mota-b / ADD_ACP

##################

Descriptions

################## in this project we are going to reduce the number of dimention from our data-Mareix with the less possible information loss; in order to represente it in a plan (Better) or a 3D env (at less);

############

Schema

############

MATRIX-data, dim(nm), information(100%) ==> Reduce_Dim_Methode() ==> Matrix-Representative(),dim(n(2|3)), information(<100%)

• Methodes { A.P.C: "Analyse by Principal Composent" }

################

Algorythme

################

mat: matrix of data, dimention (m*n);
mat_cen : centered matrix
mat_R: reduced matrix

# test if the matrix has quantitafi data
if is_quantitafi(matrix) : # we can apply acp
    
    # center the matrix (on it's own gravity point)
    mat_cen = centered(mat)

    # reduce the matrix (the data has same echelle)
    mat_R = reduced(mat_cen)

    # corelation " var/var "
    C = (1/n) * transpose(mat_R) * mat_R

    # find eigen vals "resove the equation : det( transpose(mat_R) * mat_R - landa * I) = 0 " [every landa represent a % from our tota information]

    # find eigen vectors for all landa(s) "resove the equations : transpose(mat_R) * mat_R * V_i = landa_i * V_i "

    # calculate new axes witch represente our 5 variable
    exemple: Axe[i] = tuple(persone)_from_R * eigenVect[i]

    # calculate contribution of each persone in new axes 
    exemple: for each personne in Axe(i)
        weight(personne) =  ( 1/(nbr_personne) ) * ( valu_personne_in(Axe_i)²/eigenvalue(Axe_i) )
    

else 
    # we can't apply acp