Deep Learning Toolbox - Normalising a Cell prior to LSTM Training

Hi All,

I am attempting to normalise my training data it improve the performance of the LSTM network.

The data is collected in 10 ANSYS simulations, so 10 observations, with 5 input states (dataTrain) and 4 output states.

The code partitions the train data (90% Train 10% Test). I would like to normalise the 5 signals contained in the dataTrain cell array (1x9 cell) where each individual erray is a 5x324 double (5 signal, volume, temp, pressure, CO2, and NO each with 324 steps).

Step 1.

I have attemped to first compute the maximum value of each signal contained in the 1x9 cell, my code does find a value, however, it seems to find the last indexed value (of the 9 arrays in the cell). Which does not make sense as the values should numerically decrease from array 1 to array 9, as shown below, so my code is at fault. As an example, below shows the max pressure values returned in the arrays (and not in numerical order as they should) and the computed maximum pressure from the cell.

%Normalise the Signals contained in dataTrain cell (1x9 cell) prior to extracting predictors and targets??

for i = 1:numObservationsTrain  % Find the Max value of each individual signal in the dataTrain cell
    volume_max = max(dataTrain{i}(1,:));
    temperature_max = max(dataTrain{i}(2,:));
    pressure_max = max(dataTrain{i}(3,:))
    CO2_max = max(dataTrain{i}(4,:));
    NO_max = max(dataTrain{i}(5,:));
end

Step 2.

Then I attempt to index in and norm each signal (row) in the cell using the computed maximum signal value, but again the code flags an error. See below code.

for i = 1:numObservationsTrain  % Normalise each signal in each array in the dataTrain cell with max value computed above
    dataTrain{i} = dataTrain{i}(1,:) ./ volume_max;
    dataTrain{i} = dataTrain{i}(2,:) ./ temperature_max;
    dataTrain{i} = dataTrain{i}(3,:) ./ pressure_max;
    dataTrain{i} = dataTrain{i}(4,:) ./ CO2_max;
    dataTrain{i} = dataTrain{i}(5,:) ./ NO_max;
end

Please forgive the schoolboy questions, this is the first time I have attempted to train an LSTM network with real-time data. Any suggestions as to how to mind the max and norm each signal within the 1x9 cell would be great.

Thanks in advance,

Patrick

Answer 1

[Siraj]

Hi! It is my understanding that you have the training data, which is a cell array that contains 9 matrices, each with dimensions 5x324.

To normalize each row of these matrices individually without altering the overall structure of the data, iterate over each matrix in the cell array, normalize the rows of each matrix, and store the normalized matrices back into the cell array.

Refer to the example code below for better understanding.

%generating random data. 
dataTrain = cell(1,9); 
for i = 1 : size(dataTrain,2) 
    %creating 5 signals with 324 steps.  
    dataTrain{i} = randi([1 100], 5,324); 
end 
disp("Before Normalization"); 

Before Normalization

disp(dataTrain{1}); 

  Columns 1 through 33

    61    57    58    32    97    83    59    17    32    62    93    13    48    20    65    68    14    62    93    67    89    95    95     2    88    53    88    18    56    80    67    23    71
    95    67     3    70    20    79    36    77    61    69     2    89    97    22    53    88    83    50    97     2    16    51    85    12    44    74    13    77    70    62    92    14    95
    96    48    99     9    35    86    32    96    27    90    67    13    23    68    46    97    11    99    86    35    73    40    98    49    61    64     9    34    37     6    57    52     8
    57    47    52     5    57     8    24    47     2    76    73    44    57    68    48    18    77    22    79    21    67    76    55    11    38    15    78    39    84    65    50    76    20
    38    31    79     1    17    56     5    52    29    82    88    48    52    16    81    80    60    15    86    70    81    60    50    71    72     4    16    97    24    47    18    21    37

  Columns 34 through 66

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    73    13    60    37    91    76    96    48     8    84     5    67    96   100    94    37    21    51    38    13    42    96    18     8    19    28    97    17    19    59    51     4    31
    23    45    88    36    17    25    84    74    53    11    45    95    77    39    90    67    81    33    52    57    86    35    88    44    83    33    24    89    42    16    77    81    60
    11    51    39     3    99    19     7    90    24    95     1    65    46    83    60    97    89    27    91    75    75    64    75    90    57    73    91    79    42    47    56     6    68
    32    95    86    42    91    57    50    76    22    76   100    34    93    97    91    93    71    90    85    37     8     5     3    29    73    58    90    67    76    62     4    29    27

  Columns 67 through 99

    99    34    23    78    15    47    81     3    92    51    21    72    28    49     4    37    86    97    41    31    14    58    12     8    20    74    64    78    73    86    34    47    55
    25    35    99    21    86    39    68    88    46    34    94    33    63    24    26    54    23     5    96    38    99    90    84    72     9    11    95    66    31    80    21    24    18
    18    27    87    58    81    12    57    12     2    91    37     1    42    51    11    36     6    78    84    76     1    32    12     5    57    58    69    65    67     1    90    48    55
    75    50    51    54    77    18    84    78    53    77    77    73    95     2    29    34    15    30    31    53    65    99    19    77    96    88    11    79    51    74    87    76    90
    61    12    75    62    32    64    92   100    93    20    94    42    27    75    84    16    95    91    55    58    90    77    81    89    19    80    90    57    53    52    39    89    92

  Columns 100 through 132

    19    98    37    99    42    76     1    24     2    69    40    12    11    83    68     8    46    49    37    94    64    94    64    28    17    54     1    58    46    34    34    81    29
    59    34    93    88    60    45    64     9    18    39    60    83     6    66    37    92    23    40    53    24    95    28    87     8    87    78    80    29    84    91    58    17    70
    53    72    86    96    10    40    57    96    45    62    63    27    39    69    57    25    90    37    93    79    56    28    34    21    89    83    30    73    55    70    53    92    63
    69    25    95    72    16    23    75    21    16    67     6    69    74    50    69    47     2    53    25    42    93     3    60    41    21    34     1    37    27    89    31    14    99
   100    79    35    67    67   100    90    74    93     1    23    67    39    41    86    35    38    59    43    83    78    39    29    26    70    68    45    92    35    48    89    52    61

  Columns 133 through 165

    82    17    50    83     3    48    85    27   100    48    84    38    68    75    83    93    24    97    63    79    13    54    40    21    96    11    23    27    13   100    48    62    48
    10    93    84    99    93    88    11    98   100    87    20    27    90    80    68    29     8    62    52    37    57    70    79    43    39    14    60    47    87     9    79    43    65
     1     6    79     6    27   100    75    14    68    44     2    22    82    54    13    15    48    95    29     9    73     2    80    17    45     7    70    91    84    71    75    63    91
    11    27    49    96    12    14    21     9    72    74    57    39    64    58    24    23    61    51    83    40    10    78    93    69    96    22    60    19    14    17    98    79    81
    15    86    53    28    53    48    21    72    33    18     6    10    90    62    84     3    34    63   100    32    50    21    55    82    98    31    16    11    94    11    86     1    90

  Columns 166 through 198

    46    72     4    10    87    47    18    67    61    22    72    61    73    69    77    87    27    40     9    61    51    52    39    84    95    69    73    43    20    63    63    76    12
   100    79    40     3    17    99     6    61    33    30    50    59    14     9    34    44    27    17    94    91    78    17    66     6    42    80    19    80     5    27    29    62    85
    23    52     6    28    64    13     3     6    18    24    33    76    70   100    21     9    59    82     6    87    46    18    91    33     5    94    78    96     6    77    66    30    78
   100    99    41    62    17    80    69    47    13    82    82    83    94    38    91    32    85    68    41    38    13    73    75    46    35    15    71    30     7    63    40     8    48
    51     3    82    95    46     7     9    22    58    30    86    18    83    45    47    66    36    50    75    79    83    91     3     6    95    40    53    61    12    40    88    95    31

  Columns 199 through 231

    83    17    49    32    26    68    29    81    74    75    15    10    79    18    58    59    77    40    66    64    63    80    48    94    43    73    68    60    29    94    10    93    10
    89     3     3    19    48    55    82    65    96    39    57    96    42    44     8     3    68    79    91    15    16    95    41    43    91    93    66    93    83    46    30    42    16
    33     3    93     2     5    33    62    50    51    60    11    96    19    58    60    23    56   100    11    82    25    28    13    87    39    62    90    59     1    64    98    93    66
    76     6    46    90    70    77    53    33    88    77    94    71    41    93    18    57    11    66    61    70    35    81    57    31     6    58    80    55    37    69    61    63    33
    75    43    14    41    80    60    13    85    21     5    83    70    74    23    53    82    89    56    46    51    40   100    11    75     6    84    99    50    39     6    30    58    17

  Columns 232 through 264

    53    16    84    75    41     7    77    37     3    74    45    57    36    99    63    28    79    49    95    79    51    64    64    21    12    53    95    67    43    41    65     2     4
    84    21    96    89    91    71    67    83    90    93    64    30    78    91    98    90    66    61    35    66    17    69    76    55    57    76    89     3    22    75    96    11    49
    56     3    28    49    17    22    89    12    34    57    78    80    99    85     2    86    87    54    15    22    28    17    40     2     1    16    14    52    24    60    95    21    93
    69    54    32    59    10    28    41    53    53    68   100    84    94     7     9    79    29    89    68    13    66    62    58     5    29    14    12    50    46    78    63    27     8
    28    70    89    96    12    97    81    16   100    47    40    28    19    78    34    25    19     5    50    55    20    46    22    23     2    80    43    16    18    93    21    73    67

  Columns 265 through 297

    35    42    77    42    30    44    13    34    39    52    79    76    10   100     7    43    83     5    44    86    24    69    92    88    53    14    75    24    16     6    19    45    10
    63    97    16    30    17    27    87    27    74    19    68    96    34    45    18    12    37    97    72    63    84    90    20    49    19    88    38     7    79    73    36    62    30
    50    22    53    47    16    73    67    64    43    81    82    50    72    48    49    64    79    54    52    48    69    55    31    94    16    32    41   100    45    13    43    36    72
    53    78    34    40    47    55    72    35    91    60    58    28    58    30    74    84    32    12    77    10    47    15   100    81    42    38    44    16    35    66    35    10    49
    36    45    53    51    25    31    90    92    52    24    20    52     6    93    12    73    19    45    60    14    67    63    76    43    95    53     6    55    63    32     1    69    15

  Columns 298 through 324

    59    23    80    63    33    25    68    55    75     8    91    95    77    94    46     8     8    61    24    59    88     7    83    88    84    63     1
     5    70    57    27    84    63    62    76    12    81    76    38    98    72    34    18    56    34    52    78    85    29    65    25    15    64    68
    15    87     5    31     9    57    35    13    56    95    75    78    52    19    54    65    80    98    88    65     3    47    18    53    18    45    43
    80    97    30    42     1    32    32    62    75    12    53    37    21    74    21     8    56    89    26    13    84    75    26     8    10    15    91
    90    17    88    57    34    76    21     2     1    53    63    76    64    99    21    70    39    53    47    46    60    28     5    79    24    54    81

%Normalizing the training data. 
for i = 1 : size(dataTrain,2) 
    %creating 5 signals with 324 steps.  
    raw_data = dataTrain{i}; 
    normalized_data = normalize(raw_data,2,"range"); 
    dataTrain{i} = normalized_data; 
end 

disp("After Normalization"); 

After Normalization

disp(dataTrain{1}); 

  Columns 1 through 19

    0.6061    0.5657    0.5758    0.3131    0.9697    0.8283    0.5859    0.1616    0.3131    0.6162    0.9293    0.1212    0.4747    0.1919    0.6465    0.6768    0.1313    0.6162    0.9293
    0.9490    0.6633    0.0102    0.6939    0.1837    0.7857    0.3469    0.7653    0.6020    0.6837         0    0.8878    0.9694    0.2041    0.5204    0.8776    0.8265    0.4898    0.9694
    0.9596    0.4747    0.9899    0.0808    0.3434    0.8586    0.3131    0.9596    0.2626    0.8990    0.6667    0.1212    0.2222    0.6768    0.4545    0.9697    0.1010    0.9899    0.8586
    0.5657    0.4646    0.5152    0.0404    0.5657    0.0707    0.2323    0.4646    0.0101    0.7576    0.7273    0.4343    0.5657    0.6768    0.4747    0.1717    0.7677    0.2121    0.7879
    0.3737    0.3030    0.7879         0    0.1616    0.5556    0.0404    0.5152    0.2828    0.8182    0.8788    0.4747    0.5152    0.1515    0.8081    0.7980    0.5960    0.1414    0.8586

  Columns 20 through 38

    0.6667    0.8889    0.9495    0.9495    0.0101    0.8788    0.5253    0.8788    0.1717    0.5556    0.7980    0.6667    0.2222    0.7071    1.0000    0.1414    0.9596    0.7172    0.8889
         0    0.1429    0.5000    0.8469    0.1020    0.4286    0.7347    0.1122    0.7653    0.6939    0.6122    0.9184    0.1224    0.9490    0.7245    0.1122    0.5918    0.3571    0.9082
    0.3434    0.7273    0.3939    0.9798    0.4848    0.6061    0.6364    0.0808    0.3333    0.3636    0.0505    0.5657    0.5152    0.0707    0.2222    0.4444    0.8788    0.3535    0.1616
    0.2020    0.6667    0.7576    0.5455    0.1010    0.3737    0.1414    0.7778    0.3838    0.8384    0.6465    0.4949    0.7576    0.1919    0.1010    0.5051    0.3838    0.0202    0.9899
    0.6970    0.8081    0.5960    0.4949    0.7071    0.7172    0.0303    0.1515    0.9697    0.2323    0.4646    0.1717    0.2020    0.3636    0.3131    0.9495    0.8586    0.4141    0.9091

  Columns 39 through 57

    0.2929    0.9798    0.0202    0.9293    0.0909    0.4545    0.6364    0.9394    0.0404    0.8687    0.8384    0.1717    0.5758    0.6970    0.8182    0.3636    0.3838    0.8485    0.0202
    0.7551    0.9592    0.4694    0.0612    0.8367    0.0306    0.6633    0.9592    1.0000    0.9388    0.3571    0.1939    0.5000    0.3673    0.1122    0.4082    0.9592    0.1633    0.0612
    0.2424    0.8384    0.7374    0.5253    0.1010    0.4444    0.9495    0.7677    0.3838    0.8990    0.6667    0.8081    0.3232    0.5152    0.5657    0.8586    0.3434    0.8788    0.4343
    0.1818    0.0606    0.8990    0.2323    0.9495         0    0.6465    0.4545    0.8283    0.5960    0.9697    0.8889    0.2626    0.9091    0.7475    0.7475    0.6364    0.7475    0.8990
    0.5657    0.4949    0.7576    0.2121    0.7576    1.0000    0.3333    0.9293    0.9697    0.9091    0.9293    0.7071    0.8990    0.8485    0.3636    0.0707    0.0404    0.0202    0.2828

  Columns 58 through 76

    0.5556    0.5556    0.2222    0.5253    0.6364    0.8788    0.4444    0.4141    0.0202    0.9899    0.3333    0.2222    0.7778    0.1414    0.4646    0.8081    0.0202    0.9192    0.5051
    0.1735    0.2653    0.9694    0.1531    0.1735    0.5816    0.5000    0.0204    0.2959    0.2347    0.3367    0.9898    0.1939    0.8571    0.3776    0.6735    0.8776    0.4490    0.3265
    0.8283    0.3232    0.2323    0.8889    0.4141    0.1515    0.7677    0.8081    0.5960    0.1717    0.2626    0.8687    0.5758    0.8081    0.1111    0.5657    0.1111    0.0101    0.9091
    0.5657    0.7273    0.9091    0.7879    0.4141    0.4646    0.5556    0.0505    0.6768    0.7475    0.4949    0.5051    0.5354    0.7677    0.1717    0.8384    0.7778    0.5253    0.7677
    0.7273    0.5758    0.8990    0.6667    0.7576    0.6162    0.0303    0.2828    0.2626    0.6061    0.1111    0.7475    0.6162    0.3131    0.6364    0.9192    1.0000    0.9293    0.1919

  Columns 77 through 95

    0.2020    0.7172    0.2727    0.4848    0.0303    0.3636    0.8586    0.9697    0.4040    0.3030    0.1313    0.5758    0.1111    0.0707    0.1919    0.7374    0.6364    0.7778    0.7273
    0.9388    0.3163    0.6224    0.2245    0.2449    0.5306    0.2143    0.0306    0.9592    0.3673    0.9898    0.8980    0.8367    0.7143    0.0714    0.0918    0.9490    0.6531    0.2959
    0.3636         0    0.4141    0.5051    0.1010    0.3535    0.0505    0.7778    0.8384    0.7576         0    0.3131    0.1111    0.0404    0.5657    0.5758    0.6869    0.6465    0.6667
    0.7677    0.7273    0.9495    0.0101    0.2828    0.3333    0.1414    0.2929    0.3030    0.5253    0.6465    0.9899    0.1818    0.7677    0.9596    0.8788    0.1010    0.7879    0.5051
    0.9394    0.4141    0.2626    0.7475    0.8384    0.1515    0.9495    0.9091    0.5455    0.5758    0.8990    0.7677    0.8081    0.8889    0.1818    0.7980    0.8990    0.5657    0.5253

  Columns 96 through 114

    0.8586    0.3333    0.4646    0.5455    0.1818    0.9798    0.3636    0.9899    0.4141    0.7576         0    0.2323    0.0101    0.6869    0.3939    0.1111    0.1010    0.8283    0.6768
    0.7959    0.1939    0.2245    0.1633    0.5816    0.3265    0.9286    0.8776    0.5918    0.4388    0.6327    0.0714    0.1633    0.3776    0.5918    0.8265    0.0408    0.6531    0.3571
         0    0.8990    0.4747    0.5455    0.5253    0.7172    0.8586    0.9596    0.0909    0.3939    0.5657    0.9596    0.4444    0.6162    0.6263    0.2626    0.3838    0.6869    0.5657
    0.7374    0.8687    0.7576    0.8990    0.6869    0.2424    0.9495    0.7172    0.1515    0.2222    0.7475    0.2020    0.1515    0.6667    0.0505    0.6869    0.7374    0.4949    0.6869
    0.5152    0.3838    0.8889    0.9192    1.0000    0.7879    0.3434    0.6667    0.6667    1.0000    0.8990    0.7374    0.9293         0    0.2222    0.6667    0.3838    0.4040    0.8586

  Columns 115 through 133

    0.0707    0.4545    0.4848    0.3636    0.9394    0.6364    0.9394    0.6364    0.2727    0.1616    0.5354         0    0.5758    0.4545    0.3333    0.3333    0.8081    0.2828    0.8182
    0.9184    0.2143    0.3878    0.5204    0.2245    0.9490    0.2653    0.8673    0.0612    0.8673    0.7755    0.7959    0.2755    0.8367    0.9082    0.5714    0.1531    0.6939    0.0816
    0.2424    0.8990    0.3636    0.9293    0.7879    0.5556    0.2727    0.3333    0.2020    0.8889    0.8283    0.2929    0.7273    0.5455    0.6970    0.5253    0.9192    0.6263         0
    0.4646    0.0101    0.5253    0.2424    0.4141    0.9293    0.0202    0.5960    0.4040    0.2020    0.3333         0    0.3636    0.2626    0.8889    0.3030    0.1313    0.9899    0.1010
    0.3434    0.3737    0.5859    0.4242    0.8283    0.7778    0.3838    0.2828    0.2525    0.6970    0.6768    0.4444    0.9192    0.3434    0.4747    0.8889    0.5152    0.6061    0.1414

  Columns 134 through 152

    0.1616    0.4949    0.8283    0.0202    0.4747    0.8485    0.2626    1.0000    0.4747    0.8384    0.3737    0.6768    0.7475    0.8283    0.9293    0.2323    0.9697    0.6263    0.7879
    0.9286    0.8367    0.9898    0.9286    0.8776    0.0918    0.9796    1.0000    0.8673    0.1837    0.2551    0.8980    0.7959    0.6735    0.2755    0.0612    0.6122    0.5102    0.3571
    0.0505    0.7879    0.0505    0.2626    1.0000    0.7475    0.1313    0.6768    0.4343    0.0101    0.2121    0.8182    0.5354    0.1212    0.1414    0.4747    0.9495    0.2828    0.0808
    0.2626    0.4848    0.9596    0.1111    0.1313    0.2020    0.0808    0.7172    0.7374    0.5657    0.3838    0.6364    0.5758    0.2323    0.2222    0.6061    0.5051    0.8283    0.3939
    0.8586    0.5253    0.2727    0.5253    0.4747    0.2020    0.7172    0.3232    0.1717    0.0505    0.0909    0.8990    0.6162    0.8384    0.0202    0.3333    0.6263    1.0000    0.3131

  Columns 153 through 171

    0.1212    0.5354    0.3939    0.2020    0.9596    0.1010    0.2222    0.2626    0.1212    1.0000    0.4747    0.6162    0.4747    0.4545    0.7172    0.0303    0.0909    0.8687    0.4646
    0.5612    0.6939    0.7857    0.4184    0.3776    0.1224    0.5918    0.4592    0.8673    0.0714    0.7857    0.4184    0.6429    1.0000    0.7857    0.3878    0.0102    0.1531    0.9898
    0.7273    0.0101    0.7980    0.1616    0.4444    0.0606    0.6970    0.9091    0.8384    0.7071    0.7475    0.6263    0.9091    0.2222    0.5152    0.0505    0.2727    0.6364    0.1212
    0.0909    0.7778    0.9293    0.6869    0.9596    0.2121    0.5960    0.1818    0.1313    0.1616    0.9798    0.7879    0.8081    1.0000    0.9899    0.4040    0.6162    0.1616    0.7980
    0.4949    0.2020    0.5455    0.8182    0.9798    0.3030    0.1515    0.1010    0.9394    0.1010    0.8586         0    0.8990    0.5051    0.0202    0.8182    0.9495    0.4545    0.0606

  Columns 172 through 190

    0.1717    0.6667    0.6061    0.2121    0.7172    0.6061    0.7273    0.6869    0.7677    0.8687    0.2626    0.3939    0.0808    0.6061    0.5051    0.5152    0.3838    0.8384    0.9495
    0.0408    0.6020    0.3163    0.2857    0.4898    0.5816    0.1224    0.0714    0.3265    0.4286    0.2551    0.1531    0.9388    0.9082    0.7755    0.1531    0.6531    0.0408    0.4082
    0.0202    0.0505    0.1717    0.2323    0.3232    0.7576    0.6970    1.0000    0.2020    0.0808    0.5859    0.8182    0.0505    0.8687    0.4545    0.1717    0.9091    0.3232    0.0404
    0.6869    0.4646    0.1212    0.8182    0.8182    0.8283    0.9394    0.3737    0.9091    0.3131    0.8485    0.6768    0.4040    0.3737    0.1212    0.7273    0.7475    0.4545    0.3434
    0.0808    0.2121    0.5758    0.2929    0.8586    0.1717    0.8283    0.4444    0.4646    0.6566    0.3535    0.4949    0.7475    0.7879    0.8283    0.9091    0.0202    0.0505    0.9495

  Columns 191 through 209

    0.6869    0.7273    0.4242    0.1919    0.6263    0.6263    0.7576    0.1111    0.8283    0.1616    0.4848    0.3131    0.2525    0.6768    0.2828    0.8081    0.7374    0.7475    0.1414
    0.7959    0.1735    0.7959    0.0306    0.2551    0.2755    0.6122    0.8469    0.8878    0.0102    0.0102    0.1735    0.4694    0.5408    0.8163    0.6429    0.9592    0.3776    0.5612
    0.9394    0.7778    0.9596    0.0505    0.7677    0.6566    0.2929    0.7778    0.3232    0.0202    0.9293    0.0101    0.0404    0.3232    0.6162    0.4949    0.5051    0.5960    0.1010
    0.1414    0.7071    0.2929    0.0606    0.6263    0.3939    0.0707    0.4747    0.7576    0.0505    0.4545    0.8990    0.6970    0.7677    0.5253    0.3232    0.8788    0.7677    0.9394
    0.3939    0.5253    0.6061    0.1111    0.3939    0.8788    0.9495    0.3030    0.7475    0.4242    0.1313    0.4040    0.7980    0.5960    0.1212    0.8485    0.2020    0.0404    0.8283

  Columns 210 through 228

    0.0909    0.7879    0.1717    0.5758    0.5859    0.7677    0.3939    0.6566    0.6364    0.6263    0.7980    0.4747    0.9394    0.4242    0.7273    0.6768    0.5960    0.2828    0.9394
    0.9592    0.4082    0.4286    0.0612    0.0102    0.6735    0.7857    0.9082    0.1327    0.1429    0.9490    0.3980    0.4184    0.9082    0.9286    0.6531    0.9286    0.8265    0.4490
    0.9596    0.1818    0.5758    0.5960    0.2222    0.5556    1.0000    0.1010    0.8182    0.2424    0.2727    0.1212    0.8687    0.3838    0.6162    0.8990    0.5859         0    0.6364
    0.7071    0.4040    0.9293    0.1717    0.5657    0.1010    0.6566    0.6061    0.6970    0.3434    0.8081    0.5657    0.3030    0.0505    0.5758    0.7980    0.5455    0.3636    0.6869
    0.6970    0.7374    0.2222    0.5253    0.8182    0.8889    0.5556    0.4545    0.5051    0.3939    1.0000    0.1010    0.7475    0.0505    0.8384    0.9899    0.4949    0.3838    0.0505

  Columns 229 through 247

    0.0909    0.9293    0.0909    0.5253    0.1515    0.8384    0.7475    0.4040    0.0606    0.7677    0.3636    0.0202    0.7374    0.4444    0.5657    0.3535    0.9899    0.6263    0.2727
    0.2857    0.4082    0.1429    0.8367    0.1939    0.9592    0.8878    0.9082    0.7041    0.6633    0.8265    0.8980    0.9286    0.6327    0.2857    0.7755    0.9082    0.9796    0.8980
    0.9798    0.9293    0.6566    0.5556    0.0202    0.2727    0.4848    0.1616    0.2121    0.8889    0.1111    0.3333    0.5657    0.7778    0.7980    0.9899    0.8485    0.0101    0.8586
    0.6061    0.6263    0.3232    0.6869    0.5354    0.3131    0.5859    0.0909    0.2727    0.4040    0.5253    0.5253    0.6768    1.0000    0.8384    0.9394    0.0606    0.0808    0.7879
    0.2929    0.5758    0.1616    0.2727    0.6970    0.8889    0.9596    0.1111    0.9697    0.8081    0.1515    1.0000    0.4646    0.3939    0.2727    0.1818    0.7778    0.3333    0.2424

  Columns 248 through 266

    0.7879    0.4848    0.9495    0.7879    0.5051    0.6364    0.6364    0.2020    0.1111    0.5253    0.9495    0.6667    0.4242    0.4040    0.6465    0.0101    0.0303    0.3434    0.4141
    0.6531    0.6020    0.3367    0.6531    0.1531    0.6837    0.7551    0.5408    0.5612    0.7551    0.8878    0.0102    0.2041    0.7449    0.9592    0.0918    0.4796    0.6224    0.9694
    0.8687    0.5354    0.1414    0.2121    0.2727    0.1616    0.3939    0.0101         0    0.1515    0.1313    0.5152    0.2323    0.5960    0.9495    0.2020    0.9293    0.4949    0.2121
    0.2828    0.8889    0.6768    0.1212    0.6566    0.6162    0.5758    0.0404    0.2828    0.1313    0.1111    0.4949    0.4545    0.7778    0.6263    0.2626    0.0707    0.5253    0.7778
    0.1818    0.0404    0.4949    0.5455    0.1919    0.4545    0.2121    0.2222    0.0101    0.7980    0.4242    0.1515    0.1717    0.9293    0.2020    0.7273    0.6667    0.3535    0.4444

  Columns 267 through 285

    0.7677    0.4141    0.2929    0.4343    0.1212    0.3333    0.3838    0.5152    0.7879    0.7576    0.0909    1.0000    0.0606    0.4242    0.8283    0.0404    0.4343    0.8586    0.2323
    0.1429    0.2857    0.1531    0.2551    0.8673    0.2551    0.7347    0.1735    0.6735    0.9592    0.3265    0.4388    0.1633    0.1020    0.3571    0.9694    0.7143    0.6224    0.8367
    0.5253    0.4646    0.1515    0.7273    0.6667    0.6364    0.4242    0.8081    0.8182    0.4949    0.7172    0.4747    0.4848    0.6364    0.7879    0.5354    0.5152    0.4747    0.6869
    0.3333    0.3939    0.4646    0.5455    0.7172    0.3434    0.9091    0.5960    0.5758    0.2727    0.5758    0.2929    0.7374    0.8384    0.3131    0.1111    0.7677    0.0909    0.4646
    0.5253    0.5051    0.2424    0.3030    0.8990    0.9192    0.5152    0.2323    0.1919    0.5152    0.0505    0.9293    0.1111    0.7273    0.1818    0.4444    0.5960    0.1313    0.6667

  Columns 286 through 304

    0.6869    0.9192    0.8788    0.5253    0.1313    0.7475    0.2323    0.1515    0.0505    0.1818    0.4444    0.0909    0.5859    0.2222    0.7980    0.6263    0.3232    0.2424    0.6768
    0.8980    0.1837    0.4796    0.1735    0.8776    0.3673    0.0510    0.7857    0.7245    0.3469    0.6122    0.2857    0.0306    0.6939    0.5612    0.2551    0.8367    0.6224    0.6122
    0.5455    0.3030    0.9394    0.1515    0.3131    0.4040    1.0000    0.4444    0.1212    0.4242    0.3535    0.7172    0.1414    0.8687    0.0404    0.3030    0.0808    0.5657    0.3434
    0.1414    1.0000    0.8081    0.4141    0.3737    0.4343    0.1515    0.3434    0.6566    0.3434    0.0909    0.4848    0.7980    0.9697    0.2929    0.4141         0    0.3131    0.3131
    0.6263    0.7576    0.4242    0.9495    0.5253    0.0505    0.5455    0.6263    0.3131         0    0.6869    0.1414    0.8990    0.1616    0.8788    0.5657    0.3333    0.7576    0.2020

  Columns 305 through 323

    0.5455    0.7475    0.0707    0.9091    0.9495    0.7677    0.9394    0.4545    0.0707    0.0707    0.6061    0.2323    0.5859    0.8788    0.0606    0.8283    0.8788    0.8384    0.6263
    0.7551    0.1020    0.8061    0.7551    0.3673    0.9796    0.7143    0.3265    0.1633    0.5510    0.3265    0.5102    0.7755    0.8469    0.2755    0.6429    0.2347    0.1327    0.6327
    0.1212    0.5556    0.9495    0.7475    0.7778    0.5152    0.1818    0.5354    0.6465    0.7980    0.9798    0.8788    0.6465    0.0202    0.4646    0.1717    0.5253    0.1717    0.4444
    0.6162    0.7475    0.1111    0.5253    0.3636    0.2020    0.7374    0.2020    0.0707    0.5556    0.8889    0.2525    0.1212    0.8384    0.7475    0.2525    0.0707    0.0909    0.1414
    0.0101         0    0.5253    0.6263    0.7576    0.6364    0.9899    0.2020    0.6970    0.3838    0.5253    0.4646    0.4545    0.5960    0.2727    0.0404    0.7879    0.2323    0.5354

  Column 324

         0
    0.6735
    0.4242
    0.9091
    0.8081

To learn about the "normalize" function and its different parameter options, please refer to the link provided below. It will provide detailed information on how to use the "normalize" function with different parameter settings to achieve different types of normalization.

https://www.mathworks.com/help/matlab/ref/double.normalize.html

Hope this helps.