How can I denormalize data normalized with 2-norm

Hello I need help on denormalization. I have this dataset i Have normalize using 2-norm. Please how can I denormalize the data

DT = readtable("DT.xlsx")

DT = 72×7 table
            Datetime              Tb     DH     DN     EB    GH      Z 
    _________________________    ____    ___    ___    __    ___    ___

    {''01/01/2007 00:00:00''}    22.7      0      0     0      0    155
    {''01/01/2007 01:00:00''}    22.5      0      0     0      0    144
    {''01/01/2007 02:00:00''}      22      0      0     0      0    132
    {''01/01/2007 03:00:00''}    21.8      0      0     0      0    118
    {''01/01/2007 04:00:00''}    21.6      0      0     0      0    104
    {''01/01/2007 05:00:00''}    21.7      7      0     0      7     91
    {''01/01/2007 06:00:00''}    22.2     81     27     2     84     77
    {''01/01/2007 07:00:00''}    23.6    183    134     7    190     64
    {''01/01/2007 08:00:00''}      25    311    272     0    311     51
    {''01/01/2007 09:00:00''}      26    457    371     0    457     39
    {''01/01/2007 10:00:00''}      27    536    465     0    536     31
    {''01/01/2007 11:00:00''}    27.6    566    508     0    566     28
    {''01/01/2007 12:00:00''}    27.6    506    442     0    506     32
    {''01/01/2007 13:00:00''}    27.5    361    360     0    361     41
    {''01/01/2007 14:00:00''}    27.2    313    246     0    313     53
    {''01/01/2007 15:00:00''}    26.6    209    119    12    221     65

DN = normalize(DT,"norm",...
    "DataVariables",["Tb","DH","DN","EB","GH","Z"])

DN = 72×7 table
            Datetime               Tb          DH           DN          EB           GH           Z    
    _________________________    _______    _________    ________    _________    _________    ________

    {''01/01/2007 00:00:00''}    0.11092            0           0            0            0     0.17854
    {''01/01/2007 01:00:00''}    0.10994            0           0            0            0     0.16587
    {''01/01/2007 02:00:00''}     0.1075            0           0            0            0     0.15205
    {''01/01/2007 03:00:00''}    0.10652            0           0            0            0     0.13592
    {''01/01/2007 04:00:00''}    0.10555            0           0            0            0     0.11979
    {''01/01/2007 05:00:00''}    0.10604    0.0041554           0            0    0.0023301     0.10482
    {''01/01/2007 06:00:00''}    0.10848     0.048083    0.011558    0.0012417     0.027961    0.088694
    {''01/01/2007 07:00:00''}    0.11532      0.10863     0.05736    0.0043458     0.063246     0.07372
    {''01/01/2007 08:00:00''}    0.12216      0.18462     0.11643            0      0.10352    0.058745
    {''01/01/2007 09:00:00''}    0.12705      0.27129     0.15881            0      0.15212    0.044923
    {''01/01/2007 10:00:00''}    0.13193      0.31818     0.19905            0      0.17842    0.035708
    {''01/01/2007 11:00:00''}    0.13487      0.33599     0.21746            0      0.18841    0.032252
    {''01/01/2007 12:00:00''}    0.13487      0.30037      0.1892            0      0.16843     0.03686
    {''01/01/2007 13:00:00''}    0.13438       0.2143      0.1541            0      0.12017    0.047227
    {''01/01/2007 14:00:00''}    0.13291       0.1858      0.1053            0      0.10419    0.061049
    {''01/01/2007 15:00:00''}    0.12998      0.12407    0.050939    0.0074499     0.073565    0.074872

I get this error when I try to denormalize it as below. please can I fix this? Thanks in advance

DA = denormalize(DN,"denorm",...
    "DataVariables",["Tb","DH","DN","EB","GH","Z"])

Unrecognized function or variable 'denorm'.

Answer 1

[Shaik mohammed ghouse basha]

Hello @MBUNYA NERVILLE ANYANG,

There isn't any function to directly get denormalize data from normalized data. As data and scaled version of data have same normalized values you can't get exact data from only normalized values.

Proof:

Consider data of N values of form and a scaled version of it by a constant k which will be of form .

After normalising,

an ith element in non scaled version will be

an ith element in scaled version wiil be , removing out of square root in denominator its cancels k in numerator and we are left with .

Hence we can say scaled version of a vector has same normalized values. So, we can't deduce the original data unless we know the euclidean norm of original data.

In case of 2-norm we need 2-norm of column to get denormalized values:

Normalized values are calculate by dividing each element with 2-norm of the column vector i.e, dividing a element with square root of sum of squares of all values in column. Hence by multiplying this to normalized values you can get denormalized values.

Here is an example of how to do it:

L1 = ["X"; "Y"];
L2 = [1; 7];
L3 = [2; 8];
L4 = [3; 9];
L5 = [4; 10];
L6 = [5; 11];
L7 = [6; 12];
DT = table(L1, L2, L3, L4, L5, L6, L7)

DT = 2×7 table
    L1     L2    L3    L4    L5    L6    L7
    ___    __    __    __    __    __    __

    "X"    1     2     3      4     5     6
    "Y"    7     8     9     10    11    12

DN = normalize(DT,"norm",...
    "DataVariables",["L2", "L3", "L4", "L5", "L6", "L7"])

DN = 2×7 table
    L1       L2         L3         L4         L5         L6         L7   
    ___    _______    _______    _______    _______    _______    _______

    "X"    0.14142    0.24254    0.31623    0.37139     0.4138    0.44721
    "Y"    0.98995    0.97014    0.94868    0.92848    0.91037    0.89443

DA = DN;
DA.L2 = norm(DT.L2, 2) * DA.L2;
DA.L3 = norm(DT.L3, 2) * DA.L3;
DA.L4 = norm(DT.L4, 2) * DA.L4;
DA.L5 = norm(DT.L5, 2) * DA.L5;
DA.L6 = norm(DT.L6, 2) * DA.L6;
DA.L7 = norm(DT.L7, 2) * DA.L7;
disp(DA)

    L1     L2    L3    L4    L5    L6    L7
    ___    __    __    __    __    __    __

    "X"    1     2     3      4     5     6
    "Y"    7     8     9     10    11    12

For your case, I think this should work fine but I can't run this since I don't have DT.xlsx file so I tried this method in above example:

DT = readtable("DT.xlsx");
DN = normalize(DT,"norm",...
    "DataVariables",["Tb","DH","DN","EB","GH","Z"]) ;
DA = DN;

DA.Tb = norm(DT.Tb, 2) * DA.Tb;
DA.DH = norm(DT.DH, 2) * DA.DH;
DA.DN = norm(DT.DN, 2) * DA.DN;
DA.EB = norm(DT.EB, 2) * DA.EB;
DA.GH = norm(DT.GH, 2) * DA.GH;
DA.Z = norm(DT.Z, 2) * DA.Z;

disp(DA);

[MBUNYA NERVILLE ANYANG]

Thank you very much Sir