Skip to main content

make specific cluster


I have set of coordinates. I want to make clusters in which every point is within 1.5 distance unit of it's neighbor.


ex of point coordinates:


{{-12.945, 20.6509, 12.5901}, {-13.4452, 20.307, 111.626}, 

{-12.9731, 22.8458, 12.4215}, {-13.2381, 24.8167, 10.7147}, 
{-11.3668, 23.3908,11.8499}, {-11.6828, 23.7311, 10.8839}, 
{-13.3929, 21.1835, 9.86324}, {-11.5016, 21.3324, 10.1392}, 
{-12.3079, 22.096, 8.57246}, {-12.5268, 20.9679, 10.5444}, 
{-12.1951, 24.5423, 10.1807}, {-11.8887, 22.3883, 10.0751}, 
{-14.2529, 20.4808, 9.81084}, {-11.9876, 21.8094, 11.0478}, 
{-12.3718, 23.6176, 11.8266}, {-11.6179, 20.8324, 11.2154}, 
{-12.5927, 21.7492, 12.5087}, {-12.1665, 24.6649, 11.2909}, 
{-12.3854, 21.5571, 9.51876}, {-12.2237, 23.4278, 9.9787}}


what is the quickest way in Mathematica for this (for large data sets).


I tried this to find all points that are within mentioned distance:


Table[Select[List, EuclideanDistance[List[[i]], #] < 1.5 &], {i, 1, Length[[List]]}]

but now I have troubles to join all sets that have common elements.



Answer



Here is a possible alteernative, I was working on while Kuba posted his answer :-) I also started by using FixedPoint and the inner loop seems to work but the outer one is easier with While.


c = {{-12.945, 20.6509, 12.5901}, {-13.4452, 20.307, 
    111.626}, {-12.9731, 22.8458, 12.4215}, {-13.2381, 24.8167, 
    10.7147}, {-11.3668, 23.3908, 11.8499}, {-11.6828, 23.7311, 

    10.8839}, {-13.3929, 21.1835, 9.86324}, {-11.5016, 21.3324, 
    10.1392}, {-12.3079, 22.096, 8.57246}, {-12.5268, 20.9679, 
    10.5444}, {-12.1951, 24.5423, 10.1807}, {-11.8887, 22.3883, 
    10.0751}, {-14.2529, 20.4808, 9.81084}, {-11.9876, 21.8094, 
    11.0478}, {-12.3718, 23.6176, 11.8266}, {-11.6179, 20.8324, 
    11.2154}, {-12.5927, 21.7492, 12.5087}, {-12.1665, 24.6649, 
    11.2909}, {-12.3854, 21.5571, 9.51876}, {-12.2237, 23.4278, 
    9.9787}};
MyClustering[data_List, distance_?NumericQ] :=
 Module[{dataoriginal = data, res = {}, temp = {}},

  While[dataoriginal =!= {},
   temp = {};
   AppendTo[res,
    FixedPoint[(
       Map[
        Function[p, 
         temp = Join[temp, 
           Select[dataoriginal, EuclideanDistance[#, p] < distance &]];
         dataoriginal = Complement[dataoriginal, temp]], #]; 
       temp) &, {dataoriginal[[1]]}]]];

  Return[res]]

Just few notes: dataoriginal is needed because I modify the original list and the argument of a function (data in that case) cannot be modified inside the function's body. For huge lists AppendTo is generally slow, so a possible alternative is


res = Join[{res}, FixedPoint[...]]


Comments

Post a Comment

Popular posts from this blog

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...
Post a Comment
Read more

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...
Post a Comment
Read more

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...
Post a Comment
Read more