The Wheat Seed Problem Using k-NN Classification With the scikit Library

Posted on March 14, 2023 by jamesdmccaffrey

One of my work laptops died so I tried to reimage it by reinstalling everything, including OS, from the ground up. While that was going on, I decided to entertain myself by doing a k-nearest neighbors (k-NN) classification example using the scikit library on the Wheat Seeds dataset (on one of my working machines).

The k-NN (k-nearest neighbors) classification technique is intended only for data that has strictly numeric (i.e., no categorical) predictor variables. The raw Wheat Seeds data came from archive.ics.uci.edu/ml/datasets/seeds and looks like:

15.26  14.84  0.871   5.763  3.312  2.221  5.22   1
14.88  14.57  0.8811  5.554  3.333  1.018  4.956  1
. . .
17.63  15.98  0.8673  6.191  3.561  4.076  6.06   2
16.84  15.67  0.8623  5.998  3.484  4.675  5.877  2
. . .
11.84  13.21  0.8521  5.175  2.836  3.598  5.044  3
12.3   13.34  0.8684  5.243  2.974  5.637  5.063  3

---------------------------------------------------
10.59  12.41  0.8081  4.899  2.63   0.765  4.519 (min values)
21.18  17.25  0.9183  6.675  4.033  8.456  6.55  (max values)

There are 210 data items. Each represents one of three species of wheat seeds: Kama, Rosa, Canadian. There are 70 of each species. The first 7 values on each line are the predictors: area, perimeter, compactness, length, width, asymmetry, groove. The eighth value is the one-based encoded species. The goal is to predict species from the seven predictor values.

When using the k-NN classification technique, it’s important to normalize the numeric predictors so that they all have roughly the same magnitude so that a predictor with large values doesn’t overwhelm other predictor values. As is often the case in machine learning, data preparation took most of the time an effort of my exploration.

I dropped the raw data into an Excel spreadsheet. For each predictor, I computed the min and max values of the column. Then I performed min-max normalization where each value x in a column is normalized to x’ = (x – min) / (max – min). The result is that each predictor is a value between 0.0 and 1.0.

I recoded the target class labels from one-based to zero-based. The resulting 210-item dataset looks like:

0.4410  0.5021  0.5708  0.4865  0.4861  0.1893  0.3452  0
0.4051  0.4463  0.6624  0.3688  0.5011  0.0329  0.2152  0
. . .
0.6648  0.7376  0.5372  0.7275  0.6636  0.4305  0.7587  1
0.5902  0.6736  0.4918  0.6188  0.6087  0.5084  0.6686  1
. . .
0.1917  0.2603  0.3630  0.2877  0.2003  0.3304  0.3506  2
0.2049  0.2004  0.8013  0.0980  0.3742  0.2682  0.1531  2

I split the 210-item normalized data into a 180-item training set and a 30-item test set. I used the first 60 of each target class for training and the last 10 of each target class for testing.

Using scikit is easy. After loading the training and test data into memory, a k-NN multi-class classification model is created and trained like so:

  k = 7
  print("Creating kNN model, with k=" + str(k) )
  model = KNeighborsClassifier(n_neighbors=k, algorithm='brute')
  model.fit(train_X, train_y)
  print("Done ")

The default number of nearest neighbors is k=5 but I used k=7 which gave more representative results.

Well, I wasn’t able to revive my dead laptop but I had fun with k-NN classification.


Three interesting photos of unusual-looking seed pods. Left: Brachychiton rupestris tree (Australia). Center: Cojoba arborea tree (Mexico). Right: Nelumbo nucifera (water lotus) plant (Asia).

Demo code:

# wheat_knn.py

# predict wheat seed species (0=Kama, 1=Rosa, 2=Canadian)
# from area, perimeter, compactness, length, width,
#   asymmetry, groove

# Anaconda3-2020.02  Python 3.7.6  scikit 0.22.1
# Windows 10/11

import numpy as np
from sklearn.neighbors import KNeighborsClassifier

# ---------------------------------------------------------

def show_confusion(cm):
  dim = len(cm)
  mx = np.max(cm)             # largest count in cm
  wid = len(str(mx)) + 1      # width to print
  fmt = "%" + str(wid) + "d"  # like "%3d"
  for i in range(dim):
    print("actual   ", end="")
    print("%3d:" % i, end="")
    for j in range(dim):
      print(fmt % cm[i][j], end="")
    print("")
  print("------------")
  print("predicted    ", end="")
  for j in range(dim):
    print(fmt % j, end="")
  print("")

# ---------------------------------------------------------

def main():
  # 0. prepare
  print("\nBegin Wheat Seeds k-NN using scikit ")
  np.set_printoptions(precision=4, suppress=True)
  np.random.seed(1)

  # 1. load data
  # 0.4410  0.5021  0.5708  0.4865  0.4861  0.1893  0.3452  0
  # 0.4051  0.4463  0.6624  0.3688  0.5011  0.0329  0.2152  0
  # . . .
  # 0.1917  0.2603  0.3630  0.2877  0.2003  0.3304  0.3506  2
  # 0.2049  0.2004  0.8013  0.0980  0.3742  0.2682  0.1531  2

  print("\nLoading train and test data ")
  train_file = ".\\Data\\wheat_train.txt"  # 180 items
  train_X = np.loadtxt(train_file, usecols=[0,1,2,3,4,5,6],
    delimiter="\t", dtype=np.float32, comments="#")
  train_y = np.loadtxt(train_file, usecols=[7],
    delimiter="\t", dtype=np.int64, comments="#")

  test_file = ".\\Data\\wheat_test.txt"  # 30 items
  test_X = np.loadtxt(test_file, usecols=[0,1,2,3,4,5,6],
    delimiter="\t", dtype=np.float32, comments="#")
  test_y = np.loadtxt(test_file, usecols=[7],
    delimiter="\t", dtype=np.int64, comments="#")
  
  print("\nTraining data:")
  print(train_X[0:4])
  print(". . . \n")
  print(train_y[0:4])
  print(". . . ")

  # 2. create and train model
  # KNeighborsClassifier(n_neighbors=5, *, weights='uniform',
  #   algorithm='auto', leaf_size=30, p=2, metric='minkowski',
  #   metric_params=None, n_jobs=None
  # algorithm: 'ball_tree', 'kd_tree', 'brute', 'auto'.

  k = 7
  print("\nCreating kNN model, with k=" + str(k) )
  model = KNeighborsClassifier(n_neighbors=k, algorithm='brute')
  model.fit(train_X, train_y)
  print("Done ")

  # 3. evaluate model
  train_acc = model.score(train_X, train_y)
  test_acc= model.score(test_X, test_y)
  print("\nAccuracy on train data = %0.4f " % train_acc)
  print("Accuracy on test data = %0.4f " % test_acc)

  from sklearn.metrics import confusion_matrix
  y_predicteds = model.predict(test_X)
  cm = confusion_matrix(test_y, y_predicteds)
  print("\nConfusion matrix: \n")
  # print(cm)
  show_confusion(cm)  # custom formatted

  # 4. use model
  X = np.array([[0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5]],
    dtype=np.float32)
  print("\nPredicting class for: ")
  print(X)
  probs = model.predict_proba(X)
  print("\nPrediction probs: ")
  print(probs)

  predicted = model.predict(X)
  print("\nPredicted class: ")
  print(predicted)

  # 5. TODO: save model using pickle
  import pickle
  print("\nSaving trained kNN model ")
  # path = ".\\Models\\wheat_knn_model.sav"
  # pickle.dump(model, open(path, "wb"))

  # usage:
  # X = np.array([[0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5]],
  #   dtype=np.int64)
  # with open(path, 'rb') as f:
  #   loaded_model = pickle.load(f)
  # pa = loaded_model.predict_proba(x)
  # print(pa)

  print("\nEnd demo ")

if __name__ == "__main__":
  main()

Training data. Replace commas with tabs or modify program code.

# wheat_train.txt
#
# http://archive.ics.uci.edu/ml/datasets/seeds
# 210 total items. train is first 60 each of 3 classes
# 180 training, 30 test
# area, perimeter, compactness, length, width, asymmetry, groove
# predictors are all min-max normalized
# 0 = Kama, 1 = Rosa, 2 = Canadian
#
0.4410,0.5021,0.5708,0.4865,0.4861,0.1893,0.3452,0
0.4051,0.4463,0.6624,0.3688,0.5011,0.0329,0.2152,0
0.3494,0.3471,0.8793,0.2207,0.5039,0.2515,0.1507,0
0.3069,0.3161,0.7931,0.2393,0.5339,0.1942,0.1408,0
0.5241,0.5331,0.8648,0.4274,0.6643,0.0767,0.3230,0
0.3579,0.3719,0.7895,0.2742,0.4861,0.2206,0.2152,0
0.3872,0.4298,0.6515,0.3739,0.4483,0.3668,0.3447,0
0.3324,0.3492,0.7532,0.2934,0.4790,0.2516,0.2368,0
0.5703,0.6302,0.6044,0.6498,0.5952,0.1658,0.6686,0
0.5524,0.5868,0.7250,0.5546,0.6237,0.1565,0.4993,0
0.4410,0.5041,0.5581,0.4589,0.4362,0.4912,0.3914,0
0.3248,0.3616,0.6488,0.3035,0.4070,0.1238,0.2373,0
0.3116,0.3326,0.7250,0.3041,0.4056,0.4188,0.1078,0
0.3012,0.3409,0.6152,0.3266,0.3749,0.3083,0.1738,0
0.2975,0.3388,0.6016,0.3283,0.3450,0.2817,0.1507,0
0.3777,0.3864,0.8276,0.2545,0.5011,0.4447,0.1290,0
0.3211,0.2934,1.0000,0.1239,0.5367,0.5811,0.1290,0
0.4816,0.4835,0.8866,0.3536,0.6301,0.1084,0.2595,0
0.3881,0.3719,0.9728,0.1723,0.5959,0.1303,0.0640,0
0.2011,0.2397,0.5490,0.1841,0.2986,0.4339,0.1945,0
0.3371,0.4112,0.4564,0.4274,0.3557,0.3000,0.3235,0
0.3324,0.3822,0.5817,0.3497,0.3835,0.2500,0.3447,0
0.4995,0.5145,0.8230,0.4048,0.6251,0.0000,0.2816,0
0.1407,0.1694,0.5290,0.1126,0.2181,0.0845,0.2176,0
0.4174,0.4855,0.5227,0.5011,0.4383,0.1334,0.2373,0
0.5288,0.5682,0.6969,0.5259,0.5638,0.0179,0.3880,0
0.2295,0.2789,0.5082,0.2793,0.2823,0.3391,0.1507,0
0.2030,0.2603,0.4383,0.2793,0.2324,0.2261,0.1723,0
0.3324,0.3657,0.6706,0.3615,0.4212,0.2586,0.2555,0
0.2701,0.3326,0.4746,0.3474,0.3100,0.3596,0.2846,0
0.2427,0.2913,0.5272,0.3125,0.2459,0.0117,0.2644,0
0.4627,0.5227,0.5835,0.4831,0.5282,0.3442,0.3491,0
0.3305,0.4132,0.4065,0.4606,0.3963,0.4102,0.3840,0
0.3163,0.3636,0.5871,0.3863,0.3706,0.1767,0.2427,0
0.4212,0.4690,0.6334,0.4578,0.4975,0.1773,0.4141,0
0.5222,0.5351,0.8339,0.4561,0.6094,0.1957,0.4549,0
0.5297,0.5909,0.5926,0.5220,0.5944,0.2676,0.4963,0
0.6128,0.6136,0.9056,0.5253,0.7505,0.2849,0.4751,0
0.3975,0.4360,0.6733,0.4262,0.4690,0.3052,0.3890,0
0.3484,0.3636,0.7831,0.2804,0.4761,0.7697,0.2373,0
0.2786,0.2975,0.7169,0.2528,0.3749,0.2369,0.3245,0
0.2748,0.2975,0.6996,0.2545,0.3763,0.1929,0.3235,0
0.2427,0.2355,0.8421,0.1346,0.4070,0.2205,0.1300,0
0.4636,0.5062,0.6706,0.5507,0.5460,0.5131,0.4968,0
0.4268,0.4401,0.8212,0.3829,0.5930,0.3072,0.3255,0
0.3031,0.3368,0.6470,0.2686,0.3742,0.1034,0.2176,0
0.4504,0.4855,0.7078,0.4516,0.5438,0.0783,0.3018,0
0.4155,0.4442,0.7278,0.3778,0.5324,0.2851,0.3230,0
0.3966,0.4360,0.6697,0.3637,0.4711,0.2521,0.2915,0
0.4032,0.4669,0.5399,0.4386,0.4476,0.1773,0.4097,0
0.3626,0.4112,0.6080,0.3863,0.4576,0.4174,0.3077,0
0.4901,0.5165,0.7641,0.4364,0.5731,0.6277,0.3038,0
0.3683,0.4545,0.4147,0.4595,0.3443,0.4357,0.4318,0
0.3532,0.3864,0.6806,0.3407,0.4056,0.3332,0.3471,0
0.3711,0.4525,0.4319,0.4741,0.3443,0.0931,0.4766,0
0.4193,0.4876,0.5236,0.4521,0.4148,0.1519,0.4530,0
0.3654,0.4008,0.6688,0.2753,0.5324,0.2648,0.2585,0
0.4089,0.4174,0.8394,0.2731,0.5574,0.0490,0.2802,0
0.4523,0.4876,0.7042,0.4296,0.5624,0.1604,0.3461,0
0.1435,0.2190,0.2822,0.1464,0.2865,0.0958,0.0000,0
0.6648,0.7376,0.5372,0.7275,0.6636,0.4305,0.7587,1
0.5902,0.6736,0.4918,0.6188,0.6087,0.5084,0.6686,1
0.6298,0.6860,0.6189,0.6075,0.6871,0.4907,0.6263,1
0.8045,0.7955,0.9074,0.7066,0.9266,0.2823,0.7681,1
0.5883,0.6405,0.6397,0.6295,0.6101,0.4211,0.6509,1
0.5836,0.6632,0.5054,0.5788,0.5759,0.5402,0.6283,1
0.6355,0.7231,0.4701,0.6560,0.5510,0.3977,0.6908,1
0.9556,0.9959,0.6189,0.9459,0.8439,0.4793,0.9513,1
0.7885,0.8430,0.6071,0.8705,0.7192,0.5590,0.9074,1
0.6166,0.6488,0.7359,0.5355,0.6671,0.2721,0.6041,1
0.5609,0.6054,0.6733,0.5495,0.5966,0.6198,0.6701,1
0.7677,0.7810,0.8131,0.6233,0.8746,0.5928,0.6696,1
0.9075,0.9256,0.7377,0.7804,0.8795,0.5731,0.8213,1
0.8480,0.8946,0.6334,0.8361,0.8140,0.0919,0.8636,1
0.8423,0.8884,0.6343,0.8260,0.8346,0.2856,0.8203,1
0.7252,0.7603,0.7160,0.7173,0.7277,0.2182,0.8262,1
0.7828,0.7955,0.8058,0.6672,0.8083,0.1149,0.7829,1
0.7923,0.8781,0.4619,0.9291,0.7413,0.3804,0.9744,1
1.0000,0.9917,0.8240,0.9426,1.0000,0.6521,0.8429,1
0.9717,0.9587,0.8621,0.8733,0.9993,0.5527,0.8872,1
0.8980,0.9463,0.6034,0.9471,0.8232,0.1547,0.9503,1
0.7715,0.7831,0.8194,0.7168,0.8311,0.3062,0.7553,1
0.7762,0.8017,0.7486,0.7731,0.7577,0.3214,0.7553,1
0.7554,0.7521,0.8938,0.6408,0.8767,0.6808,0.6686,1
0.7337,0.8492,0.3367,0.9949,0.6094,0.5419,0.9498,1
0.5930,0.6694,0.5145,0.6982,0.5937,0.3811,0.7129,1
0.8234,0.8636,0.6661,0.8119,0.8411,0.3526,0.8464,1
0.7923,0.8595,0.5499,0.8727,0.6572,0.1793,0.9522,1
0.7158,0.7955,0.5045,0.7725,0.6287,0.2715,0.8636,1
0.7677,0.8120,0.6615,0.7432,0.7512,0.1850,0.7770,1
0.5496,0.5868,0.7123,0.4611,0.6379,0.4488,0.5411,1
0.6988,0.7128,0.8267,0.5580,0.7584,0.1694,0.6489,1
0.8376,0.8450,0.8203,0.6836,0.8995,0.4607,0.7336,1
0.8111,0.8719,0.5771,0.8277,0.7491,0.3370,0.8419,1
0.7894,0.8285,0.6788,0.7596,0.8019,0.3384,0.8021,1
0.7781,0.8017,0.7586,0.6408,0.8239,0.2325,0.6696,1
0.7800,0.7769,0.8848,0.7055,0.8382,0.2702,0.8277,1
0.6648,0.7128,0.6525,0.6385,0.6721,0.3877,0.6942,1
0.8829,0.9318,0.6089,1.0000,0.8076,0.3234,1.0000,1
0.7517,0.7872,0.7114,0.7061,0.7441,0.1265,0.6770,1
0.7422,0.7665,0.7623,0.6802,0.8118,0.1911,0.6278,1
0.8300,0.8905,0.5762,0.7905,0.8275,0.3787,0.7120,1
0.8064,0.8058,0.8657,0.7230,0.9066,0.1747,0.6918,1
0.8074,0.8678,0.5817,0.7658,0.7890,0.7693,0.7553,1
0.9802,1.0000,0.7060,0.9369,0.9701,0.5086,0.8848,1
0.7998,0.8347,0.7015,0.8542,0.7762,0.1928,0.8095,1
0.7904,0.7831,0.9038,0.6486,0.9031,0.4640,0.6061,1
0.8083,0.8347,0.7341,0.7579,0.8446,0.3015,0.8203,1
0.7838,0.7893,0.8412,0.7477,0.8118,0.3737,0.7125,1
0.8914,0.9277,0.6624,0.8975,0.8746,0.2988,0.8868,1
0.9112,0.9298,0.7405,0.7973,0.9494,0.6678,0.8218,1
0.7129,0.7665,0.6270,0.6532,0.6650,0.3711,0.7346,1
0.5269,0.6136,0.4601,0.4859,0.5396,0.4578,0.5830,1
0.7403,0.7355,0.9038,0.6087,0.8133,0.2885,0.6824,1
0.5099,0.5124,0.8920,0.2613,0.6785,0.3343,0.3077,1
0.7705,0.7789,0.8330,0.6824,0.8831,0.4451,0.7253,1
0.7611,0.8264,0.5599,0.7804,0.6871,0.4715,0.7794,1
0.6978,0.7107,0.8276,0.6081,0.7534,0.1940,0.6893,1
0.9037,0.9545,0.5935,0.9088,0.8147,0.1489,0.8203,1
0.6572,0.6715,0.8258,0.5023,0.7555,0.5982,0.5623,1
0.2342,0.3120,0.3621,0.3226,0.2594,0.5902,0.4313,2
0.2578,0.3161,0.4828,0.3615,0.3158,0.8152,0.4535,2
0.2597,0.3182,0.4891,0.2759,0.3165,0.6800,0.3880,2
0.1539,0.1880,0.5181,0.1830,0.2402,0.6116,0.3456,2
0.1161,0.2045,0.1751,0.2337,0.1048,0.4819,0.3245,2
0.0585,0.1488,0.0780,0.2140,0.0406,0.7026,0.3722,2
0.0793,0.1488,0.2305,0.1560,0.0634,0.1893,0.3018,2
0.1794,0.2169,0.5236,0.2072,0.2402,0.4754,0.2378,2
0.1992,0.2686,0.3721,0.2742,0.2003,0.3244,0.3924,2
0.0189,0.1074,0.0236,0.2354,0.0128,0.6107,0.3323,2
0.1171,0.1694,0.3766,0.2050,0.1497,0.5760,0.3880,2
0.1341,0.2293,0.1525,0.2849,0.1041,0.8096,0.3698,2
0.1577,0.2459,0.2287,0.2866,0.1447,0.5189,0.4141,2
0.0557,0.1302,0.1679,0.1807,0.0449,0.3338,0.2373,2
0.0727,0.1322,0.2731,0.1554,0.0891,0.4269,0.3663,2
0.0567,0.1322,0.1561,0.1976,0.0321,0.6563,0.3447,2
0.0708,0.0950,0.4673,0.0867,0.1561,0.3357,0.2383,2
0.1454,0.2727,0.0000,0.2787,0.0820,0.5279,0.3452,2
0.1095,0.2293,0.0009,0.3069,0.0342,0.4698,0.3895,2
0.0850,0.1674,0.1652,0.2280,0.0463,0.6011,0.3895,2
0.1841,0.2603,0.3122,0.3108,0.1775,0.3013,0.4786,2
0.1350,0.1901,0.3829,0.2539,0.1283,0.4559,0.3885,2
0.1379,0.2066,0.3040,0.2072,0.1547,0.5491,0.2595,2
0.1851,0.2397,0.4328,0.2444,0.2409,0.4751,0.3235,2
0.0519,0.0785,0.4328,0.0631,0.1169,0.7311,0.2610,2
0.1426,0.1529,0.6461,0.1160,0.2217,0.1867,0.2644,2
0.1747,0.2438,0.3457,0.2365,0.1903,0.5408,0.3698,2
0.1473,0.2149,0.3285,0.2917,0.1475,0.3735,0.4032,2
0.0718,0.1467,0.1906,0.1560,0.0271,0.4644,0.3018,2
0.0614,0.1219,0.2523,0.1075,0.0606,0.3583,0.2802,2
0.0406,0.1219,0.0980,0.2399,0.0506,0.7762,0.3171,2
0.0907,0.1426,0.3394,0.1509,0.1532,0.7736,0.2152,2
0.0642,0.1157,0.3067,0.1064,0.0948,0.4608,0.2368,2
0.0765,0.1384,0.2668,0.1334,0.0948,0.6271,0.2806,2
0.0227,0.1136,0.0163,0.2134,0.0078,0.5743,0.3279,2
0.0198,0.0331,0.4619,0.0462,0.1361,0.5211,0.2678,2
0.0633,0.1240,0.2486,0.1616,0.0570,0.5942,0.2821,2
0.0142,0.0661,0.2250,0.1385,0.0086,0.5119,0.2186,2
0.0840,0.1322,0.3557,0.1582,0.0912,0.6645,0.2378,2
0.1530,0.2190,0.3376,0.2579,0.1875,0.1165,0.3245,2
0.0774,0.1116,0.4347,0.1075,0.1033,0.5450,0.1507,2
0.1766,0.2066,0.5672,0.1898,0.2758,0.5489,0.3092,2
0.1511,0.1963,0.4519,0.1920,0.1989,0.5320,0.3146,2
0.1001,0.1364,0.4483,0.1177,0.1568,0.5778,0.3033,2
0.2172,0.2810,0.4174,0.3356,0.2823,0.7047,0.3924,2
0.0916,0.1860,0.1062,0.2613,0.0378,0.4287,0.3264,2
0.1152,0.2149,0.1062,0.2894,0.0613,0.5374,0.4101,2
0.0302,0.0806,0.2641,0.1064,0.0321,0.4439,0.2152,2
0.0604,0.0847,0.4655,0.1070,0.1361,0.8788,0.2157,2
0.0000,0.0000,0.5145,0.0000,0.1119,0.5474,0.1354,2
0.0321,0.0806,0.2804,0.0828,0.0620,0.6024,0.2590,2
0.0642,0.0930,0.4374,0.1081,0.1240,0.4187,0.2373,2
0.1209,0.1260,0.6479,0.1312,0.2302,0.3682,0.3018,2
0.0217,0.0868,0.1588,0.1582,0.0000,0.5315,0.2806,2
0.1435,0.1777,0.5064,0.1898,0.2459,0.4378,0.2427,2
0.2087,0.2190,0.7069,0.1470,0.3535,0.5341,0.1945,2
0.2077,0.2314,0.6397,0.1830,0.3022,0.6134,0.2161,2
0.2625,0.2831,0.6969,0.2370,0.3550,0.5077,0.2816,2
0.1917,0.2603,0.3630,0.2877,0.2003,0.3304,0.3506,2
0.2049,0.2004,0.8013,0.0980,0.3742,0.2682,0.1531,2

Test data:

# wheat_test.txt
#
0.0784,0.0930,0.5463,0.0614,0.1568,0.2516,0.0433,0
0.0604,0.0455,0.6887,0.0017,0.1775,0.1955,0.0906,0
0.1671,0.1612,0.7641,0.0997,0.2937,0.3192,0.0423,0
0.2483,0.2955,0.5436,0.2793,0.3136,0.4410,0.2802,0
0.2068,0.2397,0.5762,0.2044,0.2823,0.0534,0.1295,0
0.2162,0.2252,0.7241,0.1351,0.3485,0.2063,0.0433,0
0.3541,0.4050,0.5853,0.4116,0.3991,0.0712,0.3107,0
0.3229,0.3884,0.4936,0.3998,0.3763,0.1888,0.3018,0
0.3569,0.4091,0.5853,0.3773,0.3728,0.0909,0.3845,0
0.2021,0.2769,0.3421,0.2889,0.1796,0.3599,0.2698,0
0.7280,0.7190,0.9319,0.6081,0.8019,0.2694,0.7105,1
0.7885,0.8079,0.7813,0.7010,0.8517,0.2786,0.7041,1
0.4523,0.5145,0.5672,0.5546,0.4547,0.4807,0.6283,1
0.5260,0.6033,0.5109,0.5327,0.5453,0.4552,0.6283,1
0.4693,0.5124,0.6733,0.4938,0.5545,0.5470,0.6539,1
0.4523,0.4649,0.8249,0.3255,0.5952,0.3686,0.4530,1
0.6393,0.6921,0.6388,0.7016,0.6728,0.3590,0.7149,1
0.4703,0.5661,0.4047,0.5749,0.4284,0.2438,0.6696,1
0.4731,0.5579,0.4528,0.5253,0.4676,0.2548,0.6071,1
0.5326,0.5723,0.6978,0.5479,0.6001,0.3906,0.6908,1
0.1690,0.2128,0.4791,0.1802,0.2559,0.6120,0.2590,2
0.1964,0.1880,0.8131,0.0479,0.3599,0.1996,0.1113,2
0.0557,0.0640,0.5436,0.0619,0.1283,0.4272,0.1521,2
0.1992,0.2066,0.7196,0.1599,0.3286,1.0000,0.2368,2
0.1681,0.2190,0.4410,0.1717,0.2352,0.4101,0.2373,2
0.1511,0.1632,0.6370,0.1340,0.2502,0.3726,0.1728,2
0.0604,0.0971,0.3902,0.1357,0.1176,0.4629,0.2383,2
0.2465,0.2583,0.7278,0.1898,0.4291,0.9817,0.2644,2
0.1180,0.1653,0.3993,0.1554,0.1468,0.3683,0.2585,2
0.1615,0.1921,0.5472,0.1937,0.2452,0.6335,0.2678,2
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