Multiple Correspondence Analysis (MCA) generalizes Correspondence Factor Analysis (FCA) to any number of variables and therefore allows the response modalities of more than two variables to be represented on the same mapping.
As with Principal Component Analysis (PCA), the purpose of these analyzes is to identify hidden dimensions contained in the responses to the selected variables to facilitate the interpretation of tables that are not always readable at the start.
The MCA starts from a complete disjunctive table (burt table) which presents the individuals in rows and in columns all the modalities of the qualitative variables retained.
The intersection boxes contain the value 1 if the individual meets the criterion in the column and 0 otherwise.
As in PCA, the first two axes provide a generally important part of the information contained in the initial table, the horizontal axis being, by convention, the most significant.
The proximity of the points provides information, a priori, on their associations.
The arrangement of the modalities of each variable in relation to each other helps to give meaning to each axis.
# -*- coding: utf-8 -*-"""
Created on Wed Jun 22 13:16:15 2022
@author: Ricore
"""#Librairies utiliséesimport pandas
import numpy
import matplotlib.pyplotas plt
import seaborn
seaborn.set_style("white")from prince import MCA
#Données utilisées
df = pandas.read_csv("titanic.csv")
df.head()print(df)#Calcul de ACM
mca = MCA(n_components =10)
mca.fit(df)print(mca)#Valeurs propresprint(mca.eigenvalues_)print(mca.total_inertia_)print(mca.explained_inertia_)
eig = pandas.DataFrame({"Dimension" : ["Dim" + str(x + 1)for x inrange(10)],"Valeur propre": mca.eigenvalues_,"% variance expliquée": numpy.round(mca.explained_inertia_,4) * 100,"% variance expliquée cumulée": numpy.round(numpy.cumsum(mca.explained_inertia_),4) * 100,})print(eig)#Représentation des individus
df_ind = pandas.DataFrame(mca.row_coordinates(df)).rename(columns ={i: "Dim"+str(i+1)for i inrange(10)})
df_ind.head()print(df_ind)
g_ind = seaborn.lmplot(x ="Dim1", y ="Dim2", data = df_ind, fit_reg =False,
height =4, aspect =3)
g_ind.fig.suptitle("Modalités en lignes")
plt.show()#Représentation des variables
df_var = pandas.DataFrame(mca.column_coordinates(df)).rename(columns ={i: "Dim"+str(i+1)for i inrange(10)})print(df_var)
g_var = seaborn.lmplot(x ="Dim1", y ="Dim2", data = df_var, fit_reg =False,
height =4, aspect =3)
g_var.fig.suptitle("Modalités en colonnes")for i in df_var.index:
plt.text(df_var.loc[i].Dim1, df_var.loc[i].Dim2, i, size ="xx-large")
plt.show()#Représentation simultanée
mca.plot_coordinates(df, figsize=(16,8))
plt.show()
fig = plt.figure(figsize =(16,8))
g_simult = seaborn.lmplot(x ="Dim1", y ="Dim2", data = df_ind, fit_reg =False,
height =4, aspect =3)for i in df_var.index:
plt.scatter(df_var.loc[i].Dim1, df_var.loc[i].Dim2, alpha =.25, c ="black")
plt.text(df_var.loc[i].Dim1, df_var.loc[i].Dim2, i, size ="xx-large", color ="darkred", ha ="center")
g_simult.fig.suptitle("Représentation conjointe")
plt.show()
Analyse des Correspondances Multiples (ACM) - Mastère ESD - Introduction au Machine Learning - GitHub
Class Sex Age Survived
0 1st Male Adult No
1 3rd Male Adult Yes
2 Crew Male Adult No
3 Crew Male Adult Yes
4 2nd Male Adult No
... ... ... ...
2196 Crew Male Adult Yes
2197 3rd Male Adult Yes
2198 Crew Male Adult No
2199 3rd Male Adult Yes
2200 3rd Male Adult No
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