Let’s have a look at another dataset with physical meaning as part of my exploring less known datasets series. This time we’ll look at a dataset that originates from RDatasets.

This dataset contains rock permeabilities obtained from cross-sections of cores.

Twelve core samples from petroleum reservoirs were sampled by 4 cross-sections. Each core sample was measured for permeability, and each cross-section has total area of pores, total perimeter of pores, and shape.

Source: Data from BP Research, image analysis by Ronit Katz, U. Oxford.

– https://stat.ethz.ch/R-manual/R-devel/library/datasets/html/rock.html

Unfortunately, that is all information I could find on this dataset(without spending too much time). Therefore, we don’t know in which direction it was measured. Certainly, there was no permeability tensor (9x9) derived.

Let’s load the dataset and have a look at it:

input_data = pd.read_csv("./data/rock.csv")
display(input_data.sample(10))
display(input_data.describe())


  
    

      
      Area
      Peri
      Shape
      Perm
    

  
  
    

      11
      8624
      3986.24
      0.148141
      119.0
    

    

      39
      5267
      1644.96
      0.253832
      100.0
    

    

      27
      5246
      1585.42
      0.133083
      740.0
    

    

      7
      8209
      4344.75
      0.164127
      17.1
    

    

      0
      4990
      2791.90
      0.090330
      6.3
    

    

      21
      11876
      4353.14
      0.291029
      142.0
    

    

      36
      3469
      1376.70
      0.176969
      100.0
    

    

      5
      7979
      4010.15
      0.167045
      17.1
    

    

      35
      7894
      1461.06
      0.276016
      950.0
    

    

      2
      7558
      3930.66
      0.183312
      6.3
    

  




  
    

      
      Area
      Peri
      Shape
      Perm
    

  
  
    

      count
      48.000000
      48.000000
      48.000000
      48.000000
    

    

      mean
      7187.729167
      2682.211938
      0.218110
      415.450000
    

    

      std
      2683.848862
      1431.661164
      0.083496
      437.818226
    

    

      min
      1016.000000
      308.642000
      0.090330
      6.300000
    

    

      25%
      5305.250000
      1414.907500
      0.162262
      76.450000
    

    

      50%
      7487.000000
      2536.195000
      0.198862
      130.500000
    

    

      75%
      8869.500000
      3989.522500
      0.262670
      777.500000
    

    

      max
      12212.000000
      4864.220000
      0.464125
      1300.000000

Since the dataset is really small, we are going to train the model using a 4-fold cross-validation and score it on the whole dataset. Proper train-valid-test splitting wouldn’t make much sense here because we have 4 data points for each of the 12 samples. Let’s throw some algorithms at it and see if we end up with something useful.

Well, it lookes like KNN leads to something useful.