experiment with associating mca clusters with nakr errors
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@ -57,12 +57,13 @@ function(cat, mod)
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# pre-processing for exploratory analytics of the housing dataset
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datasetHousing.mca <-
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function()
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function(dat=NULL)
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{
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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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# loading dataset in memory
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if(is.null(dat)) { dat <- read.csv(file="data/housing.csv", header=TRUE) }
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# transformation de ocean_proximity en facteur
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# transform ocean_proximity into a factor
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# a factor being R representation of categorical variables
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dat$ocean_proximity <- as.factor(dat$ocean_proximity)
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levels(dat$ocean_proximity)[levels(dat$ocean_proximity)=="<1H OCEAN"] <- "O:<1H"
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levels(dat$ocean_proximity)[levels(dat$ocean_proximity)=="ISLAND"] <- "O:ISL"
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@ -70,81 +71,83 @@ function()
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levels(dat$ocean_proximity)[levels(dat$ocean_proximity)=="NEAR BAY"] <- "O:NB"
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levels(dat$ocean_proximity)[levels(dat$ocean_proximity)=="NEAR OCEAN"] <- "O:NO"
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# quantification de longitude
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# discretization of 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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# discretization of 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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# discretization of 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$housing_median_age, unique(cuts), include.lowest = TRUE)
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dat$c_age <- cut(x = dat$housing_median_age, unique(cuts),
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include.lowest = TRUE)
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levels(dat$c_age) <- c('AG:15]','AG:25]','AG:35]','AG:51]', 'AG:52')
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# création et quantification de rooms
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# creation and discretization of 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('RO:4]','RO:6]','RO:8]', 'RO:>8')
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# création et quantification de bedrooms
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# creation and discretization of 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('BE:1]','BE:>1')
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# création et quantification de pop
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# creation and discretization of 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('PO:2]','PO:3]', 'PO:4]', 'PO:>4')
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# quantification de households
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# discretization of 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$c_households) <- c('HH:3]', 'HH:4]', 'HH:6]', 'HH:>6')
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# quantification de median_income
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# discretization of median_income
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cuts <- quantile(dat$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('IC:L', 'IC:ML', 'IC:MH', 'IC:H', 'IC:>15')
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# quantification de median_house_value
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# discretization of 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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dat$c_house_value <- cut(x = dat$median_house_value, cuts,
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include.lowest = TRUE)
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levels(dat$c_house_value) <- c('HV:A', 'HV:B', 'HV:C', 'HV:D', 'HV:E')
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# création du jeu de données quantifié
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# discretized version of the entire dataset
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dat <- dat[c('ocean_proximity', 'c_longitude', 'c_latitude', 'c_age',
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'c_rooms', 'c_bedrooms', 'c_pop', 'c_households', 'c_income',
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'c_house_value')]
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vent <- list()
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# ventilation de la modalité RO:>8 de c_rooms
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# ventilation of modality RO:>8 of variable c_rooms
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vent$c_rooms <- ventilate(dat$c_rooms, "RO:>8")
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dat$c_rooms[vent$c_rooms$sup_i] <- vent$c_rooms$smpl
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# ventilation de la modalité IC:>15 de c_income
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# ventilation of modality IC:>15 of variable c_income
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vent$c_income <- ventilate(dat$c_income, "IC:>15")
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dat$c_income[vent$c_income$sup_i] <- vent$c_income$smpl
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# ventilation de la modalité O:ISL de ocean_proximity
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# ventilation of modality O:ISL of variable ocean_proximity
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vent$ocean_proximity <- ventilate(dat$ocean_proximity, "O:ISL")
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dat$ocean_proximity[vent$ocean_proximity$sup_i] <- vent$ocean_proximity$smpl
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# ventilation des valeurs manquantes de c_bedrooms
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# ventilation of missing values of variable c_bedrooms
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vent$c_bedrooms <- ventilate(dat$c_bedrooms, "NA")
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dat$c_bedrooms[vent$c_bedrooms$sup_i] <- vent$c_bedrooms$smpl
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# suppression des modalités vides après ventilation
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# removal of empty modalities following the various ventilations
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dat <- droplevels(dat)
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# positionnement de c_house_value en variable supplémentaire
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# c_house_value, the target, is considered as a supplementary variable
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supvar <- which(names(dat) == "c_house_value")
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r <- list( vent=vent, dat=dat, supvar=supvar )
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@ -152,8 +155,7 @@ function()
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return(r)
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}
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# one hot encoding (codage disjonctif complet) of a dataframe
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# made of categorical variables
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# one hot encoding of a dataframe made of categorical variables
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onehot_enc <-
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function(dat.cat)
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{
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@ -250,9 +252,21 @@ function(dat, nclst = 100)
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# Principal coordinates of clusters' centers
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fclst <- clsti$centers
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r <- list(f=f, ctr=ctr, cor=cor, r=r, sv=sv,
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fsi=fsi, sicor=sicor, fsj=fsj, sjcor=sjcor,
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clsti=clsti)
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r <- list(f=f, # principal coordinates
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ctr=ctr, # contributions of the modalities
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# to the principal axes
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cor=cor, # correlations of the modalities
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# with the principal axes
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r=r, # marginal profile of the modalities
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sv=sv, # K (=J-Q) singular values
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fsi=fsi, # principal coordinates of the individuals
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sicor=sicor, # correlations of the individuals
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# with the principal axes
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fsj=fsj, # principal coordinates of the modalities
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# of the supplementary variables
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sjcor=sjcor, # correlations of the supplementary variables
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# with the principal axes
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clsti=clsti) # kmeans clustering of the individuals
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class(r) <- "mca"
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return(r)
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}
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@ -268,7 +282,7 @@ function(o)
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nclst <- length(o$clsti$size)
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# Correlation of clusters and factorial axes
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# Correlation of clusters' centers and factorial axes
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temp <- o$clsti$centers^2
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sum_cor <- apply(temp, 1, sum)
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clstcor <- sweep(temp, 1, sum_cor, FUN="/")
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@ -285,7 +299,8 @@ function(o)
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tblClstCor <- t(sapply(1:nclst, selMostCorFact))
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tblClstCor <- cbind(tblClstCor, o$clsti$size)
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rwithinss <- o$clsti$withinss / o$clsti$size # withinss relative to the cluster size
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rwithinss <- o$clsti$withinss / o$clsti$size # within sum of squares
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# relative to cluster size
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clstqlty <- round_preserve_sum(1000 * rwithinss / sum(rwithinss))
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tblClstCor <- cbind(tblClstCor, clstqlty)
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rownames(tblClstCor) <- paste0('clst-', 1:nclst)
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@ -304,10 +319,10 @@ function(o, d1 = NULL, d2 = NULL)
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if(is.null(d1)) d1<-1
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if(is.null(d2)) d2<-2
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# Part de l'inertie du plan factoriel d1-d2 expliquée par chaque profil
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# proportion of inertia of factorial plan d1-d2 explained by each profile
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cont <- o$r * (o$f[,d1]^2 + o$f[,d2]^2) / (o$sv[d1]^2 + o$sv[d2]^2)
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names <- rownames(o$f)
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names[cont < 0.01] <- "."
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names[cont < 0.05] <- "."
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optimPar <- nonlinearFontSize.mca(cont)
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sizes <- log(1 + exp(optimPar[1]) * cont^optimPar[2])
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sizes[cont < 0.01] <- 1
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@ -330,7 +345,8 @@ function(o, d1 = NULL, d2 = NULL)
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plot(o$f[,d1], o$f[,d2], type = "n",
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xlab="", ylab="", asp = 1, xaxt = "n", yaxt = "n")
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text(o$f[,d1], o$f[,d2], ns$names, adj = 0, cex = ns$sizes, col = 'blue', font = 2)
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text(o$f[,d1], o$f[,d2], ns$names, adj = 0, cex = ns$sizes,
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col = 'blue', font = 2)
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points(0, 0, pch = 3)
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}
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@ -366,7 +382,7 @@ function(o, d1 = NULL, d2 = NULL)
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if(is.null(d2)) d2<-2
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nsm <- textSize.mca(o, d1, d2) # names and sizes for modalities
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nsi <- textSizeClst.mca(o, d1, d2) # names and sizes for clusters of individuals
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nsi <- textSizeClst.mca(o, d1, d2) # names and sizes for clust of individuals
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plot(c(o$f[,d1], o$fsj[,d1], o$clsti$centers[,d1]),
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c(o$f[,d2], o$fsj[,d2], o$clsti$centers[,d2]),
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@ -396,10 +412,10 @@ function(o, d1 = NULL, d2 = NULL)
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clstcor <- sweep(temp, 1, sum_cor, FUN="/")
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clstcor <- rowSums(clstcor[,c(d1,d2)])
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names <- names(clstcor)
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names[clstcor < 0.01] <- "x"
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names[clstcor < 0.05] <- "x"
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optimPar <- nonlinearFontSize.mca(clstcor)
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sizes <- log(1 + exp(optimPar[1]) * clstcor^optimPar[2])
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sizes[clstcor < 0.01] <- 1
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sizes[clstcor < 0.05] <- 1
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r <- list(names=names, sizes=sizes)
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return(r)
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}
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@ -1,11 +1,16 @@
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source("04_validation_croisee_code.R")
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source("05_d_svd_mca_code.R")
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source("15_loocv_code.R")
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source("19_nystroem_approximation_code.R")
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dataset.housing <-
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function()
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{
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set.seed(1123)
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# loading dataset in memory
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dat <- read.csv(file="data/housing.csv", header=TRUE)
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# transform ocean_proximity into a factor
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dat$ocean_proximity <- as.factor(dat$ocean_proximity)
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levels(dat$ocean_proximity)[levels(dat$ocean_proximity)=="<1H OCEAN"] <- "O:<1H"
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levels(dat$ocean_proximity)[levels(dat$ocean_proximity)=="ISLAND"] <- "O:ISL"
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@ -13,33 +18,144 @@ function()
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levels(dat$ocean_proximity)[levels(dat$ocean_proximity)=="NEAR BAY"] <- "O:NB"
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levels(dat$ocean_proximity)[levels(dat$ocean_proximity)=="NEAR OCEAN"] <- "O:NO"
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# replace total_bedrooms missing values with the median value
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dat$total_bedrooms[is.na(dat$total_bedrooms)] <- median(dat$total_bedrooms, na.rm=TRUE)
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# remove individuals corresponding to the Island modality of ocean_proximity
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dat <- dat[dat$ocean_proximity != "O:ISL", ]
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# suppression des modalités vides (ici "O:ISL")
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# remove empty modalities (here, only "O:ISL")
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dat <- droplevels(dat)
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# introduce new variable for number of rooms by households
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dat['rooms'] <- dat['total_rooms'] / dat['households']
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# introduce new variable for number of bedrooms by households
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dat['bedrooms'] <- dat['total_bedrooms'] / dat['households']
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# introduce new variable for number of people by households
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dat['pop'] <- dat['population'] / dat['households']
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# remove individuals with extremely high values of the target
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dat <- dat[dat$median_house_value < 500001, ]
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# select variables to retain in the dataset
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dat <- dat[c('longitude', 'latitude', 'housing_median_age', 'households',
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'median_income', 'median_house_value', 'ocean_proximity',
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'rooms', 'bedrooms', 'pop')]
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# one-hot-enconde categorical variable ocean_proximity
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Z <- onehot_enc(dat[c('ocean_proximity')])
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dat <- cbind(dat, as.data.frame(Z))
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dat <- dat[,!(colnames(dat) %in% c('ocean_proximity'))]
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dat.all <- dat
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# separate observed variables X from the target Y
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X <- dat[,!(colnames(dat) %in% c('median_house_value'))]
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Y <- dat[,c('median_house_value')]
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names(Y) <- rownames(X)
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dat <- list(X = X, Y = Y)
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# split the dataset into train and test
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split <- splitdata(dat, 0.8)
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entr <- split$entr
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train <- split$entr
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test <- split$test
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r <- list( dat=dat.all, entr=entr, test=test )
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r <- list( dat=dat.all, train=train, test=test )
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return(r)
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}
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# create a categorical dataset for correspondence analysis of the training data
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dataset.housing.mca <-
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function(dat=NULL)
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{
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# loading dataset in memory
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if(is.null(dat)) { dat <- read.csv(file="data/housing.csv", header=TRUE) }
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# transform ocean_proximity into a factor
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dat$ocean_proximity <- as.factor(dat$ocean_proximity)
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levels(dat$ocean_proximity)[levels(dat$ocean_proximity)=="<1H OCEAN"] <- "O:<1H"
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levels(dat$ocean_proximity)[levels(dat$ocean_proximity)=="ISLAND"] <- "O:ISL"
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levels(dat$ocean_proximity)[levels(dat$ocean_proximity)=="INLAND"] <- "O:INL"
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levels(dat$ocean_proximity)[levels(dat$ocean_proximity)=="NEAR BAY"] <- "O:NB"
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levels(dat$ocean_proximity)[levels(dat$ocean_proximity)=="NEAR OCEAN"] <- "O:NO"
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# discretization of 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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# discretization of 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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# discretization of 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$housing_median_age, unique(cuts),
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include.lowest = TRUE)
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levels(dat$c_age) <- c('AG:15]','AG:25]','AG:35]','AG:51]', 'AG:52')
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# creation and discretization of 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('RO:4]','RO:6]','RO:8]', 'RO:>8')
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# creation and discretization of 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('BE:1]','BE:>1')
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# creation and discretization of 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('PO:2]','PO:3]', 'PO:4]', 'PO:>4')
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# discretization of 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$c_households) <- c('HH:3]', 'HH:4]', 'HH:6]', 'HH:>6')
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# discretization of median_income
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cuts <- quantile(dat$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('IC:L', 'IC:ML', 'IC:MH', 'IC:H', 'IC:>15')
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# discretization of median_house_value
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cuts <- c(min(dat$median_house_value), 115000, 175000, 250000,
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max(dat$median_house_value))
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dat$c_house_value <- cut(x = dat$median_house_value, cuts,
|
||||
include.lowest = TRUE)
|
||||
levels(dat$c_house_value) <- c('HV:A', 'HV:B', 'HV:C', 'HV:D')
|
||||
|
||||
# discretized version of the entire dataset
|
||||
dat <- dat[c('ocean_proximity', 'c_longitude', 'c_latitude', 'c_age',
|
||||
'c_rooms', 'c_bedrooms', 'c_pop', 'c_households', 'c_income',
|
||||
'c_house_value')]
|
||||
vent <- list()
|
||||
# ventilation of modality RO:>8 of variable c_rooms
|
||||
vent$c_rooms <- ventilate(dat$c_rooms, "RO:>8")
|
||||
dat$c_rooms[vent$c_rooms$sup_i] <- vent$c_rooms$smpl
|
||||
|
||||
# ventilation of modality IC:>15 of variable c_income
|
||||
vent$c_income <- ventilate(dat$c_income, "IC:>15")
|
||||
dat$c_income[vent$c_income$sup_i] <- vent$c_income$smpl
|
||||
|
||||
# ventilation of missing values of variable c_bedrooms
|
||||
vent$c_bedrooms <- ventilate(dat$c_bedrooms, "NA")
|
||||
dat$c_bedrooms[vent$c_bedrooms$sup_i] <- vent$c_bedrooms$smpl
|
||||
|
||||
# removal of empty modalities following the various ventilations
|
||||
dat <- droplevels(dat)
|
||||
|
||||
# c_house_value, the target, is considered as a supplementary variable
|
||||
supvar <- which(names(dat) == "c_house_value")
|
||||
|
||||
r <- list( vent=vent, dat=dat, supvar=supvar )
|
||||
|
||||
return(r)
|
||||
}
|
||||
|
||||
|
|
@ -47,20 +163,42 @@ print("load dataset")
|
|||
dat <- dataset.housing()
|
||||
|
||||
print("Nystroem approx ridge regression")
|
||||
nakrm <- nakr(dat$entr$X, dat$entr$Y)
|
||||
nakrm <- nakr(dat$train$X, dat$train$Y)
|
||||
nakrm.yh <- predict(nakrm, dat$test$X)
|
||||
nakrm.mae <- mean(abs(nakrm.yh - dat$test$Y))
|
||||
print(paste("MAE for Nystroem: ", nakrm.mae))
|
||||
print(paste("Test MAE for Nystroem: ", nakrm.mae))
|
||||
|
||||
# correspondence analysis of the training set
|
||||
rawdat <- read.csv(file="data/housing.csv", header=TRUE)
|
||||
train.rawdat <- rawdat[as.numeric(rownames(dat$train$X)),]
|
||||
dat.mca <- dataset.housing.mca(train.rawdat)
|
||||
cam <- mca(dat.mca)
|
||||
|
||||
# average of the prediction errors by clusters
|
||||
nakrm.yh.train <- predict(nakrm, dat$train$X)
|
||||
nakrm.mae.train <- mean(abs(nakrm.yh.train - dat$train$Y))
|
||||
nakrm.err.train <- abs(nakrm.yh.train - dat$train$Y)
|
||||
clst.err <- aggregate(nakrm.err.train, list(cam$clsti$cluster), FUN=mean)
|
||||
clst.err$Group.1 <- paste0("clst-", as.character(clst.err$Group.1))
|
||||
clst.tbl <- clstcor.mca(cam)
|
||||
clst.err <- clst.err[match(rownames(clst.tbl),clst.err$Group.1),]
|
||||
clst.tbl <- cbind(clst.tbl, clst.err[,2])
|
||||
colnames(clst.tbl)[ncol(clst.tbl)] <- "ERR"
|
||||
clst.tbl <- clst.tbl[order(-clst.tbl[,"ERR"]),]
|
||||
print("training set clusters obtained by correspondence analysis and ordered by amount of error")
|
||||
print(clst.tbl)
|
||||
# From these informations, we could try to understand why for some clusters the model commits greater errors...
|
||||
|
||||
print("Linear ridge regression")
|
||||
rm <- ridge(dat$entr$X, dat$entr$Y)
|
||||
rm <- ridge(dat$train$X, dat$train$Y)
|
||||
rm.yh <- predict(rm, dat$test$X)
|
||||
rm.mae <- mean(abs(rm.yh - dat$test$Y))
|
||||
print(paste("MAE for Ridge: ", rm.mae))
|
||||
print(paste("Test MAE for Ridge: ", rm.mae))
|
||||
|
||||
|
||||
print("Random forest")
|
||||
library(randomForest)
|
||||
rfm <- randomForest(dat$entr$X, dat$entr$Y)
|
||||
rfm <- randomForest(dat$train$X, dat$train$Y)
|
||||
rfm.yh <- predict(rfm, dat$test$X)
|
||||
rfm.mae <- mean(abs(rfm.yh - dat$test$Y))
|
||||
print(paste("MAE for Random Forest: ", rfm.mae))
|
||||
print(paste("Test MAE for Random Forest: ", rfm.mae))
|
||||
Loading…
Reference in New Issue