How do we cluster separate curves in a set of data?

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











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3
down vote

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Below, I have included some data. (It is long, but I don't like to host data elsewhere and provide links that might some day be broken.)



Plotting this set of data, we have:



ListPlot@data


enter image description here



There are clearly some curves in this data that "naturally" belong together, as shown below (the two curves labeled by arrows should be associated with each other, but I suspect I'll have to link those two by hand).



enter image description here



However, the data are scrambled, so I can't easily separate the data set into chunks that correspond to these separate curves. For this reason, I need to find a way to cluster this data set to separate the curves.



While I'm not sure that FindClusters is the right tool for the job, the best I've been able to manage using this function is the following:



ListPlot[FindClusters[data, 7, Method -> "Agglomerate", "Linkage" -> "Complete"]]


resulting in



enter image description here



We can see that the two clusters that almost cross are clustered together, and also split apart in a strange way. Alternatively, I tried



ListPlot[FindClusters[data, 7, Method -> "Agglomerate"]]


resulting in



enter image description here



which is better in that it's not obviously splitting up pieces of a curve that should be together, but it's worse in that it's clustering two clearly separated curves.



  • Is FindClusters the right tool for the job, and if so, how do we use it to separate the curves?


  • If it's not the right tool for the job, what is? Is there a built-in Mathematica function that will do this job for us, or is there some clustering algorithm specifically designed to find curves like this?


  • Note that there are other data sets as well, similar to this one, that I'll need to cluster. The different curves are not always separated vertically as they are here, and there's always one outer curve that subsumes some number of the smaller curves inside it.


  • I understand that this will require some amount of manual tinkering at the end, but I'd like to get most of the way there using some automated procedure.


data = 0.00001, 1.19442, 0.00001, 1.90161, 0.00001, 2.14588, 
0.00001, 2.14588, 0.00001, 2.97948, 0.00001, 3.80987, 
0.00001, 4.85379, 0.00001, 5.71745, 0.00001, 6.74646, 
0.00001, 7.62493, 0.00001, 8.6456, 0.00001, 9.53239, 
0.06001, 0.0880935, 0.06001, 0.0880935, 0.06001, 0.285726, 
0.06001, 1.13484, 0.06001, 1.9261, 0.06001, 2.97527, 
0.06001, 3.82167, 0.06001, 4.85268, 0.06001, 5.72497, 
0.06001, 6.74611, 0.06001, 7.63031, 0.06001, 8.64556, 
0.06001, 9.53648, 0.12001, 0.601368, 0.12001, 1.0439, 
0.12001, 1.94366, 0.12001, 2.97182, 0.12001, 3.82973, 
0.12001, 4.85236, 0.12001, 5.72981, 0.12001, 6.74655, 
0.12001, 7.63353, 0.12001, 8.64632, 0.12001, 9.53873, 
0.18001, 1.95572, 0.18001, 2.96907, 0.18001, 3.83448, 
0.18001, 4.85289, 0.18001, 5.73217, 0.18001, 6.74786, 
0.18001, 7.63471, 0.18001, 8.64794, 0.18001, 9.53919, 
0.24001, 1.96422, 0.24001, 2.96694, 0.24001, 3.83652, 
0.24001, 4.85433, 0.24001, 5.73238, 0.24001, 6.75011, 
0.24001, 7.63403, 0.24001, 8.65051, 0.24001, 9.53798, 
0.30001, 0.00258367, 0.30001, 0.00258367, 0.30001, 0.00258367, 
0.30001, 1.97092, 0.30001, 2.9654, 0.30001, 3.83636, 
0.30001, 4.85679, 0.30001, 5.73068, 0.30001, 6.75344, 
0.30001, 7.63163, 0.30001, 8.65417, 0.30001, 9.53518, 
0.36001, 1.97727, 0.36001, 2.96438, 0.36001, 3.83435, 
0.36001, 4.86039, 0.36001, 5.72718, 0.36001, 6.758, 
0.36001, 7.62754, 0.36001, 8.65908, 0.36001, 9.53077, 
0.42001, 0.00726357, 0.42001, 0.00726357, 0.42001, 0.00726357, 
0.42001, 1.98438, 0.42001, 2.96386, 0.42001, 3.83069, 
0.42001, 4.86531, 0.42001, 5.7219, 0.42001, 6.76402, 
0.42001, 7.62169, 0.42001, 8.66548, 0.42001, 9.52465, 
0.48001, 1.99315, 0.48001, 2.96376, 0.48001, 3.82547, 
0.48001, 4.87176, 0.48001, 5.71471, 0.48001, 6.77175, 
0.48001, 7.61391, 0.48001, 8.67365, 0.48001, 9.51659, 
0.54001, 0.0139354, 0.54001, 2.00429, 0.54001, 2.96404, 
0.54001, 3.81869, 0.54001, 4.88002, 0.54001, 5.70541, 
0.54001, 6.78153, 0.54001, 7.6039, 0.54001, 8.68393, 
0.54001, 9.50629, 0.60001, 0.017363, 0.60001, 2.01834, 
0.60001, 2.96463, 0.60001, 3.81027, 0.60001, 4.89045, 
0.60001, 5.69365, 0.60001, 6.79381, 0.60001, 7.59126, 
0.60001, 8.69681, 0.60001, 9.49331, 0.66001, 0.0203981, 
0.66001, 2.03573, 0.66001, 2.96545, 0.66001, 3.80007, 
0.66001, 4.90352, 0.66001, 5.67898, 0.66001, 6.80918, 
0.66001, 7.57543, 0.66001, 8.71291, 0.66001, 9.47705, 
0.72001, 2.05681, 0.72001, 2.96643, 0.72001, 3.7879, 
0.72001, 4.91988, 0.72001, 5.66073, 0.72001, 6.82843, 
0.72001, 7.5556, 0.72001, 8.73308, 0.72001, 9.45666, 
0.78001, 2.08187, 0.78001, 2.96745, 0.78001, 3.7735, 
0.78001, 4.94042, 0.78001, 5.638, 0.78001, 6.85271, 
0.78001, 7.53065, 0.78001, 8.75855, 0.78001, 9.43091, 
0.84001, 2.11123, 0.84001, 2.96839, 0.84001, 3.75656, 
0.84001, 4.96648, 0.84001, 5.60943, 0.84001, 6.88378, 
0.84001, 7.49879, 0.84001, 8.79126, 0.84001, 9.39788, 
0.90001, 2.14523, 0.90001, 2.96907, 0.90001, 3.73667, 
0.90001, 5.00024, 0.90001, 5.00024, 0.90001, 5.00024, 
0.90001, 5.57278, 0.90001, 6.92475, 0.90001, 7.45692, 
0.90001, 8.83466, 0.90001, 9.35412, 0.96001, 2.18434, 
0.96001, 2.96929, 0.96001, 3.71336, 0.96001, 5.0459, 
0.96001, 5.52388, 0.96001, 6.98234, 0.96001, 7.39833, 
0.96001, 8.89666, 0.96001, 9.29171, 1.02001, 2.22921, 
1.02001, 2.96872, 1.02001, 3.686, 1.02001, 5.11431, 
1.02001, 5.45183, 1.02001, 7.08229, 1.02001, 7.08229, 
1.02001, 7.08229, 1.02001, 7.29726, 1.02001, 9.01467, 
1.02001, 9.17323, 1.08001, 2.28081, 1.08001, 2.96687, 
1.08001, 3.65384, 1.14001, 0.0440134, 1.14001, 2.34068, 
1.14001, 2.96295, 1.14001, 3.61585, 1.20001, 0.0524166, 
1.20001, 2.41148, 1.20001, 2.95537, 1.20001, 3.57069, 
1.26001, 0.0618122, 1.26001, 2.49856, 1.26001, 2.94044, 
1.26001, 3.51641, 1.32001, 0.0722359, 1.32001, 2.61739, 
1.32001, 2.90528, 1.32001, 3.45017, 1.38001, 0.0837295, 
1.38001, 3.36789, 1.38001, 3.36789, 1.38001, 3.36789, 
1.44001, 0.0963406, 1.44001, 3.26654, 1.44001, 3.26654, 
1.44001, 3.26654, 1.44001, 3.26654, 1.50001, 0.110122, 
1.50001, 3.1645, 1.50001, 3.1645, 1.50001, 3.1645, 
1.50001, 3.1645, 1.50001, 3.1645, 1.50001, 3.1645, 
1.50001, 3.1645, 1.56001, 0.125131, 1.56001, 3.10205, 
1.56001, 3.10205, 1.56001, 3.10205, 1.56001, 3.10205, 
1.56001, 3.10205, 1.62001, 0.141433, 1.62001, 3.06998, 
1.62001, 3.06998, 1.62001, 3.06998, 1.62001, 3.06998, 
1.62001, 3.06998, 1.68001, 0.159097, 1.68001, 3.0501, 
1.68001, 3.0501, 1.68001, 3.0501, 1.68001, 3.0501, 
1.68001, 3.0501, 1.74001, 0.178202, 1.74001, 3.0349, 
1.74001, 3.0349, 1.74001, 3.0349, 1.74001, 3.0349, 
1.74001, 3.0349, 1.74001, 3.0349, 1.74001, 3.0349, 
1.80001, 0.198834, 1.80001, 3.02131, 1.80001, 3.02131, 
1.80001, 3.02131, 1.80001, 3.02131, 1.80001, 3.02131, 
1.80001, 3.02131, 1.80001, 3.02131, 1.86001, 0.221089, 
1.86001, 3.00786, 1.86001, 3.00786, 1.86001, 3.00786, 
1.86001, 3.00786, 1.86001, 3.00786, 1.86001, 3.00786, 
1.86001, 3.00786, 1.92001, 0.245072, 1.92001, 2.99369, 
1.92001, 2.99369, 1.92001, 2.99369, 1.92001, 2.99369, 
1.92001, 2.99369, 1.98001, 0.270904, 1.98001, 2.97826, 
1.98001, 2.97826, 1.98001, 2.97826, 1.98001, 2.97826, 
1.98001, 2.97826, 2.04001, 0.298719, 2.04001, 2.96116, 
2.04001, 2.96116, 2.04001, 2.96116, 2.04001, 2.96116, 
2.04001, 2.96116, 2.10001, 0.328668, 2.10001, 2.94206, 
2.10001, 2.94206, 2.10001, 2.94206, 2.10001, 2.94206, 
2.10001, 2.94206, 2.16001, 0.360928, 2.16001, 0.360928, 
2.16001, 0.360928, 2.16001, 2.92066, 2.16001, 2.92066, 
2.16001, 2.92066, 2.16001, 2.92066, 2.16001, 2.92066, 
2.22001, 0.3957, 2.22001, 2.89665, 2.22001, 2.89665, 
2.22001, 2.89665, 2.22001, 2.89665, 2.22001, 2.89665, 
2.28001, 0.433221, 2.28001, 2.86974, 2.28001, 2.86974, 
2.28001, 2.86974, 2.28001, 2.86974, 2.28001, 2.86974, 
2.28001, 2.86974, 2.34001, 0.473772, 2.34001, 2.8396, 
2.34001, 2.8396, 2.34001, 2.8396, 2.34001, 2.8396, 
2.34001, 2.8396, 2.34001, 2.8396, 2.34001, 2.8396, 
2.34001, 2.8396, 2.34001, 2.8396, 2.40001, 0.517693, 
2.40001, 2.80585, 2.40001, 2.80585, 2.40001, 2.80585, 
2.40001, 2.80585, 2.40001, 2.80585, 2.46001, 0.5654, 
2.46001, 2.76805, 2.46001, 2.76805, 2.46001, 2.76805, 
2.46001, 2.76805, 2.46001, 2.76805, 2.52001, 0.617417, 
2.52001, 0.617417, 2.52001, 0.617417, 2.52001, 2.72566, 
2.52001, 2.72566, 2.52001, 2.72566, 2.58001, 0.674419, 
2.58001, 2.678, 2.58001, 2.678, 2.58001, 2.678, 
2.58001, 2.678, 2.64001, 0.737304, 2.64001, 2.62416, 
2.64001, 2.62416, 2.64001, 2.62416, 2.64001, 2.62416, 
2.70001, 2.56289, 2.70001, 2.56289, 2.76001, 0.886298, 
2.88001, 1.08495, 2.88001, 1.08495, 2.94001, 1.22081, 
2.94001, 2.18143, 2.94001, 1.22081;





list-manipulation cluster-analysis







share|improve this question

























    up vote
    3
    down vote

    favorite












    Below, I have included some data. (It is long, but I don't like to host data elsewhere and provide links that might some day be broken.)



    Plotting this set of data, we have:



    ListPlot@data


    enter image description here



    There are clearly some curves in this data that "naturally" belong together, as shown below (the two curves labeled by arrows should be associated with each other, but I suspect I'll have to link those two by hand).



    enter image description here



    However, the data are scrambled, so I can't easily separate the data set into chunks that correspond to these separate curves. For this reason, I need to find a way to cluster this data set to separate the curves.



    While I'm not sure that FindClusters is the right tool for the job, the best I've been able to manage using this function is the following:



    ListPlot[FindClusters[data, 7, Method -> "Agglomerate", "Linkage" -> "Complete"]]


    resulting in



    enter image description here



    We can see that the two clusters that almost cross are clustered together, and also split apart in a strange way. Alternatively, I tried



    ListPlot[FindClusters[data, 7, Method -> "Agglomerate"]]


    resulting in



    enter image description here



    which is better in that it's not obviously splitting up pieces of a curve that should be together, but it's worse in that it's clustering two clearly separated curves.



    • Is FindClusters the right tool for the job, and if so, how do we use it to separate the curves?


    • If it's not the right tool for the job, what is? Is there a built-in Mathematica function that will do this job for us, or is there some clustering algorithm specifically designed to find curves like this?


    • Note that there are other data sets as well, similar to this one, that I'll need to cluster. The different curves are not always separated vertically as they are here, and there's always one outer curve that subsumes some number of the smaller curves inside it.


    • I understand that this will require some amount of manual tinkering at the end, but I'd like to get most of the way there using some automated procedure.


    data = 0.00001, 1.19442, 0.00001, 1.90161, 0.00001, 2.14588, 
    0.00001, 2.14588, 0.00001, 2.97948, 0.00001, 3.80987, 
    0.00001, 4.85379, 0.00001, 5.71745, 0.00001, 6.74646, 
    0.00001, 7.62493, 0.00001, 8.6456, 0.00001, 9.53239, 
    0.06001, 0.0880935, 0.06001, 0.0880935, 0.06001, 0.285726, 
    0.06001, 1.13484, 0.06001, 1.9261, 0.06001, 2.97527, 
    0.06001, 3.82167, 0.06001, 4.85268, 0.06001, 5.72497, 
    0.06001, 6.74611, 0.06001, 7.63031, 0.06001, 8.64556, 
    0.06001, 9.53648, 0.12001, 0.601368, 0.12001, 1.0439, 
    0.12001, 1.94366, 0.12001, 2.97182, 0.12001, 3.82973, 
    0.12001, 4.85236, 0.12001, 5.72981, 0.12001, 6.74655, 
    0.12001, 7.63353, 0.12001, 8.64632, 0.12001, 9.53873, 
    0.18001, 1.95572, 0.18001, 2.96907, 0.18001, 3.83448, 
    0.18001, 4.85289, 0.18001, 5.73217, 0.18001, 6.74786, 
    0.18001, 7.63471, 0.18001, 8.64794, 0.18001, 9.53919, 
    0.24001, 1.96422, 0.24001, 2.96694, 0.24001, 3.83652, 
    0.24001, 4.85433, 0.24001, 5.73238, 0.24001, 6.75011, 
    0.24001, 7.63403, 0.24001, 8.65051, 0.24001, 9.53798, 
    0.30001, 0.00258367, 0.30001, 0.00258367, 0.30001, 0.00258367, 
    0.30001, 1.97092, 0.30001, 2.9654, 0.30001, 3.83636, 
    0.30001, 4.85679, 0.30001, 5.73068, 0.30001, 6.75344, 
    0.30001, 7.63163, 0.30001, 8.65417, 0.30001, 9.53518, 
    0.36001, 1.97727, 0.36001, 2.96438, 0.36001, 3.83435, 
    0.36001, 4.86039, 0.36001, 5.72718, 0.36001, 6.758, 
    0.36001, 7.62754, 0.36001, 8.65908, 0.36001, 9.53077, 
    0.42001, 0.00726357, 0.42001, 0.00726357, 0.42001, 0.00726357, 
    0.42001, 1.98438, 0.42001, 2.96386, 0.42001, 3.83069, 
    0.42001, 4.86531, 0.42001, 5.7219, 0.42001, 6.76402, 
    0.42001, 7.62169, 0.42001, 8.66548, 0.42001, 9.52465, 
    0.48001, 1.99315, 0.48001, 2.96376, 0.48001, 3.82547, 
    0.48001, 4.87176, 0.48001, 5.71471, 0.48001, 6.77175, 
    0.48001, 7.61391, 0.48001, 8.67365, 0.48001, 9.51659, 
    0.54001, 0.0139354, 0.54001, 2.00429, 0.54001, 2.96404, 
    0.54001, 3.81869, 0.54001, 4.88002, 0.54001, 5.70541, 
    0.54001, 6.78153, 0.54001, 7.6039, 0.54001, 8.68393, 
    0.54001, 9.50629, 0.60001, 0.017363, 0.60001, 2.01834, 
    0.60001, 2.96463, 0.60001, 3.81027, 0.60001, 4.89045, 
    0.60001, 5.69365, 0.60001, 6.79381, 0.60001, 7.59126, 
    0.60001, 8.69681, 0.60001, 9.49331, 0.66001, 0.0203981, 
    0.66001, 2.03573, 0.66001, 2.96545, 0.66001, 3.80007, 
    0.66001, 4.90352, 0.66001, 5.67898, 0.66001, 6.80918, 
    0.66001, 7.57543, 0.66001, 8.71291, 0.66001, 9.47705, 
    0.72001, 2.05681, 0.72001, 2.96643, 0.72001, 3.7879, 
    0.72001, 4.91988, 0.72001, 5.66073, 0.72001, 6.82843, 
    0.72001, 7.5556, 0.72001, 8.73308, 0.72001, 9.45666, 
    0.78001, 2.08187, 0.78001, 2.96745, 0.78001, 3.7735, 
    0.78001, 4.94042, 0.78001, 5.638, 0.78001, 6.85271, 
    0.78001, 7.53065, 0.78001, 8.75855, 0.78001, 9.43091, 
    0.84001, 2.11123, 0.84001, 2.96839, 0.84001, 3.75656, 
    0.84001, 4.96648, 0.84001, 5.60943, 0.84001, 6.88378, 
    0.84001, 7.49879, 0.84001, 8.79126, 0.84001, 9.39788, 
    0.90001, 2.14523, 0.90001, 2.96907, 0.90001, 3.73667, 
    0.90001, 5.00024, 0.90001, 5.00024, 0.90001, 5.00024, 
    0.90001, 5.57278, 0.90001, 6.92475, 0.90001, 7.45692, 
    0.90001, 8.83466, 0.90001, 9.35412, 0.96001, 2.18434, 
    0.96001, 2.96929, 0.96001, 3.71336, 0.96001, 5.0459, 
    0.96001, 5.52388, 0.96001, 6.98234, 0.96001, 7.39833, 
    0.96001, 8.89666, 0.96001, 9.29171, 1.02001, 2.22921, 
    1.02001, 2.96872, 1.02001, 3.686, 1.02001, 5.11431, 
    1.02001, 5.45183, 1.02001, 7.08229, 1.02001, 7.08229, 
    1.02001, 7.08229, 1.02001, 7.29726, 1.02001, 9.01467, 
    1.02001, 9.17323, 1.08001, 2.28081, 1.08001, 2.96687, 
    1.08001, 3.65384, 1.14001, 0.0440134, 1.14001, 2.34068, 
    1.14001, 2.96295, 1.14001, 3.61585, 1.20001, 0.0524166, 
    1.20001, 2.41148, 1.20001, 2.95537, 1.20001, 3.57069, 
    1.26001, 0.0618122, 1.26001, 2.49856, 1.26001, 2.94044, 
    1.26001, 3.51641, 1.32001, 0.0722359, 1.32001, 2.61739, 
    1.32001, 2.90528, 1.32001, 3.45017, 1.38001, 0.0837295, 
    1.38001, 3.36789, 1.38001, 3.36789, 1.38001, 3.36789, 
    1.44001, 0.0963406, 1.44001, 3.26654, 1.44001, 3.26654, 
    1.44001, 3.26654, 1.44001, 3.26654, 1.50001, 0.110122, 
    1.50001, 3.1645, 1.50001, 3.1645, 1.50001, 3.1645, 
    1.50001, 3.1645, 1.50001, 3.1645, 1.50001, 3.1645, 
    1.50001, 3.1645, 1.56001, 0.125131, 1.56001, 3.10205, 
    1.56001, 3.10205, 1.56001, 3.10205, 1.56001, 3.10205, 
    1.56001, 3.10205, 1.62001, 0.141433, 1.62001, 3.06998, 
    1.62001, 3.06998, 1.62001, 3.06998, 1.62001, 3.06998, 
    1.62001, 3.06998, 1.68001, 0.159097, 1.68001, 3.0501, 
    1.68001, 3.0501, 1.68001, 3.0501, 1.68001, 3.0501, 
    1.68001, 3.0501, 1.74001, 0.178202, 1.74001, 3.0349, 
    1.74001, 3.0349, 1.74001, 3.0349, 1.74001, 3.0349, 
    1.74001, 3.0349, 1.74001, 3.0349, 1.74001, 3.0349, 
    1.80001, 0.198834, 1.80001, 3.02131, 1.80001, 3.02131, 
    1.80001, 3.02131, 1.80001, 3.02131, 1.80001, 3.02131, 
    1.80001, 3.02131, 1.80001, 3.02131, 1.86001, 0.221089, 
    1.86001, 3.00786, 1.86001, 3.00786, 1.86001, 3.00786, 
    1.86001, 3.00786, 1.86001, 3.00786, 1.86001, 3.00786, 
    1.86001, 3.00786, 1.92001, 0.245072, 1.92001, 2.99369, 
    1.92001, 2.99369, 1.92001, 2.99369, 1.92001, 2.99369, 
    1.92001, 2.99369, 1.98001, 0.270904, 1.98001, 2.97826, 
    1.98001, 2.97826, 1.98001, 2.97826, 1.98001, 2.97826, 
    1.98001, 2.97826, 2.04001, 0.298719, 2.04001, 2.96116, 
    2.04001, 2.96116, 2.04001, 2.96116, 2.04001, 2.96116, 
    2.04001, 2.96116, 2.10001, 0.328668, 2.10001, 2.94206, 
    2.10001, 2.94206, 2.10001, 2.94206, 2.10001, 2.94206, 
    2.10001, 2.94206, 2.16001, 0.360928, 2.16001, 0.360928, 
    2.16001, 0.360928, 2.16001, 2.92066, 2.16001, 2.92066, 
    2.16001, 2.92066, 2.16001, 2.92066, 2.16001, 2.92066, 
    2.22001, 0.3957, 2.22001, 2.89665, 2.22001, 2.89665, 
    2.22001, 2.89665, 2.22001, 2.89665, 2.22001, 2.89665, 
    2.28001, 0.433221, 2.28001, 2.86974, 2.28001, 2.86974, 
    2.28001, 2.86974, 2.28001, 2.86974, 2.28001, 2.86974, 
    2.28001, 2.86974, 2.34001, 0.473772, 2.34001, 2.8396, 
    2.34001, 2.8396, 2.34001, 2.8396, 2.34001, 2.8396, 
    2.34001, 2.8396, 2.34001, 2.8396, 2.34001, 2.8396, 
    2.34001, 2.8396, 2.34001, 2.8396, 2.40001, 0.517693, 
    2.40001, 2.80585, 2.40001, 2.80585, 2.40001, 2.80585, 
    2.40001, 2.80585, 2.40001, 2.80585, 2.46001, 0.5654, 
    2.46001, 2.76805, 2.46001, 2.76805, 2.46001, 2.76805, 
    2.46001, 2.76805, 2.46001, 2.76805, 2.52001, 0.617417, 
    2.52001, 0.617417, 2.52001, 0.617417, 2.52001, 2.72566, 
    2.52001, 2.72566, 2.52001, 2.72566, 2.58001, 0.674419, 
    2.58001, 2.678, 2.58001, 2.678, 2.58001, 2.678, 
    2.58001, 2.678, 2.64001, 0.737304, 2.64001, 2.62416, 
    2.64001, 2.62416, 2.64001, 2.62416, 2.64001, 2.62416, 
    2.70001, 2.56289, 2.70001, 2.56289, 2.76001, 0.886298, 
    2.88001, 1.08495, 2.88001, 1.08495, 2.94001, 1.22081, 
    2.94001, 2.18143, 2.94001, 1.22081;





    list-manipulation cluster-analysis







    share|improve this question























      up vote
      3
      down vote

      favorite









      up vote
      3
      down vote

      favorite











      Below, I have included some data. (It is long, but I don't like to host data elsewhere and provide links that might some day be broken.)



      Plotting this set of data, we have:



      ListPlot@data


      enter image description here



      There are clearly some curves in this data that "naturally" belong together, as shown below (the two curves labeled by arrows should be associated with each other, but I suspect I'll have to link those two by hand).



      enter image description here



      However, the data are scrambled, so I can't easily separate the data set into chunks that correspond to these separate curves. For this reason, I need to find a way to cluster this data set to separate the curves.



      While I'm not sure that FindClusters is the right tool for the job, the best I've been able to manage using this function is the following:



      ListPlot[FindClusters[data, 7, Method -> "Agglomerate", "Linkage" -> "Complete"]]


      resulting in



      enter image description here



      We can see that the two clusters that almost cross are clustered together, and also split apart in a strange way. Alternatively, I tried



      ListPlot[FindClusters[data, 7, Method -> "Agglomerate"]]


      resulting in



      enter image description here



      which is better in that it's not obviously splitting up pieces of a curve that should be together, but it's worse in that it's clustering two clearly separated curves.



      • Is FindClusters the right tool for the job, and if so, how do we use it to separate the curves?


      • If it's not the right tool for the job, what is? Is there a built-in Mathematica function that will do this job for us, or is there some clustering algorithm specifically designed to find curves like this?


      • Note that there are other data sets as well, similar to this one, that I'll need to cluster. The different curves are not always separated vertically as they are here, and there's always one outer curve that subsumes some number of the smaller curves inside it.


      • I understand that this will require some amount of manual tinkering at the end, but I'd like to get most of the way there using some automated procedure.


      data = 0.00001, 1.19442, 0.00001, 1.90161, 0.00001, 2.14588, 
      0.00001, 2.14588, 0.00001, 2.97948, 0.00001, 3.80987, 
      0.00001, 4.85379, 0.00001, 5.71745, 0.00001, 6.74646, 
      0.00001, 7.62493, 0.00001, 8.6456, 0.00001, 9.53239, 
      0.06001, 0.0880935, 0.06001, 0.0880935, 0.06001, 0.285726, 
      0.06001, 1.13484, 0.06001, 1.9261, 0.06001, 2.97527, 
      0.06001, 3.82167, 0.06001, 4.85268, 0.06001, 5.72497, 
      0.06001, 6.74611, 0.06001, 7.63031, 0.06001, 8.64556, 
      0.06001, 9.53648, 0.12001, 0.601368, 0.12001, 1.0439, 
      0.12001, 1.94366, 0.12001, 2.97182, 0.12001, 3.82973, 
      0.12001, 4.85236, 0.12001, 5.72981, 0.12001, 6.74655, 
      0.12001, 7.63353, 0.12001, 8.64632, 0.12001, 9.53873, 
      0.18001, 1.95572, 0.18001, 2.96907, 0.18001, 3.83448, 
      0.18001, 4.85289, 0.18001, 5.73217, 0.18001, 6.74786, 
      0.18001, 7.63471, 0.18001, 8.64794, 0.18001, 9.53919, 
      0.24001, 1.96422, 0.24001, 2.96694, 0.24001, 3.83652, 
      0.24001, 4.85433, 0.24001, 5.73238, 0.24001, 6.75011, 
      0.24001, 7.63403, 0.24001, 8.65051, 0.24001, 9.53798, 
      0.30001, 0.00258367, 0.30001, 0.00258367, 0.30001, 0.00258367, 
      0.30001, 1.97092, 0.30001, 2.9654, 0.30001, 3.83636, 
      0.30001, 4.85679, 0.30001, 5.73068, 0.30001, 6.75344, 
      0.30001, 7.63163, 0.30001, 8.65417, 0.30001, 9.53518, 
      0.36001, 1.97727, 0.36001, 2.96438, 0.36001, 3.83435, 
      0.36001, 4.86039, 0.36001, 5.72718, 0.36001, 6.758, 
      0.36001, 7.62754, 0.36001, 8.65908, 0.36001, 9.53077, 
      0.42001, 0.00726357, 0.42001, 0.00726357, 0.42001, 0.00726357, 
      0.42001, 1.98438, 0.42001, 2.96386, 0.42001, 3.83069, 
      0.42001, 4.86531, 0.42001, 5.7219, 0.42001, 6.76402, 
      0.42001, 7.62169, 0.42001, 8.66548, 0.42001, 9.52465, 
      0.48001, 1.99315, 0.48001, 2.96376, 0.48001, 3.82547, 
      0.48001, 4.87176, 0.48001, 5.71471, 0.48001, 6.77175, 
      0.48001, 7.61391, 0.48001, 8.67365, 0.48001, 9.51659, 
      0.54001, 0.0139354, 0.54001, 2.00429, 0.54001, 2.96404, 
      0.54001, 3.81869, 0.54001, 4.88002, 0.54001, 5.70541, 
      0.54001, 6.78153, 0.54001, 7.6039, 0.54001, 8.68393, 
      0.54001, 9.50629, 0.60001, 0.017363, 0.60001, 2.01834, 
      0.60001, 2.96463, 0.60001, 3.81027, 0.60001, 4.89045, 
      0.60001, 5.69365, 0.60001, 6.79381, 0.60001, 7.59126, 
      0.60001, 8.69681, 0.60001, 9.49331, 0.66001, 0.0203981, 
      0.66001, 2.03573, 0.66001, 2.96545, 0.66001, 3.80007, 
      0.66001, 4.90352, 0.66001, 5.67898, 0.66001, 6.80918, 
      0.66001, 7.57543, 0.66001, 8.71291, 0.66001, 9.47705, 
      0.72001, 2.05681, 0.72001, 2.96643, 0.72001, 3.7879, 
      0.72001, 4.91988, 0.72001, 5.66073, 0.72001, 6.82843, 
      0.72001, 7.5556, 0.72001, 8.73308, 0.72001, 9.45666, 
      0.78001, 2.08187, 0.78001, 2.96745, 0.78001, 3.7735, 
      0.78001, 4.94042, 0.78001, 5.638, 0.78001, 6.85271, 
      0.78001, 7.53065, 0.78001, 8.75855, 0.78001, 9.43091, 
      0.84001, 2.11123, 0.84001, 2.96839, 0.84001, 3.75656, 
      0.84001, 4.96648, 0.84001, 5.60943, 0.84001, 6.88378, 
      0.84001, 7.49879, 0.84001, 8.79126, 0.84001, 9.39788, 
      0.90001, 2.14523, 0.90001, 2.96907, 0.90001, 3.73667, 
      0.90001, 5.00024, 0.90001, 5.00024, 0.90001, 5.00024, 
      0.90001, 5.57278, 0.90001, 6.92475, 0.90001, 7.45692, 
      0.90001, 8.83466, 0.90001, 9.35412, 0.96001, 2.18434, 
      0.96001, 2.96929, 0.96001, 3.71336, 0.96001, 5.0459, 
      0.96001, 5.52388, 0.96001, 6.98234, 0.96001, 7.39833, 
      0.96001, 8.89666, 0.96001, 9.29171, 1.02001, 2.22921, 
      1.02001, 2.96872, 1.02001, 3.686, 1.02001, 5.11431, 
      1.02001, 5.45183, 1.02001, 7.08229, 1.02001, 7.08229, 
      1.02001, 7.08229, 1.02001, 7.29726, 1.02001, 9.01467, 
      1.02001, 9.17323, 1.08001, 2.28081, 1.08001, 2.96687, 
      1.08001, 3.65384, 1.14001, 0.0440134, 1.14001, 2.34068, 
      1.14001, 2.96295, 1.14001, 3.61585, 1.20001, 0.0524166, 
      1.20001, 2.41148, 1.20001, 2.95537, 1.20001, 3.57069, 
      1.26001, 0.0618122, 1.26001, 2.49856, 1.26001, 2.94044, 
      1.26001, 3.51641, 1.32001, 0.0722359, 1.32001, 2.61739, 
      1.32001, 2.90528, 1.32001, 3.45017, 1.38001, 0.0837295, 
      1.38001, 3.36789, 1.38001, 3.36789, 1.38001, 3.36789, 
      1.44001, 0.0963406, 1.44001, 3.26654, 1.44001, 3.26654, 
      1.44001, 3.26654, 1.44001, 3.26654, 1.50001, 0.110122, 
      1.50001, 3.1645, 1.50001, 3.1645, 1.50001, 3.1645, 
      1.50001, 3.1645, 1.50001, 3.1645, 1.50001, 3.1645, 
      1.50001, 3.1645, 1.56001, 0.125131, 1.56001, 3.10205, 
      1.56001, 3.10205, 1.56001, 3.10205, 1.56001, 3.10205, 
      1.56001, 3.10205, 1.62001, 0.141433, 1.62001, 3.06998, 
      1.62001, 3.06998, 1.62001, 3.06998, 1.62001, 3.06998, 
      1.62001, 3.06998, 1.68001, 0.159097, 1.68001, 3.0501, 
      1.68001, 3.0501, 1.68001, 3.0501, 1.68001, 3.0501, 
      1.68001, 3.0501, 1.74001, 0.178202, 1.74001, 3.0349, 
      1.74001, 3.0349, 1.74001, 3.0349, 1.74001, 3.0349, 
      1.74001, 3.0349, 1.74001, 3.0349, 1.74001, 3.0349, 
      1.80001, 0.198834, 1.80001, 3.02131, 1.80001, 3.02131, 
      1.80001, 3.02131, 1.80001, 3.02131, 1.80001, 3.02131, 
      1.80001, 3.02131, 1.80001, 3.02131, 1.86001, 0.221089, 
      1.86001, 3.00786, 1.86001, 3.00786, 1.86001, 3.00786, 
      1.86001, 3.00786, 1.86001, 3.00786, 1.86001, 3.00786, 
      1.86001, 3.00786, 1.92001, 0.245072, 1.92001, 2.99369, 
      1.92001, 2.99369, 1.92001, 2.99369, 1.92001, 2.99369, 
      1.92001, 2.99369, 1.98001, 0.270904, 1.98001, 2.97826, 
      1.98001, 2.97826, 1.98001, 2.97826, 1.98001, 2.97826, 
      1.98001, 2.97826, 2.04001, 0.298719, 2.04001, 2.96116, 
      2.04001, 2.96116, 2.04001, 2.96116, 2.04001, 2.96116, 
      2.04001, 2.96116, 2.10001, 0.328668, 2.10001, 2.94206, 
      2.10001, 2.94206, 2.10001, 2.94206, 2.10001, 2.94206, 
      2.10001, 2.94206, 2.16001, 0.360928, 2.16001, 0.360928, 
      2.16001, 0.360928, 2.16001, 2.92066, 2.16001, 2.92066, 
      2.16001, 2.92066, 2.16001, 2.92066, 2.16001, 2.92066, 
      2.22001, 0.3957, 2.22001, 2.89665, 2.22001, 2.89665, 
      2.22001, 2.89665, 2.22001, 2.89665, 2.22001, 2.89665, 
      2.28001, 0.433221, 2.28001, 2.86974, 2.28001, 2.86974, 
      2.28001, 2.86974, 2.28001, 2.86974, 2.28001, 2.86974, 
      2.28001, 2.86974, 2.34001, 0.473772, 2.34001, 2.8396, 
      2.34001, 2.8396, 2.34001, 2.8396, 2.34001, 2.8396, 
      2.34001, 2.8396, 2.34001, 2.8396, 2.34001, 2.8396, 
      2.34001, 2.8396, 2.34001, 2.8396, 2.40001, 0.517693, 
      2.40001, 2.80585, 2.40001, 2.80585, 2.40001, 2.80585, 
      2.40001, 2.80585, 2.40001, 2.80585, 2.46001, 0.5654, 
      2.46001, 2.76805, 2.46001, 2.76805, 2.46001, 2.76805, 
      2.46001, 2.76805, 2.46001, 2.76805, 2.52001, 0.617417, 
      2.52001, 0.617417, 2.52001, 0.617417, 2.52001, 2.72566, 
      2.52001, 2.72566, 2.52001, 2.72566, 2.58001, 0.674419, 
      2.58001, 2.678, 2.58001, 2.678, 2.58001, 2.678, 
      2.58001, 2.678, 2.64001, 0.737304, 2.64001, 2.62416, 
      2.64001, 2.62416, 2.64001, 2.62416, 2.64001, 2.62416, 
      2.70001, 2.56289, 2.70001, 2.56289, 2.76001, 0.886298, 
      2.88001, 1.08495, 2.88001, 1.08495, 2.94001, 1.22081, 
      2.94001, 2.18143, 2.94001, 1.22081;





      list-manipulation cluster-analysis







      share|improve this question













      Below, I have included some data. (It is long, but I don't like to host data elsewhere and provide links that might some day be broken.)



      Plotting this set of data, we have:



      ListPlot@data


      enter image description here



      There are clearly some curves in this data that "naturally" belong together, as shown below (the two curves labeled by arrows should be associated with each other, but I suspect I'll have to link those two by hand).



      enter image description here



      However, the data are scrambled, so I can't easily separate the data set into chunks that correspond to these separate curves. For this reason, I need to find a way to cluster this data set to separate the curves.



      While I'm not sure that FindClusters is the right tool for the job, the best I've been able to manage using this function is the following:



      ListPlot[FindClusters[data, 7, Method -> "Agglomerate", "Linkage" -> "Complete"]]


      resulting in



      enter image description here



      We can see that the two clusters that almost cross are clustered together, and also split apart in a strange way. Alternatively, I tried



      ListPlot[FindClusters[data, 7, Method -> "Agglomerate"]]


      resulting in



      enter image description here



      which is better in that it's not obviously splitting up pieces of a curve that should be together, but it's worse in that it's clustering two clearly separated curves.



      • Is FindClusters the right tool for the job, and if so, how do we use it to separate the curves?


      • If it's not the right tool for the job, what is? Is there a built-in Mathematica function that will do this job for us, or is there some clustering algorithm specifically designed to find curves like this?


      • Note that there are other data sets as well, similar to this one, that I'll need to cluster. The different curves are not always separated vertically as they are here, and there's always one outer curve that subsumes some number of the smaller curves inside it.


      • I understand that this will require some amount of manual tinkering at the end, but I'd like to get most of the way there using some automated procedure.


      data = 0.00001, 1.19442, 0.00001, 1.90161, 0.00001, 2.14588, 
      0.00001, 2.14588, 0.00001, 2.97948, 0.00001, 3.80987, 
      0.00001, 4.85379, 0.00001, 5.71745, 0.00001, 6.74646, 
      0.00001, 7.62493, 0.00001, 8.6456, 0.00001, 9.53239, 
      0.06001, 0.0880935, 0.06001, 0.0880935, 0.06001, 0.285726, 
      0.06001, 1.13484, 0.06001, 1.9261, 0.06001, 2.97527, 
      0.06001, 3.82167, 0.06001, 4.85268, 0.06001, 5.72497, 
      0.06001, 6.74611, 0.06001, 7.63031, 0.06001, 8.64556, 
      0.06001, 9.53648, 0.12001, 0.601368, 0.12001, 1.0439, 
      0.12001, 1.94366, 0.12001, 2.97182, 0.12001, 3.82973, 
      0.12001, 4.85236, 0.12001, 5.72981, 0.12001, 6.74655, 
      0.12001, 7.63353, 0.12001, 8.64632, 0.12001, 9.53873, 
      0.18001, 1.95572, 0.18001, 2.96907, 0.18001, 3.83448, 
      0.18001, 4.85289, 0.18001, 5.73217, 0.18001, 6.74786, 
      0.18001, 7.63471, 0.18001, 8.64794, 0.18001, 9.53919, 
      0.24001, 1.96422, 0.24001, 2.96694, 0.24001, 3.83652, 
      0.24001, 4.85433, 0.24001, 5.73238, 0.24001, 6.75011, 
      0.24001, 7.63403, 0.24001, 8.65051, 0.24001, 9.53798, 
      0.30001, 0.00258367, 0.30001, 0.00258367, 0.30001, 0.00258367, 
      0.30001, 1.97092, 0.30001, 2.9654, 0.30001, 3.83636, 
      0.30001, 4.85679, 0.30001, 5.73068, 0.30001, 6.75344, 
      0.30001, 7.63163, 0.30001, 8.65417, 0.30001, 9.53518, 
      0.36001, 1.97727, 0.36001, 2.96438, 0.36001, 3.83435, 
      0.36001, 4.86039, 0.36001, 5.72718, 0.36001, 6.758, 
      0.36001, 7.62754, 0.36001, 8.65908, 0.36001, 9.53077, 
      0.42001, 0.00726357, 0.42001, 0.00726357, 0.42001, 0.00726357, 
      0.42001, 1.98438, 0.42001, 2.96386, 0.42001, 3.83069, 
      0.42001, 4.86531, 0.42001, 5.7219, 0.42001, 6.76402, 
      0.42001, 7.62169, 0.42001, 8.66548, 0.42001, 9.52465, 
      0.48001, 1.99315, 0.48001, 2.96376, 0.48001, 3.82547, 
      0.48001, 4.87176, 0.48001, 5.71471, 0.48001, 6.77175, 
      0.48001, 7.61391, 0.48001, 8.67365, 0.48001, 9.51659, 
      0.54001, 0.0139354, 0.54001, 2.00429, 0.54001, 2.96404, 
      0.54001, 3.81869, 0.54001, 4.88002, 0.54001, 5.70541, 
      0.54001, 6.78153, 0.54001, 7.6039, 0.54001, 8.68393, 
      0.54001, 9.50629, 0.60001, 0.017363, 0.60001, 2.01834, 
      0.60001, 2.96463, 0.60001, 3.81027, 0.60001, 4.89045, 
      0.60001, 5.69365, 0.60001, 6.79381, 0.60001, 7.59126, 
      0.60001, 8.69681, 0.60001, 9.49331, 0.66001, 0.0203981, 
      0.66001, 2.03573, 0.66001, 2.96545, 0.66001, 3.80007, 
      0.66001, 4.90352, 0.66001, 5.67898, 0.66001, 6.80918, 
      0.66001, 7.57543, 0.66001, 8.71291, 0.66001, 9.47705, 
      0.72001, 2.05681, 0.72001, 2.96643, 0.72001, 3.7879, 
      0.72001, 4.91988, 0.72001, 5.66073, 0.72001, 6.82843, 
      0.72001, 7.5556, 0.72001, 8.73308, 0.72001, 9.45666, 
      0.78001, 2.08187, 0.78001, 2.96745, 0.78001, 3.7735, 
      0.78001, 4.94042, 0.78001, 5.638, 0.78001, 6.85271, 
      0.78001, 7.53065, 0.78001, 8.75855, 0.78001, 9.43091, 
      0.84001, 2.11123, 0.84001, 2.96839, 0.84001, 3.75656, 
      0.84001, 4.96648, 0.84001, 5.60943, 0.84001, 6.88378, 
      0.84001, 7.49879, 0.84001, 8.79126, 0.84001, 9.39788, 
      0.90001, 2.14523, 0.90001, 2.96907, 0.90001, 3.73667, 
      0.90001, 5.00024, 0.90001, 5.00024, 0.90001, 5.00024, 
      0.90001, 5.57278, 0.90001, 6.92475, 0.90001, 7.45692, 
      0.90001, 8.83466, 0.90001, 9.35412, 0.96001, 2.18434, 
      0.96001, 2.96929, 0.96001, 3.71336, 0.96001, 5.0459, 
      0.96001, 5.52388, 0.96001, 6.98234, 0.96001, 7.39833, 
      0.96001, 8.89666, 0.96001, 9.29171, 1.02001, 2.22921, 
      1.02001, 2.96872, 1.02001, 3.686, 1.02001, 5.11431, 
      1.02001, 5.45183, 1.02001, 7.08229, 1.02001, 7.08229, 
      1.02001, 7.08229, 1.02001, 7.29726, 1.02001, 9.01467, 
      1.02001, 9.17323, 1.08001, 2.28081, 1.08001, 2.96687, 
      1.08001, 3.65384, 1.14001, 0.0440134, 1.14001, 2.34068, 
      1.14001, 2.96295, 1.14001, 3.61585, 1.20001, 0.0524166, 
      1.20001, 2.41148, 1.20001, 2.95537, 1.20001, 3.57069, 
      1.26001, 0.0618122, 1.26001, 2.49856, 1.26001, 2.94044, 
      1.26001, 3.51641, 1.32001, 0.0722359, 1.32001, 2.61739, 
      1.32001, 2.90528, 1.32001, 3.45017, 1.38001, 0.0837295, 
      1.38001, 3.36789, 1.38001, 3.36789, 1.38001, 3.36789, 
      1.44001, 0.0963406, 1.44001, 3.26654, 1.44001, 3.26654, 
      1.44001, 3.26654, 1.44001, 3.26654, 1.50001, 0.110122, 
      1.50001, 3.1645, 1.50001, 3.1645, 1.50001, 3.1645, 
      1.50001, 3.1645, 1.50001, 3.1645, 1.50001, 3.1645, 
      1.50001, 3.1645, 1.56001, 0.125131, 1.56001, 3.10205, 
      1.56001, 3.10205, 1.56001, 3.10205, 1.56001, 3.10205, 
      1.56001, 3.10205, 1.62001, 0.141433, 1.62001, 3.06998, 
      1.62001, 3.06998, 1.62001, 3.06998, 1.62001, 3.06998, 
      1.62001, 3.06998, 1.68001, 0.159097, 1.68001, 3.0501, 
      1.68001, 3.0501, 1.68001, 3.0501, 1.68001, 3.0501, 
      1.68001, 3.0501, 1.74001, 0.178202, 1.74001, 3.0349, 
      1.74001, 3.0349, 1.74001, 3.0349, 1.74001, 3.0349, 
      1.74001, 3.0349, 1.74001, 3.0349, 1.74001, 3.0349, 
      1.80001, 0.198834, 1.80001, 3.02131, 1.80001, 3.02131, 
      1.80001, 3.02131, 1.80001, 3.02131, 1.80001, 3.02131, 
      1.80001, 3.02131, 1.80001, 3.02131, 1.86001, 0.221089, 
      1.86001, 3.00786, 1.86001, 3.00786, 1.86001, 3.00786, 
      1.86001, 3.00786, 1.86001, 3.00786, 1.86001, 3.00786, 
      1.86001, 3.00786, 1.92001, 0.245072, 1.92001, 2.99369, 
      1.92001, 2.99369, 1.92001, 2.99369, 1.92001, 2.99369, 
      1.92001, 2.99369, 1.98001, 0.270904, 1.98001, 2.97826, 
      1.98001, 2.97826, 1.98001, 2.97826, 1.98001, 2.97826, 
      1.98001, 2.97826, 2.04001, 0.298719, 2.04001, 2.96116, 
      2.04001, 2.96116, 2.04001, 2.96116, 2.04001, 2.96116, 
      2.04001, 2.96116, 2.10001, 0.328668, 2.10001, 2.94206, 
      2.10001, 2.94206, 2.10001, 2.94206, 2.10001, 2.94206, 
      2.10001, 2.94206, 2.16001, 0.360928, 2.16001, 0.360928, 
      2.16001, 0.360928, 2.16001, 2.92066, 2.16001, 2.92066, 
      2.16001, 2.92066, 2.16001, 2.92066, 2.16001, 2.92066, 
      2.22001, 0.3957, 2.22001, 2.89665, 2.22001, 2.89665, 
      2.22001, 2.89665, 2.22001, 2.89665, 2.22001, 2.89665, 
      2.28001, 0.433221, 2.28001, 2.86974, 2.28001, 2.86974, 
      2.28001, 2.86974, 2.28001, 2.86974, 2.28001, 2.86974, 
      2.28001, 2.86974, 2.34001, 0.473772, 2.34001, 2.8396, 
      2.34001, 2.8396, 2.34001, 2.8396, 2.34001, 2.8396, 
      2.34001, 2.8396, 2.34001, 2.8396, 2.34001, 2.8396, 
      2.34001, 2.8396, 2.34001, 2.8396, 2.40001, 0.517693, 
      2.40001, 2.80585, 2.40001, 2.80585, 2.40001, 2.80585, 
      2.40001, 2.80585, 2.40001, 2.80585, 2.46001, 0.5654, 
      2.46001, 2.76805, 2.46001, 2.76805, 2.46001, 2.76805, 
      2.46001, 2.76805, 2.46001, 2.76805, 2.52001, 0.617417, 
      2.52001, 0.617417, 2.52001, 0.617417, 2.52001, 2.72566, 
      2.52001, 2.72566, 2.52001, 2.72566, 2.58001, 0.674419, 
      2.58001, 2.678, 2.58001, 2.678, 2.58001, 2.678, 
      2.58001, 2.678, 2.64001, 0.737304, 2.64001, 2.62416, 
      2.64001, 2.62416, 2.64001, 2.62416, 2.64001, 2.62416, 
      2.70001, 2.56289, 2.70001, 2.56289, 2.76001, 0.886298, 
      2.88001, 1.08495, 2.88001, 1.08495, 2.94001, 1.22081, 
      2.94001, 2.18143, 2.94001, 1.22081;





      list-manipulation cluster-analysis




      list-manipulation cluster-analysis






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked 3 hours ago









      march

      17k22769




      17k22769




















          1 Answer
          1






          active

          oldest

          votes

















          up vote
          3
          down vote













          EDIT: Added missing definition



          This uses a little manual intervention



          segments = Reverse[data[[#]] & /@ FindCurvePath[data]];

          segments = 
           ReplacePart[
           segments, -1 -> 
           Sequence[
           ss = Select[segments[[-1]], 1.5 < #[[2]] < 3 && #[[1]] < 1.4 &], 
           Complement[segments[[-1]], ss]]];


          ListPlot[segments, PlotLegends -> Automatic]


          enter image description here






          share|improve this answer






















          • I can't seem to get your code to run (because segments isn't defined before you use it inside ReplacePart), but I get the general gist: essentially, we need to manually select the curve that's "inside" the other one, but the rest will work fine. It doesn't look like FindCurvePath has any customization at all, so there's no way to tell it to fiddle with it the way we can fiddle with FindClusters, which is too bad. Nonetheless, this is a hopeful approach, since it does most of the work.
            – march
            1 hour ago










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          oldest

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          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes








          up vote
          3
          down vote













          EDIT: Added missing definition



          This uses a little manual intervention



          segments = Reverse[data[[#]] & /@ FindCurvePath[data]];

          segments = 
           ReplacePart[
           segments, -1 -> 
           Sequence[
           ss = Select[segments[[-1]], 1.5 < #[[2]] < 3 && #[[1]] < 1.4 &], 
           Complement[segments[[-1]], ss]]];


          ListPlot[segments, PlotLegends -> Automatic]


          enter image description here






          share|improve this answer






















          • I can't seem to get your code to run (because segments isn't defined before you use it inside ReplacePart), but I get the general gist: essentially, we need to manually select the curve that's "inside" the other one, but the rest will work fine. It doesn't look like FindCurvePath has any customization at all, so there's no way to tell it to fiddle with it the way we can fiddle with FindClusters, which is too bad. Nonetheless, this is a hopeful approach, since it does most of the work.
            – march
            1 hour ago














          up vote
          3
          down vote













          EDIT: Added missing definition



          This uses a little manual intervention



          segments = Reverse[data[[#]] & /@ FindCurvePath[data]];

          segments = 
           ReplacePart[
           segments, -1 -> 
           Sequence[
           ss = Select[segments[[-1]], 1.5 < #[[2]] < 3 && #[[1]] < 1.4 &], 
           Complement[segments[[-1]], ss]]];


          ListPlot[segments, PlotLegends -> Automatic]


          enter image description here






          share|improve this answer






















          • I can't seem to get your code to run (because segments isn't defined before you use it inside ReplacePart), but I get the general gist: essentially, we need to manually select the curve that's "inside" the other one, but the rest will work fine. It doesn't look like FindCurvePath has any customization at all, so there's no way to tell it to fiddle with it the way we can fiddle with FindClusters, which is too bad. Nonetheless, this is a hopeful approach, since it does most of the work.
            – march
            1 hour ago












          up vote
          3
          down vote










          up vote
          3
          down vote









          EDIT: Added missing definition



          This uses a little manual intervention



          segments = Reverse[data[[#]] & /@ FindCurvePath[data]];

          segments = 
           ReplacePart[
           segments, -1 -> 
           Sequence[
           ss = Select[segments[[-1]], 1.5 < #[[2]] < 3 && #[[1]] < 1.4 &], 
           Complement[segments[[-1]], ss]]];


          ListPlot[segments, PlotLegends -> Automatic]


          enter image description here






          share|improve this answer














          EDIT: Added missing definition



          This uses a little manual intervention



          segments = Reverse[data[[#]] & /@ FindCurvePath[data]];

          segments = 
           ReplacePart[
           segments, -1 -> 
           Sequence[
           ss = Select[segments[[-1]], 1.5 < #[[2]] < 3 && #[[1]] < 1.4 &], 
           Complement[segments[[-1]], ss]]];


          ListPlot[segments, PlotLegends -> Automatic]


          enter image description here







          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited 1 hour ago

























          answered 1 hour ago









          Bob Hanlon

          56.4k23590




          56.4k23590











          • I can't seem to get your code to run (because segments isn't defined before you use it inside ReplacePart), but I get the general gist: essentially, we need to manually select the curve that's "inside" the other one, but the rest will work fine. It doesn't look like FindCurvePath has any customization at all, so there's no way to tell it to fiddle with it the way we can fiddle with FindClusters, which is too bad. Nonetheless, this is a hopeful approach, since it does most of the work.
            – march
            1 hour ago
















          • I can't seem to get your code to run (because segments isn't defined before you use it inside ReplacePart), but I get the general gist: essentially, we need to manually select the curve that's "inside" the other one, but the rest will work fine. It doesn't look like FindCurvePath has any customization at all, so there's no way to tell it to fiddle with it the way we can fiddle with FindClusters, which is too bad. Nonetheless, this is a hopeful approach, since it does most of the work.
            – march
            1 hour ago















          I can't seem to get your code to run (because segments isn't defined before you use it inside ReplacePart), but I get the general gist: essentially, we need to manually select the curve that's "inside" the other one, but the rest will work fine. It doesn't look like FindCurvePath has any customization at all, so there's no way to tell it to fiddle with it the way we can fiddle with FindClusters, which is too bad. Nonetheless, this is a hopeful approach, since it does most of the work.
          – march
          1 hour ago




          I can't seem to get your code to run (because segments isn't defined before you use it inside ReplacePart), but I get the general gist: essentially, we need to manually select the curve that's "inside" the other one, but the rest will work fine. It doesn't look like FindCurvePath has any customization at all, so there's no way to tell it to fiddle with it the way we can fiddle with FindClusters, which is too bad. Nonetheless, this is a hopeful approach, since it does most of the work.
          – march
          1 hour ago

















           

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