change date of last update and change in pad
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@ -4,7 +4,7 @@ author: "Pierre-Edouard Portier"
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documentclass: book
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geometry: margin=2cm
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fontsize: 12pt
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date: "Jan 2023"
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date: "15 Jan 2023"
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toc: true
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classoption: fleqn
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bibliography: intro_to_ml.bib
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197
pad.R
197
pad.R
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@ -25,200 +25,3 @@
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# adj = 0, cex = 0.6)
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# points(0, 0, pch = 3)
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# ```
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# Extrait de 05_d_svd_mca.Rmd
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## Synthèse des transformations opérées sur le jeu de données
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Nous rappelons ci-dessous l'ensemble des transformations opérées sur le jeu de données.
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```{r, eval = FALSE}
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source('05_d_svd_mca_code.R')
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# chargement du jeu de données
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dat <- read.csv(file="data/housing.csv", header=TRUE)
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# transformation de ocean_proximity en facteur
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dat$ocean_proximity <- as.factor(dat$ocean_proximity)
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# quantification de longitude
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cuts <- kcuts(x = dat$longitude, centers = 4)
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dat$c_longitude <- cut(x = dat$longitude, unique(cuts), include.lowest = TRUE)
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levels(dat$c_longitude) <- c('LO-W', 'LO-MW', 'LO-ME', 'LO-E')
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# quantification de latitude
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cuts <- kcuts(x = dat$latitude, centers = 4)
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dat$c_latitude <- cut(x = dat$latitude, unique(cuts), include.lowest = TRUE)
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levels(dat$c_latitude) <- c('LA-S','LA-MS','LA-MN','LA-N')
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# quantification de housing_median_age
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cuts <- c(min(dat$housing_median_age), 15, 25, 35, 51, 52)
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dat$c_age <- cut(x = dat$housing_median_age, unique(cuts), include.lowest = TRUE)
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levels(dat$c_age) <- c('A<=15','A(15,25]','A(25,35]','A(35,51]', 'A=52')
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# création et quantification de rooms
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dat$rooms <- dat$total_rooms / dat$households
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cuts <- c(min(dat$rooms), 4, 6, 8, max(dat$rooms))
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dat$c_rooms <- cut(x = dat$rooms, unique(cuts), include.lowest = TRUE)
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levels(dat$c_rooms) <- c('R<=4','R(4,6]','R(6,8]', 'R>8')
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# création et quantification de bedrooms
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dat$bedrooms <- dat$total_bedrooms / dat$households
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cuts <- c(min(dat$bedrooms, na.rm = TRUE), 1.1, max(dat$bedrooms, na.rm = TRUE))
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dat$c_bedrooms <- cut(x = dat$bedrooms, unique(cuts), include.lowest = TRUE)
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levels(dat$c_bedrooms) <- c('B<=1','B>1')
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# création et quantification de pop
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dat$pop <- dat$population / dat$households
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cuts <- c(min(dat$pop), 2, 3, 4, max(dat$pop))
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dat$c_pop <- cut(x = dat$pop, unique(cuts), include.lowest = TRUE)
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levels(dat$c_pop) <- c('P<=2','P(2,3]', 'P(3,4]', 'P>4')
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# quantification de households
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cuts <- c(min(dat$households), 300, 400, 600, max(dat$households))
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dat$c_households <- cut(x = dat$households, cuts, include.lowest = TRUE)
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levels(dat$c_households) <- c('H<=3', 'H(3,4]', 'H(4,6]', 'H>6')
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# quantification de median_income
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cuts <- quantile(dat$median_income, probs = seq(0,1,1/4))
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cuts <- c(cuts[1:length(cuts)-1], 15, max(dat$median_income))
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dat$c_income <- cut(x = dat$median_income, cuts, include.lowest = TRUE)
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levels(dat$c_income) <- c('IL', 'IML', 'IMH', 'IH', 'I>15')
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# quantification de median_house_value
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cuts <- c(min(dat$median_house_value), 115000, 175000, 250000, 500000,
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max(dat$median_house_value))
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dat$c_house_value <- cut(x = dat$median_house_value, cuts, include.lowest = TRUE)
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levels(dat$c_house_value) <- c('V<=115', 'V(115,175]', 'V(175,250]', 'V(250,500]',
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'V>500')
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# création du jeu de données quantifié
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dat.all <- dat
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dat <- dat.all[c('ocean_proximity', 'c_longitude', 'c_latitude', 'c_age',
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'c_rooms', 'c_bedrooms', 'c_pop', 'c_households', 'c_income',
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'c_house_value')]
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# ventilation de la modalité R>8 de c_rooms
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c_rooms_sup <- ventilate(dat$c_rooms, "R>8")
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dat$c_rooms[c_rooms_sup$sup_i] <- c_rooms_sup$smpl
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# ventilation de la modalité I>15 de c_income
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c_income_sup <- ventilate(dat$c_income, "I>15")
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dat$c_income[c_income_sup$sup_i] <- c_income_sup$smpl
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# ventilation de la modalité ISLAND de ocean_proximity
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ocean_proximity_sup <- ventilate(dat$ocean_proximity, "ISLAND")
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dat$ocean_proximity[ocean_proximity_sup$sup_i] <- ocean_proximity_sup$smpl
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# ventilation des valeurs manquantes de c_bedrooms
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c_bedrooms_sup <- ventilate(dat$c_bedrooms, "NA")
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dat$c_bedrooms[c_bedrooms_sup$sup_i] <- c_bedrooms_sup$smpl
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# suppression des modalités vides après ventilation
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dat <- droplevels(dat)
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# positionnement de c_house_value en variable supplémentaire
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sup_ind <- which(names(dat) == "c_house_value")
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dat_act <- dat[,-sup_ind]
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dat_sup <- dat[,sup_ind]
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I <- dim(dat_act)[1]
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Q <- dim(dat_act)[2]
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# construction du tableau disjonctif complet
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lev_n <- unlist(lapply(dat, nlevels))
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n <- cumsum(lev_n)
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J_t <- sum(lev_n)
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Q_t <- dim(dat)[2]
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Z <- matrix(0, nrow = I, ncol = J_t)
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numdat <- lapply(dat, as.numeric)
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offset <- c(0, n[-length(n)])
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for (i in 1:Q_t)
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Z[1:I + (I * (offset[i] + numdat[[i]] - 1))] <- 1
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cn <- rep(names(dat), lev_n)
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ln <- unlist(lapply(dat, levels))
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dimnames(Z)[[1]] <- as.character(1:I)
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dimnames(Z)[[2]] <- paste(cn, ln, sep = "")
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Z_sup_min <- n[sup_ind[1] - 1] + 1
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Z_sup_max <- n[sup_ind[length(sup_ind)]]
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Z_sup_ind <- Z_sup_min : Z_sup_max
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Z_act <- Z[,-Z_sup_ind]
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J <- dim(Z_act)[2]
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# Construction de la matrice de Burt
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B <- t(Z_act) %*% Z_act
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# Analyse des correspondances
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P <- B / sum(B)
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r <- apply(P, 2, sum)
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rr <- r %*% t(r)
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S <- (P - rr) / sqrt(rr)
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dec <- eigen(S)
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# les Q dernières valeurs propres sont nécessairement nulles.
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delt <- dec$values[1 : (J-Q)]
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# Calcul des coordonnées standard (a) et principales (f)
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K <- J - Q
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a <- sweep(dec$vectors, 1, sqrt(r), FUN = "/")
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a <- a[,(1 : K)]
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f <- a %*% diag(delt)
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# Noms des facteurs et des modalités
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lbl_dic <- c(
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"O:<1H" = "ocean_proximity<1H OCEAN",
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"O:INL" = "ocean_proximityINLAND",
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"O:NB" = "ocean_proximityNEAR BAY",
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"O:NO" = "ocean_proximityNEAR OCEAN",
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"LO:W" = "c_longitudeLO-W",
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"LO:MW" = "c_longitudeLO-MW",
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"LO:ME" = "c_longitudeLO-ME",
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"LO:E" = "c_longitudeLO-E",
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"LA:S" = "c_latitudeLA-S",
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"LA:MS" = "c_latitudeLA-MS",
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"LA:MN" = "c_latitudeLA-MN",
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"LA:N" = "c_latitudeLA-N",
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"AG:15]" = "c_ageA<=15",
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"AG:25]" = "c_ageA(15,25]",
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"AG:35]" = "c_ageA(25,35]",
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"AG:51]" = "c_ageA(35,51]",
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"AG:52" = "c_ageA=52",
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"RO:4]" = "c_roomsR<=4",
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"RO:6]" = "c_roomsR(4,6]",
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"RO:8]" = "c_roomsR(6,8]",
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"BE:1]" = "c_bedroomsB<=1",
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"BE:>1" = "c_bedroomsB>1",
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"PO:2]" = "c_popP<=2",
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"PO:3]" = "c_popP(2,3]",
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"PO:4]" = "c_popP(3,4]",
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"PO:>4" = "c_popP>4",
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"HH:3]" = "c_householdsH<=3",
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"HH:4]" = "c_householdsH(3,4]",
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"HH:6]" = "c_householdsH(4,6]",
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"HH:>6" = "c_householdsH>6",
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"IC:L" = "c_incomeIL",
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"IC:ML" = "c_incomeIML",
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"IC:MH" = "c_incomeIMH",
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"IC:H" = "c_incomeIH",
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"HV:A" = "c_house_valueV<=115",
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"HV:B" = "c_house_valueV(115,175]",
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"HV:C" = "c_house_valueV(175,250]",
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"HV:D" = "c_house_valueV(250,500]",
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"HV:E" = "c_house_valueV>500"
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)
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lbl_act_dic <- lbl_dic[1:J]
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fac_names <- paste("F", paste(1 : K), sep = "")
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rownames(a) <- names(lbl_act_dic)
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colnames(a) <- fac_names
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rownames(f) <- names(lbl_act_dic)
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colnames(f) <- fac_names
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# Calcul des contributions
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temp <- sweep(f^2, 1, r, FUN = "*")
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sum_ctr <- apply(temp, 2, sum)
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ctr <- sweep(temp, 2, sum_ctr, FUN = "/")
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# Calcul des corrélations
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temp <- f^2
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sum_cor <- apply(temp, 1, sum)
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cor <- sweep(temp, 1, sum_cor, FUN="/")
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```
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