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# Font /mnt/font/InputMonoNarrow-Regular/20a/font
# rm(list=ls())
# bookdown::render_book()
# :/^\#
# bash make_chapter 19_nystroem_approximation.Rmd
# knitr::purl("05_c_svd_ca.Rmd")
# Extrait de 05_c_svd_ca.Rmd
#
# Affichons encore une carte avec les coordonnées principales sur les dimensions n°1 et n°2, mais uniquement pour les profils lignes et les profils colonnes considérés importants.
#
# ```{r}
# selI <- CTRI > (1/I)
# selI12 <- selI[,1] | selI[,2]
# selJ <- CTRJ > (1/J)
# selJ12 <- selJ[,1] | selJ[,2]
# par(pty="s") # square plotting region
# plot(c(F[selI12,1], G[selJ12,1]), c(F[selI12,2], G[selJ12,2]),
# main = "x: d1, y: d2", type = "n",
# xlab="", ylab="", asp = 1, xaxt = "n", yaxt = "n")
# text(c(F[selI12,1], G[selJ12,1]), c(F[selI12,2], G[selJ12,2]),
# c(rownames(P)[selI12], colnames(P)[selJ12]),
# adj = 0, cex = 0.6)
# points(0, 0, pch = 3)
# ```
# Extrait de 05_d_svd_mca.Rmd
## Synthèse des transformations opérées sur le jeu de données
Nous rappelons ci-dessous l'ensemble des transformations opérées sur le jeu de données.
```{r, eval = FALSE}
source('05_d_svd_mca_code.R')
# chargement du jeu de données
dat <- read.csv(file="data/housing.csv", header=TRUE)
# transformation de ocean_proximity en facteur
dat$ocean_proximity <- as.factor(dat$ocean_proximity)
# quantification de longitude
cuts <- kcuts(x = dat$longitude, centers = 4)
dat$c_longitude <- cut(x = dat$longitude, unique(cuts), include.lowest = TRUE)
levels(dat$c_longitude) <- c('LO-W', 'LO-MW', 'LO-ME', 'LO-E')
# quantification de latitude
cuts <- kcuts(x = dat$latitude, centers = 4)
dat$c_latitude <- cut(x = dat$latitude, unique(cuts), include.lowest = TRUE)
levels(dat$c_latitude) <- c('LA-S','LA-MS','LA-MN','LA-N')
# quantification de housing_median_age
cuts <- c(min(dat$housing_median_age), 15, 25, 35, 51, 52)
dat$c_age <- cut(x = dat$housing_median_age, unique(cuts), include.lowest = TRUE)
levels(dat$c_age) <- c('A<=15','A(15,25]','A(25,35]','A(35,51]', 'A=52')
# création et quantification de rooms
dat$rooms <- dat$total_rooms / dat$households
cuts <- c(min(dat$rooms), 4, 6, 8, max(dat$rooms))
dat$c_rooms <- cut(x = dat$rooms, unique(cuts), include.lowest = TRUE)
levels(dat$c_rooms) <- c('R<=4','R(4,6]','R(6,8]', 'R>8')
# création et quantification de bedrooms
dat$bedrooms <- dat$total_bedrooms / dat$households
cuts <- c(min(dat$bedrooms, na.rm = TRUE), 1.1, max(dat$bedrooms, na.rm = TRUE))
dat$c_bedrooms <- cut(x = dat$bedrooms, unique(cuts), include.lowest = TRUE)
levels(dat$c_bedrooms) <- c('B<=1','B>1')
# création et quantification de pop
dat$pop <- dat$population / dat$households
cuts <- c(min(dat$pop), 2, 3, 4, max(dat$pop))
dat$c_pop <- cut(x = dat$pop, unique(cuts), include.lowest = TRUE)
levels(dat$c_pop) <- c('P<=2','P(2,3]', 'P(3,4]', 'P>4')
# quantification de households
cuts <- c(min(dat$households), 300, 400, 600, max(dat$households))
dat$c_households <- cut(x = dat$households, cuts, include.lowest = TRUE)
levels(dat$c_households) <- c('H<=3', 'H(3,4]', 'H(4,6]', 'H>6')
# quantification de median_income
cuts <- quantile(dat$median_income, probs = seq(0,1,1/4))
cuts <- c(cuts[1:length(cuts)-1], 15, max(dat$median_income))
dat$c_income <- cut(x = dat$median_income, cuts, include.lowest = TRUE)
levels(dat$c_income) <- c('IL', 'IML', 'IMH', 'IH', 'I>15')
# quantification de median_house_value
cuts <- c(min(dat$median_house_value), 115000, 175000, 250000, 500000,
max(dat$median_house_value))
dat$c_house_value <- cut(x = dat$median_house_value, cuts, include.lowest = TRUE)
levels(dat$c_house_value) <- c('V<=115', 'V(115,175]', 'V(175,250]', 'V(250,500]',
'V>500')
# création du jeu de données quantifié
dat.all <- dat
dat <- dat.all[c('ocean_proximity', 'c_longitude', 'c_latitude', 'c_age',
'c_rooms', 'c_bedrooms', 'c_pop', 'c_households', 'c_income',
'c_house_value')]
# ventilation de la modalité R>8 de c_rooms
c_rooms_sup <- ventilate(dat$c_rooms, "R>8")
dat$c_rooms[c_rooms_sup$sup_i] <- c_rooms_sup$smpl
# ventilation de la modalité I>15 de c_income
c_income_sup <- ventilate(dat$c_income, "I>15")
dat$c_income[c_income_sup$sup_i] <- c_income_sup$smpl
# ventilation de la modalité ISLAND de ocean_proximity
ocean_proximity_sup <- ventilate(dat$ocean_proximity, "ISLAND")
dat$ocean_proximity[ocean_proximity_sup$sup_i] <- ocean_proximity_sup$smpl
# ventilation des valeurs manquantes de c_bedrooms
c_bedrooms_sup <- ventilate(dat$c_bedrooms, "NA")
dat$c_bedrooms[c_bedrooms_sup$sup_i] <- c_bedrooms_sup$smpl
# suppression des modalités vides après ventilation
dat <- droplevels(dat)
# positionnement de c_house_value en variable supplémentaire
sup_ind <- which(names(dat) == "c_house_value")
dat_act <- dat[,-sup_ind]
dat_sup <- dat[,sup_ind]
I <- dim(dat_act)[1]
Q <- dim(dat_act)[2]
# construction du tableau disjonctif complet
lev_n <- unlist(lapply(dat, nlevels))
n <- cumsum(lev_n)
J_t <- sum(lev_n)
Q_t <- dim(dat)[2]
Z <- matrix(0, nrow = I, ncol = J_t)
numdat <- lapply(dat, as.numeric)
offset <- c(0, n[-length(n)])
for (i in 1:Q_t)
Z[1:I + (I * (offset[i] + numdat[[i]] - 1))] <- 1
cn <- rep(names(dat), lev_n)
ln <- unlist(lapply(dat, levels))
dimnames(Z)[[1]] <- as.character(1:I)
dimnames(Z)[[2]] <- paste(cn, ln, sep = "")
Z_sup_min <- n[sup_ind[1] - 1] + 1
Z_sup_max <- n[sup_ind[length(sup_ind)]]
Z_sup_ind <- Z_sup_min : Z_sup_max
Z_act <- Z[,-Z_sup_ind]
J <- dim(Z_act)[2]
# Construction de la matrice de Burt
B <- t(Z_act) %*% Z_act
# Analyse des correspondances
P <- B / sum(B)
r <- apply(P, 2, sum)
rr <- r %*% t(r)
S <- (P - rr) / sqrt(rr)
dec <- eigen(S)
# les Q dernières valeurs propres sont nécessairement nulles.
delt <- dec$values[1 : (J-Q)]
# Calcul des coordonnées standard (a) et principales (f)
K <- J - Q
a <- sweep(dec$vectors, 1, sqrt(r), FUN = "/")
a <- a[,(1 : K)]
f <- a %*% diag(delt)
# Noms des facteurs et des modalités
lbl_dic <- c(
"O:<1H" = "ocean_proximity<1H OCEAN",
"O:INL" = "ocean_proximityINLAND",
"O:NB" = "ocean_proximityNEAR BAY",
"O:NO" = "ocean_proximityNEAR OCEAN",
"LO:W" = "c_longitudeLO-W",
"LO:MW" = "c_longitudeLO-MW",
"LO:ME" = "c_longitudeLO-ME",
"LO:E" = "c_longitudeLO-E",
"LA:S" = "c_latitudeLA-S",
"LA:MS" = "c_latitudeLA-MS",
"LA:MN" = "c_latitudeLA-MN",
"LA:N" = "c_latitudeLA-N",
"AG:15]" = "c_ageA<=15",
"AG:25]" = "c_ageA(15,25]",
"AG:35]" = "c_ageA(25,35]",
"AG:51]" = "c_ageA(35,51]",
"AG:52" = "c_ageA=52",
"RO:4]" = "c_roomsR<=4",
"RO:6]" = "c_roomsR(4,6]",
"RO:8]" = "c_roomsR(6,8]",
"BE:1]" = "c_bedroomsB<=1",
"BE:>1" = "c_bedroomsB>1",
"PO:2]" = "c_popP<=2",
"PO:3]" = "c_popP(2,3]",
"PO:4]" = "c_popP(3,4]",
"PO:>4" = "c_popP>4",
"HH:3]" = "c_householdsH<=3",
"HH:4]" = "c_householdsH(3,4]",
"HH:6]" = "c_householdsH(4,6]",
"HH:>6" = "c_householdsH>6",
"IC:L" = "c_incomeIL",
"IC:ML" = "c_incomeIML",
"IC:MH" = "c_incomeIMH",
"IC:H" = "c_incomeIH",
"HV:A" = "c_house_valueV<=115",
"HV:B" = "c_house_valueV(115,175]",
"HV:C" = "c_house_valueV(175,250]",
"HV:D" = "c_house_valueV(250,500]",
"HV:E" = "c_house_valueV>500"
)
lbl_act_dic <- lbl_dic[1:J]
fac_names <- paste("F", paste(1 : K), sep = "")
rownames(a) <- names(lbl_act_dic)
colnames(a) <- fac_names
rownames(f) <- names(lbl_act_dic)
colnames(f) <- fac_names
# Calcul des contributions
temp <- sweep(f^2, 1, r, FUN = "*")
sum_ctr <- apply(temp, 2, sum)
ctr <- sweep(temp, 2, sum_ctr, FUN = "/")
# Calcul des corrélations
temp <- f^2
sum_cor <- apply(temp, 1, sum)
cor <- sweep(temp, 1, sum_cor, FUN="/")
```
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