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MathGroup Archive 2006

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Re: Custom distance function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72108] Re: Custom distance function
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Wed, 13 Dec 2006 06:38:21 -0500 (EST)
  • Organization: The Open University, Milton Keynes, UK
  • References: <eljbf3$7he$1@smc.vnet.net>

bentheo at gmail.com wrote:
> \!\(wcity[A_, B_]\  := \ â??\+\(i =
> 1\)\%7\((weights[\([i]\)]*\((Abs[A[\([i]\)] \
> - B[\([i]\)]])\))\)\)
> 
> I was wondering if anyone could lend me a hand with a problem I'm
> having. I'm trying to use the standard clusteranalysis package with
> Mathematica. Now, I've defined a new distance function, which is
> essentially the standard manhattan distance function, but it uses
> weights. The function works on lists, and the documentation leads me to
> believe it is a legit function, but when I try to use it i get
> DistanceMatrix::optx: "Unknown option DistanceFuntion in \
> \!\(DistanceMatrix[{{226.3382425`, 0.286908795`, \[LeftSkeleton]4\
> \[RightSkeleton], 0.742291389`}, \[LeftSkeleton]9\[RightSkeleton], \
> \[LeftSkeleton]3353\[RightSkeleton]},
> \[LeftSkeleton]1\[RightSkeleton]]\). \!\
> \( \*ButtonBox[\(Moreâ?¦\), ButtonData:>\"General::optx\", \
> ButtonStyle->\"RefGuideLinkText\", ButtonFrame->\"None\"]\)
> 
> 
> Any ideas what I'm doing wrong?
> 

I have just make up an example and your function /wcity/ seems to work 
fine. (See below.)

In[1]:=
Needs["Statistics`ClusterAnalysis`"]

In[2]:=
wcity[A_, B_] := Sum[weights[[i]]*
     Abs[A[[i]] - B[[i]]], {i, 1, 7}]

In[3]:=
weights = 1/Range[1, 7]

Out[3]=
{1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7}

In[4]:=
data = Table[Random[Integer, {1, 20}], {10}, {7}]

Out[4]=
{{10, 1, 5, 11, 4, 1, 18}, {1, 19, 7, 13, 14, 16, 2},
   {20, 12, 20, 15, 5, 3, 13}, {19, 6, 4, 17, 10, 7,
    19}, {19, 6, 2, 13, 19, 2, 13},
   {5, 17, 17, 11, 20, 14, 11}, {19, 14, 18, 14, 4, 5,
    1}, {19, 18, 16, 16, 16, 7, 16},
   {9, 3, 8, 17, 13, 19, 7}, {15, 7, 6, 16, 18, 19, 5}}

In[5]:=
FindClusters[data, DistanceFunction -> wcity]

Out[5]=
{{{10, 1, 5, 11, 4, 1, 18}, {9, 3, 8, 17, 13, 19, 7},
    {15, 7, 6, 16, 18, 19, 5}},
   {{1, 19, 7, 13, 14, 16, 2}, {5, 17, 17, 11, 20, 14,
     11}}, {{20, 12, 20, 15, 5, 3, 13},
    {19, 6, 4, 17, 10, 7, 19}, {19, 6, 2, 13, 19, 2,
     13}, {19, 14, 18, 14, 4, 5, 1},
    {19, 18, 16, 16, 16, 7, 16}}}

Regards,
Jean-Marc


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