Given the following code:
# import required to process csv files with pandas
import pandas as pd
#for array manipulation
import numpy as np
# use pandas to import a csv file
multifeature_csv = pd.read_csv(r'C:\Users\james\Anaconda3JamesData\AI_Multifeature_LSTM_series_100.csv', header=None, na_values='float64')
# remove the first column
myData_firstColumnRemoved = multifeature_csv.iloc[:, 1:8].values
# transform to numpy array
myData = np.array(myData_firstColumnRemoved)
print (myData)
[[125.258 125.493 125.157 125.476 26.793 10.51 34.097]
[125.476 125.564 124.386 124.584 31.196 9.556 40.766]
[124.585 124.873 123.875 124.187 35.836 7.996 42.47 ]
[124.187 124.335 123.95 124.076 39.896 7.485 39.757]
[124.075 124.083 123.517 123.524 44.008 6.793 43.151]
[123.524 123.536 117.85 122.016 49.876 3.388 71.481]
[122.015 122.029 121.26 121.502 55.01 3.156 66.591]
[121.502 122.809 121.323 122.46 57.18 9.337 58.247]
[122.459 122.479 121.928 122.446 59.079 8.89 55.456]
[122.446 123.398 122.045 123.123 58.185 15.564 49.187]
[123.121 123.124 122.351 122.351 57.402 14.546 45.97 ]
[122.34 123.096 122.336 122.967 56.732 13.599 43.105]
[122.968 123.574 122.926 123.29 54.766 17.012 40.659]
[123.29 123.343 122.921 123.175 53.051 16.358 39.14 ]
[123.174 123.338 123.041 123.142 51.551 15.891 38.024]
[123.143 123.787 122.834 123.68 49.145 18.706 36.554]
[123.681 123.847 123.588 123.628 46.857 18.822 35.609]
[123.576 123.904 123.576 123.757 44.692 18.772 34.514]
[123.757 123.769 123.424 123.58 43.074 18.067 34.873]
[123.58 123.847 123.394 123.78 41.434 18.024 33.44 ]
[123.78 124.156 123.718 124.14 38.896 20.674 31.752]
[124.141 124.575 124.052 124.55 35.302 24.317 29.807]
[124.548 124.789 124.53 124.725 31.499 26.173 28.858]
[124.73 124.849 124.244 124.274 28.755 24.961 30.23 ]
[124.274 124.69 124.23 124.481 26.392 23.517 28.658]
[124.48 124.795 124.417 124.669 23.959 23.726 27.254]
[124.669 124.714 124.324 124.405 22.119 22.494 27.077]
[124.404 124.608 124.111 124.371 21.172 20.99 28.132]
[124.371 124.495 124.259 124.406 20.343 20.293 27.197]
[124.375 124.699 124.339 124.638 18.736 22.187 25.781]
[124.637 124.85 124.637 124.744 16.699 23.761 24.948]
[124.744 124.955 124.642 124.804 14.745 24.239 23.727]
[124.805 124.841 124.542 124.64 13.199 23.071 24.196]
[124.64 125.082 124.449 124.907 11.893 24.564 23.25 ]
[124.908 125.039 124.678 124.83 10.75 23.141 21.903]
[124.83 125.056 124.516 124.751 9.739 21.426 22.598]
[124.749 124.844 124.6 124.746 8.854 20.562 21.687]
[124.746 124.778 124.449 124.57 8.812 19.419 23.033]
[124.57 124.77 124.493 124.639 8.775 18.482 21.922]
[124.639 124.78 124.349 124.716 9.401 17.266 22.786]
[124.716 124.782 124.452 124.694 9.935 16.287 21.447]
[124.694 124.881 124.51 124.842 9.718 16.981 20.015]
[124.846 124.913 124.711 124.818 9.304 16.938 19.257]
[124.818 124.987 124.718 124.801 8.412 17.486 18.259]
[124.802 124.963 124.64 124.722 8.163 16.381 18.631]
[124.723 124.755 124.225 124.477 10.294 14.728 24.654]
[124.477 124.526 124.33 124.436 12.158 14.155 23.696]
[124.228 124.42 124.127 124.163 14.755 13.274 26.311]
[124.165 124.227 123.943 124.079 17.799 12.499 28.557]
[124.08 124.199 123.869 123.954 20.757 11.644 28.137]
[123.953 124.056 123.759 123.979 23.772 10.916 28.694]
[123.979 124.332 123.863 124.151 23.927 15.549 25.92 ]
[124.151 124.167 124.021 124.03 24.062 15.058 25.101]
[124.029 124.599 123.988 124.496 21.224 22.026 22.635]
[124.495 124.842 124.487 124.828 19.767 25.418 20.981]
[124.827 124.843 124.008 124.115 18.658 21.447 26.691]
[124.115 124.271 123.626 123.936 19.236 18.958 30.468]
[123.937 124.316 123.665 123.702 19.474 17.601 27.036]
[123.701 124.077 123.387 123.98 20.712 15.585 28.554]
[123.981 124.033 123.537 123.574 21.796 14.309 26.216]
[123.573 123.824 123.511 123.779 22.844 13.551 25.267]
[123.779 124.021 123.651 123.939 22.375 16.074 23.661]
[123.94 124.065 123.775 123.921 21.665 16.028 22.449]
[123.922 124.224 123.881 124.206 19.974 17.895 21.066]
[124.207 124.404 124.096 124.28 17.574 20.187 19.876]
[124.28 124.343 124.023 124.071 15.721 18.979 20.051]
[124.071 124.168 124.007 124.052 14.199 18.38 19.732]
[124.051 124.055 123.727 123.876 14.495 17.183 24.007]
[123.877 124.144 123.845 124.052 14.107 17.944 22.556]
[124.053 124.188 123.895 124.072 13.444 17.767 21.196]
[124.072 124.666 124.034 124.409 13.584 24.913 18.579]
[124.41 124.655 124.062 124.6 13.706 22.134 16.507]
[124.601 124.664 124.507 124.541 13.864 21.626 15.995]
[124.541 124.89 124.508 124.874 15.212 24.461 14.787]
[124.873 124.961 124.659 124.708 16.743 24.403 13.889]
[124.709 124.82 124.418 124.747 16.161 22.438 17.599]
[124.747 124.812 124.642 124.727 15.651 21.639 16.973]
[124.32 124.739 124.32 124.584 14.413 19.761 22.169]
[124.584 124.818 124.575 124.637 12.793 20.42 21.023]
[124.636 124.79 124.595 124.702 11.376 19.542 20.119]
[124.702 124.766 124.544 124.588 10.503 18.557 20.263]
[124.588 124.659 124.531 124.624 9.837 17.991 19.954]
[124.625 124.7 124.579 124.595 8.897 18.473 19.35 ]
[124.596 124.699 124.514 124.634 8.619 17.59 20.104]
[124.635 124.647 124.235 124.276 10.377 15.772 25.026]
[124.275 124.393 124.099 124.35 12.718 14.604 26.597]
[124.35 124.444 124.109 124.16 14.24 14.656 24.371]
[124.16 124.369 124.04 124.28 16. 13.458 24.093]
[124.279 124.323 124.032 124.22 17.591 12.48 22.542]
[124.22 124.645 124.194 124.62 15.779 18.886 20.091]
[124.619 124.774 124.568 124.613 14.445 21.119 19.066]
[124.612 124.743 124.371 124.523 13.529 19.201 22.143]
[124.522 124.757 124.486 124.71 12.609 18.263 20.662]
[124.709 124.926 124.598 124.693 11.642 20.944 18.997]
[124.694 124.829 124.651 124.717 10.796 19.996 18.137]
[124.707 124.854 124.62 124.658 9.98 19.432 17.841]
[124.657 124.794 124.582 124.789 8.904 18.343 17.846]
[124.79 124.888 124.371 124.516 8.586 18.322 20.81 ]
[124.516 124.642 123.968 124.176 10.857 15.497 26.82 ]
[124.177 124.586 123.852 123.91 13.427 13.112 25.124]]
So here we have a 2 dimensional data set. In this experiment I want to normalize the first 4 columns and then denormalize them back to their original state. Effectively a reverse transform. I’ve been playing with MinMaxScaler but it’s been producing some wierd results for me so I want to try a different way.
First I will try to normalize all the values in the first 4 columns between 0 and 1.
The formula to do this is as follows:
$latex x=\frac{y-min}{max-min}&s=4 $
Rearranging the above algebra to reverse the transformation we have:
$latex \displaystyle (max-min)+min=y&s=2$
# get the maximum value of all the values in the first 4 columns
maximumFirst4Columns=myData[:,0:4].max() # x,y # all rows selecting columns 0,1,2,3 = 0:4
minimumFirst4Columns=myData[:,0:4].min() # x,y # all rows selecting columns 0,1,2,3 = 0:4
# get the maximum value of all the values in the first 4 columns
maximumFirst4Columns=myData[:,0:4].max() # x,y # all rows selecting columns 0,1,2,3 = 0:4
minimumFirst4Columns=myData[:,0:4].min() # x,y # all rows selecting columns 0,1,2,3 = 0:4
# normalize data of first 4 columns from 0-1
myData[:,0:4] = (myData[:,0:4] - minimumFirst4Columns)/(maximumFirst4Columns - minimumFirst4Columns)
print (myData)
# denormalize data (reverse the transformation) of first 4 columns from 0-1
myData[:,0:4] = (myData[:,0:4] * (maximumFirst4Columns - minimumFirst4Columns))+minimumFirst4Columns
print (myData)
[[ 0.96033186 0.99079596 0.94723879 0.98859217 26.793 10.51
34.097 ]
[ 0.98859217 1. 0.84729064 0.87295826 31.196 9.556
40.766 ]
[ 0.87308789 0.91042261 0.78104745 0.82149339 35.836 7.996
42.47 ]
[ 0.82149339 0.84067928 0.79077003 0.80710397 39.896 7.485
39.757 ]
[ 0.80697433 0.80801141 0.73463832 0.73554576 44.008 6.793
43.151 ]
[ 0.73554576 0.73710137 0. 0.54005704 49.876 3.388
71.481 ]
[ 0.5399274 0.54174229 0.44205341 0.47342494 55.01 3.156
66.591 ]
[ 0.47342494 0.64285714 0.45022038 0.59761473 57.18 9.337
58.247 ]
[ 0.59748509 0.60007778 0.52864921 0.59579984 59.079 8.89
55.456 ]
[ 0.59579984 0.71921182 0.54381644 0.68356235 58.185 15.564
49.187 ]
[ 0.68330309 0.68369199 0.58348457 0.58348457 57.402 14.546
45.97 ]
[ 0.58205859 0.68006222 0.58154006 0.66333938 56.732 13.599
43.105 ]
[ 0.66346902 0.74202748 0.65802437 0.7052113 54.766 17.012
40.659 ]
[ 0.7052113 0.71208193 0.6573762 0.69030334 53.051 16.358
39.14 ]
[ 0.69017371 0.71143376 0.67293233 0.68602541 51.551 15.891
38.024 ]
[ 0.68615504 0.76963962 0.646098 0.75576873 49.145 18.706
36.554 ]
[ 0.75589837 0.77741768 0.74384236 0.74902774 46.857 18.822
35.609 ]
[ 0.74228675 0.78480684 0.74228675 0.76575058 44.692 18.772
34.514 ]
[ 0.76575058 0.7673062 0.72258232 0.74280529 43.074 18.067
34.873 ]
[ 0.74280529 0.77741768 0.71869328 0.76873218 41.434 18.024
33.44 ]
[ 0.76873218 0.81747472 0.76069484 0.81540057 38.896 20.674
31.752 ]
[ 0.8155302 0.87179155 0.80399274 0.86855069 35.302 24.317
29.807 ]
[ 0.86829142 0.89953332 0.865958 0.89123671 31.499 26.173
28.858 ]
[ 0.89188488 0.90731138 0.82888255 0.83277158 28.755 24.961
30.23 ]
[ 0.83277158 0.88669951 0.82706767 0.85960591 26.392 23.517
28.658 ]
[ 0.85947628 0.90031112 0.85130931 0.88397718 23.959 23.726
27.254 ]
[ 0.88397718 0.88981073 0.83925331 0.84975369 22.119 22.494
27.077 ]
[ 0.84962406 0.87606948 0.81164117 0.84534612 21.172 20.99
28.132 ]
[ 0.84534612 0.86142079 0.83082707 0.84988333 20.343 20.293
27.197 ]
[ 0.84586466 0.88786622 0.84119782 0.87995852 18.736 22.187
25.781 ]
[ 0.87982888 0.90744102 0.87982888 0.89369977 16.699 23.761
24.948 ]
[ 0.89369977 0.92105263 0.88047705 0.90147783 14.745 24.239
23.727 ]
[ 0.90160747 0.90627431 0.86751361 0.88021779 13.199 23.071
24.196 ]
[ 0.88021779 0.9375162 0.85545761 0.91483018 11.893 24.564
23.25 ]
[ 0.91495981 0.93194192 0.88514389 0.90484833 10.75 23.141
21.903 ]
[ 0.90484833 0.93414571 0.86414312 0.89460721 9.739 21.426
22.598 ]
[ 0.89434794 0.90666321 0.87503241 0.89395904 8.854 20.562
21.687 ]
[ 0.89395904 0.89810734 0.85545761 0.87114338 8.812 19.419
23.033 ]
[ 0.87114338 0.89707026 0.86116152 0.88008815 8.775 18.482
21.922 ]
[ 0.88008815 0.89836661 0.84249417 0.89007 9.401 17.266
22.786 ]
[ 0.89007 0.89862588 0.85584651 0.88721805 9.935 16.287
21.447 ]
[ 0.88721805 0.91145968 0.86336531 0.90640394 9.718 16.981
20.015 ]
[ 0.90692248 0.91560799 0.88942183 0.90329271 9.304 16.938
19.257 ]
[ 0.90329271 0.92520093 0.89032927 0.90108893 8.412 17.486
18.259 ]
[ 0.90121856 0.92208971 0.88021779 0.89084781 8.163 16.381
18.631 ]
[ 0.89097744 0.89512575 0.8264195 0.85908737 10.294 14.728
24.654 ]
[ 0.85908737 0.86543946 0.84003111 0.85377236 12.158 14.155
23.696 ]
[ 0.8268084 0.85169821 0.81371532 0.81838216 14.755 13.274
26.311 ]
[ 0.81864143 0.82667877 0.78986259 0.80749287 17.799 12.499
28.557 ]
[ 0.8076225 0.823049 0.78026964 0.79128857 20.757 11.644
28.137 ]
[ 0.79115893 0.80451128 0.76600985 0.79452943 23.772 10.916
28.694 ]
[ 0.79452943 0.84029038 0.77949183 0.81682655 23.927 15.549
25.92 ]
[ 0.81682655 0.8189007 0.79997407 0.80114078 24.062 15.058
25.101 ]
[ 0.80101115 0.87490277 0.79569614 0.86155043 21.224 22.026
22.635 ]
[ 0.86142079 0.90640394 0.86038372 0.90458906 19.767 25.418
20.981 ]
[ 0.90445942 0.90653358 0.79828883 0.81215971 18.658 21.447
26.691 ]
[ 0.81215971 0.83238268 0.74876847 0.78895515 19.236 18.958
30.468 ]
[ 0.78908478 0.83821623 0.75382422 0.75862069 19.474 17.601
27.036 ]
[ 0.75849106 0.8072336 0.71778584 0.79465906 20.712 15.585
28.554 ]
[ 0.7947887 0.80152969 0.73723101 0.74202748 21.796 14.309
26.216 ]
[ 0.74189785 0.77443609 0.73386051 0.76860254 22.844 13.551
25.267 ]
[ 0.76860254 0.79997407 0.75200933 0.78934405 22.375 16.074
23.661 ]
[ 0.78947368 0.80567799 0.768084 0.78701063 21.665 16.028
22.449 ]
[ 0.78714026 0.82628986 0.78182525 0.82395644 19.974 17.895
21.066 ]
[ 0.82408608 0.84962406 0.80969666 0.83354939 17.574 20.187
19.876 ]
[ 0.83354939 0.84171636 0.80023334 0.80645579 15.721 18.979
20.051 ]
[ 0.80645579 0.81903033 0.79815919 0.80399274 14.199 18.38
19.732 ]
[ 0.80386311 0.80438164 0.76186155 0.78117708 14.495 17.183
24.007 ]
[ 0.78130672 0.81591911 0.77715841 0.80399274 14.107 17.944
22.556 ]
[ 0.80412237 0.82162302 0.78364013 0.80658543 13.444 17.767
21.196 ]
[ 0.80658543 0.88358828 0.80165932 0.85027223 13.584 24.913
18.579 ]
[ 0.85040187 0.8821623 0.80528908 0.87503241 13.706 22.134
16.507 ]
[ 0.87516204 0.88332901 0.86297641 0.86738398 13.864 21.626
15.995 ]
[ 0.86738398 0.91262639 0.86310604 0.91055224 15.212 24.461
14.787 ]
[ 0.91042261 0.92183044 0.88268084 0.88903293 16.743 24.403
13.889 ]
[ 0.88916256 0.90355198 0.85143894 0.89408867 16.161 22.438
17.599 ]
[ 0.89408867 0.90251491 0.88047705 0.89149598 15.651 21.639
16.973 ]
[ 0.83873477 0.89305159 0.83873477 0.87295826 14.413 19.761
22.169 ]
[ 0.87295826 0.90329271 0.87179155 0.87982888 12.793 20.42
21.023 ]
[ 0.87969925 0.89966295 0.87438424 0.88825512 11.376 19.542
20.119 ]
[ 0.88825512 0.89655172 0.86777288 0.8734768 10.503 18.557
20.263 ]
[ 0.8734768 0.88268084 0.86608763 0.87814363 9.837 17.991
19.954 ]
[ 0.87827327 0.88799585 0.87231009 0.87438424 8.897 18.473
19.35 ]
[ 0.87451387 0.88786622 0.86388385 0.87943998 8.619 17.59
20.104 ]
[ 0.87956961 0.88112523 0.82771584 0.83303085 10.377 15.772
25.026 ]
[ 0.83290122 0.84819808 0.81008556 0.8426238 12.718 14.604
26.597 ]
[ 0.8426238 0.85480944 0.8113819 0.81799326 14.24 14.656
24.371 ]
[ 0.81799326 0.84508686 0.80243713 0.83354939 16. 13.458
24.093 ]
[ 0.83341976 0.83912367 0.80140005 0.82577132 17.591 12.48
22.542 ]
[ 0.82577132 0.88086596 0.82240083 0.8776251 15.779 18.886
20.091 ]
[ 0.87749546 0.8975888 0.87088411 0.87671766 14.445 21.119
19.066 ]
[ 0.87658802 0.89357013 0.84534612 0.86505056 13.529 19.201
22.143 ]
[ 0.86492092 0.89538501 0.86025408 0.8892922 12.609 18.263
20.662 ]
[ 0.88916256 0.91729323 0.87477314 0.88708841 11.642 20.944
18.997 ]
[ 0.88721805 0.90471869 0.88164376 0.89019964 10.796 19.996
18.137 ]
[ 0.88890329 0.90795955 0.8776251 0.88255121 9.98 19.432
17.841 ]
[ 0.88242157 0.90018149 0.87269899 0.89953332 8.904 18.343
17.846 ]
[ 0.89966295 0.91236712 0.84534612 0.86414312 8.586 18.322
20.81 ]
[ 0.86414312 0.88047705 0.79310345 0.82006741 10.857 15.497
26.82 ]
[ 0.82019704 0.87321753 0.77806585 0.78558465 13.427 13.112
25.124 ]]
[[125.258 125.493 125.157 125.476 26.793 10.51 34.097]
[125.476 125.564 124.386 124.584 31.196 9.556 40.766]
[124.585 124.873 123.875 124.187 35.836 7.996 42.47 ]
[124.187 124.335 123.95 124.076 39.896 7.485 39.757]
[124.075 124.083 123.517 123.524 44.008 6.793 43.151]
[123.524 123.536 117.85 122.016 49.876 3.388 71.481]
[122.015 122.029 121.26 121.502 55.01 3.156 66.591]
[121.502 122.809 121.323 122.46 57.18 9.337 58.247]
[122.459 122.479 121.928 122.446 59.079 8.89 55.456]
[122.446 123.398 122.045 123.123 58.185 15.564 49.187]
[123.121 123.124 122.351 122.351 57.402 14.546 45.97 ]
[122.34 123.096 122.336 122.967 56.732 13.599 43.105]
[122.968 123.574 122.926 123.29 54.766 17.012 40.659]
[123.29 123.343 122.921 123.175 53.051 16.358 39.14 ]
[123.174 123.338 123.041 123.142 51.551 15.891 38.024]
[123.143 123.787 122.834 123.68 49.145 18.706 36.554]
[123.681 123.847 123.588 123.628 46.857 18.822 35.609]
[123.576 123.904 123.576 123.757 44.692 18.772 34.514]
[123.757 123.769 123.424 123.58 43.074 18.067 34.873]
[123.58 123.847 123.394 123.78 41.434 18.024 33.44 ]
[123.78 124.156 123.718 124.14 38.896 20.674 31.752]
[124.141 124.575 124.052 124.55 35.302 24.317 29.807]
[124.548 124.789 124.53 124.725 31.499 26.173 28.858]
[124.73 124.849 124.244 124.274 28.755 24.961 30.23 ]
[124.274 124.69 124.23 124.481 26.392 23.517 28.658]
[124.48 124.795 124.417 124.669 23.959 23.726 27.254]
[124.669 124.714 124.324 124.405 22.119 22.494 27.077]
[124.404 124.608 124.111 124.371 21.172 20.99 28.132]
[124.371 124.495 124.259 124.406 20.343 20.293 27.197]
[124.375 124.699 124.339 124.638 18.736 22.187 25.781]
[124.637 124.85 124.637 124.744 16.699 23.761 24.948]
[124.744 124.955 124.642 124.804 14.745 24.239 23.727]
[124.805 124.841 124.542 124.64 13.199 23.071 24.196]
[124.64 125.082 124.449 124.907 11.893 24.564 23.25 ]
[124.908 125.039 124.678 124.83 10.75 23.141 21.903]
[124.83 125.056 124.516 124.751 9.739 21.426 22.598]
[124.749 124.844 124.6 124.746 8.854 20.562 21.687]
[124.746 124.778 124.449 124.57 8.812 19.419 23.033]
[124.57 124.77 124.493 124.639 8.775 18.482 21.922]
[124.639 124.78 124.349 124.716 9.401 17.266 22.786]
[124.716 124.782 124.452 124.694 9.935 16.287 21.447]
[124.694 124.881 124.51 124.842 9.718 16.981 20.015]
[124.846 124.913 124.711 124.818 9.304 16.938 19.257]
[124.818 124.987 124.718 124.801 8.412 17.486 18.259]
[124.802 124.963 124.64 124.722 8.163 16.381 18.631]
[124.723 124.755 124.225 124.477 10.294 14.728 24.654]
[124.477 124.526 124.33 124.436 12.158 14.155 23.696]
[124.228 124.42 124.127 124.163 14.755 13.274 26.311]
[124.165 124.227 123.943 124.079 17.799 12.499 28.557]
[124.08 124.199 123.869 123.954 20.757 11.644 28.137]
[123.953 124.056 123.759 123.979 23.772 10.916 28.694]
[123.979 124.332 123.863 124.151 23.927 15.549 25.92 ]
[124.151 124.167 124.021 124.03 24.062 15.058 25.101]
[124.029 124.599 123.988 124.496 21.224 22.026 22.635]
[124.495 124.842 124.487 124.828 19.767 25.418 20.981]
[124.827 124.843 124.008 124.115 18.658 21.447 26.691]
[124.115 124.271 123.626 123.936 19.236 18.958 30.468]
[123.937 124.316 123.665 123.702 19.474 17.601 27.036]
[123.701 124.077 123.387 123.98 20.712 15.585 28.554]
[123.981 124.033 123.537 123.574 21.796 14.309 26.216]
[123.573 123.824 123.511 123.779 22.844 13.551 25.267]
[123.779 124.021 123.651 123.939 22.375 16.074 23.661]
[123.94 124.065 123.775 123.921 21.665 16.028 22.449]
[123.922 124.224 123.881 124.206 19.974 17.895 21.066]
[124.207 124.404 124.096 124.28 17.574 20.187 19.876]
[124.28 124.343 124.023 124.071 15.721 18.979 20.051]
[124.071 124.168 124.007 124.052 14.199 18.38 19.732]
[124.051 124.055 123.727 123.876 14.495 17.183 24.007]
[123.877 124.144 123.845 124.052 14.107 17.944 22.556]
[124.053 124.188 123.895 124.072 13.444 17.767 21.196]
[124.072 124.666 124.034 124.409 13.584 24.913 18.579]
[124.41 124.655 124.062 124.6 13.706 22.134 16.507]
[124.601 124.664 124.507 124.541 13.864 21.626 15.995]
[124.541 124.89 124.508 124.874 15.212 24.461 14.787]
[124.873 124.961 124.659 124.708 16.743 24.403 13.889]
[124.709 124.82 124.418 124.747 16.161 22.438 17.599]
[124.747 124.812 124.642 124.727 15.651 21.639 16.973]
[124.32 124.739 124.32 124.584 14.413 19.761 22.169]
[124.584 124.818 124.575 124.637 12.793 20.42 21.023]
[124.636 124.79 124.595 124.702 11.376 19.542 20.119]
[124.702 124.766 124.544 124.588 10.503 18.557 20.263]
[124.588 124.659 124.531 124.624 9.837 17.991 19.954]
[124.625 124.7 124.579 124.595 8.897 18.473 19.35 ]
[124.596 124.699 124.514 124.634 8.619 17.59 20.104]
[124.635 124.647 124.235 124.276 10.377 15.772 25.026]
[124.275 124.393 124.099 124.35 12.718 14.604 26.597]
[124.35 124.444 124.109 124.16 14.24 14.656 24.371]
[124.16 124.369 124.04 124.28 16. 13.458 24.093]
[124.279 124.323 124.032 124.22 17.591 12.48 22.542]
[124.22 124.645 124.194 124.62 15.779 18.886 20.091]
[124.619 124.774 124.568 124.613 14.445 21.119 19.066]
[124.612 124.743 124.371 124.523 13.529 19.201 22.143]
[124.522 124.757 124.486 124.71 12.609 18.263 20.662]
[124.709 124.926 124.598 124.693 11.642 20.944 18.997]
[124.694 124.829 124.651 124.717 10.796 19.996 18.137]
[124.707 124.854 124.62 124.658 9.98 19.432 17.841]
[124.657 124.794 124.582 124.789 8.904 18.343 17.846]
[124.79 124.888 124.371 124.516 8.586 18.322 20.81 ]
[124.516 124.642 123.968 124.176 10.857 15.497 26.82 ]
[124.177 124.586 123.852 123.91 13.427 13.112 25.124]]
We can see this works very well. The first 4 columns of the data is nomalized and then this normalization is reversed restoring the data back to it’s original form.
Let’s say we don’t want to normalize
We can use the formula:
$latex x=0.001+(\frac{y-min}{max-min} * 0.999)&s=4 $
To reverse the equation above (by re-arranging it) we get:
$latex y=min+\frac{(x-0.001)(max-min)}{0.999} &s=4 $
In code, the two normalization statements for nomalizing inbetween 0.001 and 1 and inverse transforming (denormalizing) the data is as follows.
# normalize data of first 4 columns from 0.001 to 1
myData[:,0:4] = 0.001+((myData[:,0:4] - minimumFirst4Columns)/(maximumFirst4Columns - minimumFirst4Columns)*0.999)
print (myData)
# denormalize data (reverse the transformation) of first 4 columns to the original data
myData[:,0:4] =minimumFirst4Columns+ (((myData[:,0:4]-0.001)*(maximumFirst4Columns - minimumFirst4Columns))/0.999)
print (myData)
[[9.60371532e-01 9.90805159e-01 9.47291548e-01 9.88603578e-01
2.67930000e+01 1.05100000e+01 3.40970000e+01]
[9.88603578e-01 1.00000000e+00 8.47443350e-01 8.73085299e-01
3.11960000e+01 9.55600000e+00 4.07660000e+01]
[8.73214804e-01 9.10512186e-01 7.81266399e-01 8.21671895e-01
3.58360000e+01 7.99600000e+00 4.24700000e+01]
[8.21671895e-01 8.40838605e-01 7.90979258e-01 8.07296863e-01
3.98960000e+01 7.48500000e+00 3.97570000e+01]
[8.07167358e-01 8.08203396e-01 7.34903682e-01 7.35810215e-01
4.40080000e+01 6.79300000e+00 4.31510000e+01]
[7.35810215e-01 7.37364273e-01 1.00000000e-03 5.40516982e-01
4.98760000e+01 3.38800000e+00 7.14810000e+01]
[5.40387477e-01 5.42200544e-01 4.42611356e-01 4.73951517e-01
5.50100000e+01 3.15600000e+00 6.65910000e+01]
[4.73951517e-01 6.43214286e-01 4.50770158e-01 5.98017112e-01
5.71800000e+01 9.33700000e+00 5.82470000e+01]
[5.97887607e-01 6.00477703e-01 5.29120560e-01 5.96204045e-01
5.90790000e+01 8.89000000e+00 5.54560000e+01]
[5.96204045e-01 7.19492611e-01 5.44272621e-01 6.83878792e-01
5.81850000e+01 1.55640000e+01 4.91870000e+01]
[6.83619782e-01 6.84008297e-01 5.83901089e-01 5.83901089e-01
5.74020000e+01 1.45460000e+01 4.59700000e+01]
[5.82476536e-01 6.80382162e-01 5.81958517e-01 6.63676044e-01
5.67320000e+01 1.35990000e+01 4.31050000e+01]
[6.63805548e-01 7.42285455e-01 6.58366347e-01 7.05506093e-01
5.47660000e+01 1.70120000e+01 4.06590000e+01]
[7.05506093e-01 7.12369847e-01 6.57718823e-01 6.90613041e-01
5.30510000e+01 1.63580000e+01 3.91400000e+01]
[6.90483536e-01 7.11722323e-01 6.73259398e-01 6.86339383e-01
5.15510000e+01 1.58910000e+01 3.80240000e+01]
[6.86468888e-01 7.69869977e-01 6.46451906e-01 7.56012963e-01
4.91450000e+01 1.87060000e+01 3.65540000e+01]
[7.56142468e-01 7.77640264e-01 7.44098522e-01 7.49278714e-01
4.68570000e+01 1.88220000e+01 3.56090000e+01]
[7.42544465e-01 7.85022038e-01 7.42544465e-01 7.65984833e-01
4.46920000e+01 1.87720000e+01 3.45140000e+01]
[7.65984833e-01 7.67538890e-01 7.22859736e-01 7.43062484e-01
4.30740000e+01 1.80670000e+01 3.48730000e+01]
[7.43062484e-01 7.77640264e-01 7.18974592e-01 7.68963443e-01
4.14340000e+01 1.80240000e+01 3.34400000e+01]
[7.68963443e-01 8.17657247e-01 7.60934146e-01 8.15585170e-01
3.88960000e+01 2.06740000e+01 3.17520000e+01]
[8.15714675e-01 8.71919756e-01 8.04188748e-01 8.68682136e-01
3.53020000e+01 2.43170000e+01 2.98070000e+01]
[8.68423127e-01 8.99633783e-01 8.66092040e-01 8.91345476e-01
3.14990000e+01 2.61730000e+01 2.88580000e+01]
[8.91993000e-01 9.07404071e-01 8.29053669e-01 8.32938813e-01
2.87550000e+01 2.49610000e+01 3.02300000e+01]
[8.32938813e-01 8.86812808e-01 8.27240602e-01 8.59746305e-01
2.63920000e+01 2.35170000e+01 2.86580000e+01]
[8.59616801e-01 9.00410812e-01 8.51457998e-01 8.84093207e-01
2.39590000e+01 2.37260000e+01 2.72540000e+01]
[8.84093207e-01 8.89920923e-01 8.39414052e-01 8.49903941e-01
2.21190000e+01 2.24940000e+01 2.70770000e+01]
[8.49774436e-01 8.76193415e-01 8.11829531e-01 8.45500778e-01
2.11720000e+01 2.09900000e+01 2.81320000e+01]
[8.45500778e-01 8.61559373e-01 8.30996241e-01 8.50033446e-01
2.03430000e+01 2.02930000e+01 2.71970000e+01]
[8.46018797e-01 8.87978351e-01 8.41356624e-01 8.80078558e-01
1.87360000e+01 2.21870000e+01 2.57810000e+01]
[8.79949054e-01 9.07533575e-01 8.79949054e-01 8.93806067e-01
1.66990000e+01 2.37610000e+01 2.49480000e+01]
[8.93806067e-01 9.21131579e-01 8.80596578e-01 9.01576355e-01
1.47450000e+01 2.42390000e+01 2.37270000e+01]
[9.01705859e-01 9.06368032e-01 8.67646098e-01 8.80337568e-01
1.31990000e+01 2.30710000e+01 2.41960000e+01]
[8.80337568e-01 9.37578688e-01 8.55602152e-01 9.14915349e-01
1.18930000e+01 2.45640000e+01 2.32500000e+01]
[9.15044854e-01 9.32009982e-01 8.85258750e-01 9.04943479e-01
1.07500000e+01 2.31410000e+01 2.19030000e+01]
[9.04943479e-01 9.34211563e-01 8.64278973e-01 8.94712600e-01
9.73900000e+00 2.14260000e+01 2.25980000e+01]
[8.94453591e-01 9.06756547e-01 8.75157376e-01 8.94065076e-01
8.85400000e+00 2.05620000e+01 2.16870000e+01]
[8.94065076e-01 8.98209230e-01 8.55602152e-01 8.71272232e-01
8.81200000e+00 1.94190000e+01 2.30330000e+01]
[8.71272232e-01 8.97173192e-01 8.61300363e-01 8.80208063e-01
8.77500000e+00 1.84820000e+01 2.19220000e+01]
[8.80208063e-01 8.98468240e-01 8.42651672e-01 8.90179933e-01
9.40100000e+00 1.72660000e+01 2.27860000e+01]
[8.90179933e-01 8.98727249e-01 8.55990666e-01 8.87330827e-01
9.93500000e+00 1.62870000e+01 2.14470000e+01]
[8.87330827e-01 9.11548224e-01 8.63501945e-01 9.06497537e-01
9.71800000e+00 1.69810000e+01 2.00150000e+01]
[9.07015556e-01 9.15692377e-01 8.89532409e-01 9.03389422e-01
9.30400000e+00 1.69380000e+01 1.92570000e+01]
[9.03389422e-01 9.25275732e-01 8.90438942e-01 9.01187840e-01
8.41200000e+00 1.74860000e+01 1.82590000e+01]
[9.01317345e-01 9.22167617e-01 8.80337568e-01 8.90956961e-01
8.16300000e+00 1.63810000e+01 1.86310000e+01]
[8.91086466e-01 8.95230620e-01 8.26593078e-01 8.59228286e-01
1.02940000e+01 1.47280000e+01 2.46540000e+01]
[8.59228286e-01 8.65574021e-01 8.40191081e-01 8.53918590e-01
1.21580000e+01 1.41550000e+01 2.36960000e+01]
[8.26981592e-01 8.51846513e-01 8.13901607e-01 8.18563780e-01
1.47550000e+01 1.32740000e+01 2.63110000e+01]
[8.18822790e-01 8.26852087e-01 7.90072725e-01 8.07685377e-01
1.77990000e+01 1.24990000e+01 2.85570000e+01]
[8.07814882e-01 8.23225953e-01 7.80489370e-01 7.91497278e-01
2.07570000e+01 1.16440000e+01 2.81370000e+01]
[7.91367773e-01 8.04706767e-01 7.66243842e-01 7.94734898e-01
2.37720000e+01 1.09160000e+01 2.86940000e+01]
[7.94734898e-01 8.40450091e-01 7.79712341e-01 8.17009723e-01
2.39270000e+01 1.55490000e+01 2.59200000e+01]
[8.17009723e-01 8.19081799e-01 8.00174099e-01 8.01339642e-01
2.40620000e+01 1.50580000e+01 2.51010000e+01]
[8.01210137e-01 8.75027871e-01 7.95900441e-01 8.61688877e-01
2.12240000e+01 2.20260000e+01 2.26350000e+01]
[8.61559373e-01 9.06497537e-01 8.60523334e-01 9.04684470e-01
1.97670000e+01 2.54180000e+01 2.09810000e+01]
[9.04554965e-01 9.06627042e-01 7.98490537e-01 8.12347550e-01
1.86580000e+01 2.14470000e+01 2.66910000e+01]
[8.12347550e-01 8.32550298e-01 7.49019704e-01 7.89166191e-01
1.92360000e+01 1.89580000e+01 3.04680000e+01]
[7.89295696e-01 8.38378014e-01 7.54070391e-01 7.58862069e-01
1.94740000e+01 1.76010000e+01 2.70360000e+01]
[7.58732564e-01 8.07426368e-01 7.18068058e-01 7.94864402e-01
2.07120000e+01 1.55850000e+01 2.85540000e+01]
[7.94993907e-01 8.01728157e-01 7.37493778e-01 7.42285455e-01
2.17960000e+01 1.43090000e+01 2.62160000e+01]
[7.42155950e-01 7.74661654e-01 7.34126653e-01 7.68833938e-01
2.28440000e+01 1.35510000e+01 2.52670000e+01]
[7.68833938e-01 8.00174099e-01 7.52257324e-01 7.89554706e-01
2.23750000e+01 1.60740000e+01 2.36610000e+01]
[7.89684211e-01 8.05872310e-01 7.68315919e-01 7.87223619e-01
2.16650000e+01 1.60280000e+01 2.24490000e+01]
[7.87353124e-01 8.26463573e-01 7.82043428e-01 8.24132486e-01
1.99740000e+01 1.78950000e+01 2.10660000e+01]
[8.24261991e-01 8.49774436e-01 8.09886959e-01 8.33715841e-01
1.75740000e+01 2.01870000e+01 1.98760000e+01]
[8.33715841e-01 8.41874644e-01 8.00433109e-01 8.06649339e-01
1.57210000e+01 1.89790000e+01 2.00510000e+01]
[8.06649339e-01 8.19211304e-01 7.98361032e-01 8.04188748e-01
1.41990000e+01 1.83800000e+01 1.97320000e+01]
[8.04059243e-01 8.04577262e-01 7.62099689e-01 7.81395904e-01
1.44950000e+01 1.71830000e+01 2.40070000e+01]
[7.81525408e-01 8.16103189e-01 7.77381255e-01 8.04188748e-01
1.41070000e+01 1.79440000e+01 2.25560000e+01]
[8.04318253e-01 8.21801400e-01 7.83856495e-01 8.06778844e-01
1.34440000e+01 1.77670000e+01 2.11960000e+01]
[8.06778844e-01 8.83704693e-01 8.01857661e-01 8.50421960e-01
1.35840000e+01 2.49130000e+01 1.85790000e+01]
[8.50551465e-01 8.82280140e-01 8.05483796e-01 8.75157376e-01
1.37060000e+01 2.21340000e+01 1.65070000e+01]
[8.75286881e-01 8.83445683e-01 8.63113430e-01 8.67516593e-01
1.38640000e+01 2.16260000e+01 1.59950000e+01]
[8.67516593e-01 9.12713767e-01 8.63242935e-01 9.10641690e-01
1.52120000e+01 2.44610000e+01 1.47870000e+01]
[9.10512186e-01 9.21908608e-01 8.82798159e-01 8.89143894e-01
1.67430000e+01 2.44030000e+01 1.38890000e+01]
[8.89273399e-01 9.03648431e-01 8.51587503e-01 8.94194581e-01
1.61610000e+01 2.24380000e+01 1.75990000e+01]
[8.94194581e-01 9.02612393e-01 8.80596578e-01 8.91604485e-01
1.56510000e+01 2.16390000e+01 1.69730000e+01]
[8.38896033e-01 8.93158543e-01 8.38896033e-01 8.73085299e-01
1.44130000e+01 1.97610000e+01 2.21690000e+01]
[8.73085299e-01 9.03389422e-01 8.71919756e-01 8.79949054e-01
1.27930000e+01 2.04200000e+01 2.10230000e+01]
[8.79819549e-01 8.99763288e-01 8.74509852e-01 8.88366865e-01
1.13760000e+01 1.95420000e+01 2.01190000e+01]
[8.88366865e-01 8.96655172e-01 8.67905108e-01 8.73603319e-01
1.05030000e+01 1.85570000e+01 2.02630000e+01]
[8.73603319e-01 8.82798159e-01 8.66221545e-01 8.78265491e-01
9.83700000e+00 1.79910000e+01 1.99540000e+01]
[8.78394996e-01 8.88107856e-01 8.72437775e-01 8.74509852e-01
8.89700000e+00 1.84730000e+01 1.93500000e+01]
[8.74639357e-01 8.87978351e-01 8.64019964e-01 8.79560539e-01
8.61900000e+00 1.75900000e+01 2.01040000e+01]
[8.79690044e-01 8.81244102e-01 8.27888125e-01 8.33197822e-01
1.03770000e+01 1.57720000e+01 2.50260000e+01]
[8.33068317e-01 8.48349883e-01 8.10275473e-01 8.42781177e-01
1.27180000e+01 1.46040000e+01 2.65970000e+01]
[8.42781177e-01 8.54954628e-01 8.11570521e-01 8.18175266e-01
1.42400000e+01 1.46560000e+01 2.43710000e+01]
[8.18175266e-01 8.45241768e-01 8.02634690e-01 8.33715841e-01
1.60000000e+01 1.34580000e+01 2.40930000e+01]
[8.33586337e-01 8.39284548e-01 8.01598652e-01 8.25945554e-01
1.75910000e+01 1.24800000e+01 2.25420000e+01]
[8.25945554e-01 8.80985092e-01 8.22578429e-01 8.77747472e-01
1.57790000e+01 1.88860000e+01 2.00910000e+01]
[8.77617967e-01 8.97691211e-01 8.71013223e-01 8.76840939e-01
1.44450000e+01 2.11190000e+01 1.90660000e+01]
[8.76711434e-01 8.93676562e-01 8.45500778e-01 8.65185507e-01
1.35290000e+01 1.92010000e+01 2.21430000e+01]
[8.65056002e-01 8.95489629e-01 8.60393829e-01 8.89402904e-01
1.26090000e+01 1.82630000e+01 2.06620000e+01]
[8.89273399e-01 9.17375940e-01 8.74898367e-01 8.87201322e-01
1.16420000e+01 2.09440000e+01 1.89970000e+01]
[8.87330827e-01 9.04813975e-01 8.81762121e-01 8.90309437e-01
1.07960000e+01 1.99960000e+01 1.81370000e+01]
[8.89014389e-01 9.08051595e-01 8.77747472e-01 8.82668654e-01
9.98000000e+00 1.94320000e+01 1.78410000e+01]
[8.82539150e-01 9.00281307e-01 8.72826290e-01 8.99633783e-01
8.90400000e+00 1.83430000e+01 1.78460000e+01]
[8.99763288e-01 9.12454758e-01 8.45500778e-01 8.64278973e-01
8.58600000e+00 1.83220000e+01 2.08100000e+01]
[8.64278973e-01 8.80596578e-01 7.93310345e-01 8.20247342e-01
1.08570000e+01 1.54970000e+01 2.68200000e+01]
[8.20376847e-01 8.73344309e-01 7.78287788e-01 7.85799067e-01
1.34270000e+01 1.31120000e+01 2.51240000e+01]]
[[125.258 125.493 125.157 125.476 26.793 10.51 34.097]
[125.476 125.564 124.386 124.584 31.196 9.556 40.766]
[124.585 124.873 123.875 124.187 35.836 7.996 42.47 ]
[124.187 124.335 123.95 124.076 39.896 7.485 39.757]
[124.075 124.083 123.517 123.524 44.008 6.793 43.151]
[123.524 123.536 117.85 122.016 49.876 3.388 71.481]
[122.015 122.029 121.26 121.502 55.01 3.156 66.591]
[121.502 122.809 121.323 122.46 57.18 9.337 58.247]
[122.459 122.479 121.928 122.446 59.079 8.89 55.456]
[122.446 123.398 122.045 123.123 58.185 15.564 49.187]
[123.121 123.124 122.351 122.351 57.402 14.546 45.97 ]
[122.34 123.096 122.336 122.967 56.732 13.599 43.105]
[122.968 123.574 122.926 123.29 54.766 17.012 40.659]
[123.29 123.343 122.921 123.175 53.051 16.358 39.14 ]
[123.174 123.338 123.041 123.142 51.551 15.891 38.024]
[123.143 123.787 122.834 123.68 49.145 18.706 36.554]
[123.681 123.847 123.588 123.628 46.857 18.822 35.609]
[123.576 123.904 123.576 123.757 44.692 18.772 34.514]
[123.757 123.769 123.424 123.58 43.074 18.067 34.873]
[123.58 123.847 123.394 123.78 41.434 18.024 33.44 ]
[123.78 124.156 123.718 124.14 38.896 20.674 31.752]
[124.141 124.575 124.052 124.55 35.302 24.317 29.807]
[124.548 124.789 124.53 124.725 31.499 26.173 28.858]
[124.73 124.849 124.244 124.274 28.755 24.961 30.23 ]
[124.274 124.69 124.23 124.481 26.392 23.517 28.658]
[124.48 124.795 124.417 124.669 23.959 23.726 27.254]
[124.669 124.714 124.324 124.405 22.119 22.494 27.077]
[124.404 124.608 124.111 124.371 21.172 20.99 28.132]
[124.371 124.495 124.259 124.406 20.343 20.293 27.197]
[124.375 124.699 124.339 124.638 18.736 22.187 25.781]
[124.637 124.85 124.637 124.744 16.699 23.761 24.948]
[124.744 124.955 124.642 124.804 14.745 24.239 23.727]
[124.805 124.841 124.542 124.64 13.199 23.071 24.196]
[124.64 125.082 124.449 124.907 11.893 24.564 23.25 ]
[124.908 125.039 124.678 124.83 10.75 23.141 21.903]
[124.83 125.056 124.516 124.751 9.739 21.426 22.598]
[124.749 124.844 124.6 124.746 8.854 20.562 21.687]
[124.746 124.778 124.449 124.57 8.812 19.419 23.033]
[124.57 124.77 124.493 124.639 8.775 18.482 21.922]
[124.639 124.78 124.349 124.716 9.401 17.266 22.786]
[124.716 124.782 124.452 124.694 9.935 16.287 21.447]
[124.694 124.881 124.51 124.842 9.718 16.981 20.015]
[124.846 124.913 124.711 124.818 9.304 16.938 19.257]
[124.818 124.987 124.718 124.801 8.412 17.486 18.259]
[124.802 124.963 124.64 124.722 8.163 16.381 18.631]
[124.723 124.755 124.225 124.477 10.294 14.728 24.654]
[124.477 124.526 124.33 124.436 12.158 14.155 23.696]
[124.228 124.42 124.127 124.163 14.755 13.274 26.311]
[124.165 124.227 123.943 124.079 17.799 12.499 28.557]
[124.08 124.199 123.869 123.954 20.757 11.644 28.137]
[123.953 124.056 123.759 123.979 23.772 10.916 28.694]
[123.979 124.332 123.863 124.151 23.927 15.549 25.92 ]
[124.151 124.167 124.021 124.03 24.062 15.058 25.101]
[124.029 124.599 123.988 124.496 21.224 22.026 22.635]
[124.495 124.842 124.487 124.828 19.767 25.418 20.981]
[124.827 124.843 124.008 124.115 18.658 21.447 26.691]
[124.115 124.271 123.626 123.936 19.236 18.958 30.468]
[123.937 124.316 123.665 123.702 19.474 17.601 27.036]
[123.701 124.077 123.387 123.98 20.712 15.585 28.554]
[123.981 124.033 123.537 123.574 21.796 14.309 26.216]
[123.573 123.824 123.511 123.779 22.844 13.551 25.267]
[123.779 124.021 123.651 123.939 22.375 16.074 23.661]
[123.94 124.065 123.775 123.921 21.665 16.028 22.449]
[123.922 124.224 123.881 124.206 19.974 17.895 21.066]
[124.207 124.404 124.096 124.28 17.574 20.187 19.876]
[124.28 124.343 124.023 124.071 15.721 18.979 20.051]
[124.071 124.168 124.007 124.052 14.199 18.38 19.732]
[124.051 124.055 123.727 123.876 14.495 17.183 24.007]
[123.877 124.144 123.845 124.052 14.107 17.944 22.556]
[124.053 124.188 123.895 124.072 13.444 17.767 21.196]
[124.072 124.666 124.034 124.409 13.584 24.913 18.579]
[124.41 124.655 124.062 124.6 13.706 22.134 16.507]
[124.601 124.664 124.507 124.541 13.864 21.626 15.995]
[124.541 124.89 124.508 124.874 15.212 24.461 14.787]
[124.873 124.961 124.659 124.708 16.743 24.403 13.889]
[124.709 124.82 124.418 124.747 16.161 22.438 17.599]
[124.747 124.812 124.642 124.727 15.651 21.639 16.973]
[124.32 124.739 124.32 124.584 14.413 19.761 22.169]
[124.584 124.818 124.575 124.637 12.793 20.42 21.023]
[124.636 124.79 124.595 124.702 11.376 19.542 20.119]
[124.702 124.766 124.544 124.588 10.503 18.557 20.263]
[124.588 124.659 124.531 124.624 9.837 17.991 19.954]
[124.625 124.7 124.579 124.595 8.897 18.473 19.35 ]
[124.596 124.699 124.514 124.634 8.619 17.59 20.104]
[124.635 124.647 124.235 124.276 10.377 15.772 25.026]
[124.275 124.393 124.099 124.35 12.718 14.604 26.597]
[124.35 124.444 124.109 124.16 14.24 14.656 24.371]
[124.16 124.369 124.04 124.28 16. 13.458 24.093]
[124.279 124.323 124.032 124.22 17.591 12.48 22.542]
[124.22 124.645 124.194 124.62 15.779 18.886 20.091]
[124.619 124.774 124.568 124.613 14.445 21.119 19.066]
[124.612 124.743 124.371 124.523 13.529 19.201 22.143]
[124.522 124.757 124.486 124.71 12.609 18.263 20.662]
[124.709 124.926 124.598 124.693 11.642 20.944 18.997]
[124.694 124.829 124.651 124.717 10.796 19.996 18.137]
[124.707 124.854 124.62 124.658 9.98 19.432 17.841]
[124.657 124.794 124.582 124.789 8.904 18.343 17.846]
[124.79 124.888 124.371 124.516 8.586 18.322 20.81 ]
[124.516 124.642 123.968 124.176 10.857 15.497 26.82 ]
[124.177 124.586 123.852 123.91 13.427 13.112 25.124]]
The key to inversing the effect of the normalization is the make sure you have the original maximum and minimum values of the data you normalized in the first place.