster x and end cluster y
is the sum of edge weights of edges between x and y as a fraction
of the sum of all edge weights of edges leaving x.
</div></td>
</tr>
</table>
</div>
<a name="author"></a>
<h2>AUTHOR</h2>
<p style="text-align:justify">
Stijn van Dongen.
<a name="references"></a>
<h2>REFERENCES</h2>
<p style="text-align:justify">
<a name="pcfgcmce">[1]</a>
Stijn van Dongen. <i>Performance criteria for graph clustering and Markov
cluster experiments</i>. Technical Report INS-R0012, National Research
Institute for Mathematics and Computer Science in the Netherlands,
Amsterdam, May 2000.<br>
<a class="extern" href="http://www.cwi.nl/ftp/CWIreports/INS/INS-R0012.ps.Z">http://www.cwi.nl/ftp/CWIreports/INS/INS-R0012.ps.Z</a>
<a name="seealso"></a>
<h2>SEE ALSO</h2>
<p style="text-align:justify">
<a class="local" href="mclfamily.html">mclfamily</a> for an overview of all the documentation
and the utilities in the mcl family.
</body>
</html>
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