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glmtree: logistic regression trees for efficient segmentation

Adrien Ehrhardt

2024-03-06

Segmentation

Three clusters, one predictive law

Simulation

library(glmtree)
data <- generateData(n = 1000, scenario = "no tree", visualize = TRUE)

int_train <- sample.int(n = 1000, size = 0.2 * 1000)

test <- data[-int_train, ]
data <- data[int_train, ]

PCA

library(FactoMineR)
mixed <- PCA(data[, c("x1", "x2")])

data$pca1 <- predict(mixed, data)$coord[, 1]
data$pca2 <- predict(mixed, data)$coord[, 2]
test$pca1 <- predict(mixed, test)$coord[, 1]
test$pca2 <- predict(mixed, test)$coord[, 2]

data$cluster <- ifelse(data$pca1 > 1, 1, ifelse(data$pca1 > 0, 2, 3))
test$cluster <- ifelse(test$pca1 > 1, 1, ifelse(test$pca1 > 0, 2, 3))

pred <- matrix(0, nrow = 0.2 * 1000, ncol = 1)

for (j in 1:3) {
  modele <- glm(y ~ x1 + x2, data = data[data$cluster == j, ], family = binomial(link = "logit"))
  pred[test$cluster == j] <- predict(modele, test[test$cluster == j, ], type = "response")
}

normalizedGini(test$y, pred)

## [1] 0.6203462

plot(mixed, choix = "ind", label = "none")

MOB

if (require(partykit, quietly = TRUE)) {
  mob_data <- partykit::glmtree(formula = y ~ x1 + x2 | x1 + x2, data = data, family = binomial)
  plot(mob_data)
  normalizedGini(test$y, predict(mob_data, test))
}

## 
## Attaching package: 'partykit'

## The following object is masked from 'package:glmtree':
## 
##     glmtree

## [1] 0.6493551

`glmtree` approach

tree <- glmtree::glmtree(x = data[, c("x1", "x2")], y = data$y)

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plot(unlist(tree@performance$criterionEvolution), type = "l")

data$c_map <- factor(apply(predict(tree@best.tree$tree, data, type = "prob"), 1, function(p) names(which.max(p))))
test$c_map <- factor(apply(predict(tree@best.tree$tree, data, type = "prob"), 1, function(p) names(which.max(p))))

table(data$c_map)

## 
##   4 
## 200

plot(data[, 1], data[, 2], pch = 2 + data[, 3], col = as.numeric(data$c_map), xlab = "First coordinate", ylab = "Second coordinate")

plot(tree@best.tree$tree)

pred <- matrix(0, nrow = 0.2 * 1000, ncol = 1)

for (j in levels(data$c_map)) {
  modele <- glm(y ~ x1 + x2, data = data[data$c_map == j, ], family = binomial(link = "logit"))
  pred[test$c_map == j] <- predict(modele, test[test$c_map == j, ], type = "response")
}

normalizedGini(test$y, pred)

## [1] 0.6493551

One “cluster”, three predictive laws

Simulation

data <- generateData(n = 1000, scenario = "tree", visualize = TRUE)

int_train <- sample.int(n = 1000, size = 0.2 * 1000)

test <- data[-int_train, ]
data <- data[int_train, ]

PCA

mixed <- FAMD(data[, c("x1", "x2", "x3")])

## Warning: ggrepel: 189 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps

## Warning: ggrepel: 189 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps

dim_famd <- predict(mixed, test)$coord[, "Dim 1"] < 0

pred <- matrix(0, nrow = 0.2 * 1000, ncol = 1)

for (j in c(TRUE, FALSE)) {
  modele <- glm(y ~ x1 + x2 + x3, data = data[dim_famd == j, ], family = binomial(link = "logit"))
  pred[dim_famd == j] <- predict(modele, test[dim_famd == j, ], type = "response")
}

normalizedGini(test$y, pred)

## [1] 0.2555439

MOB

if (require(partykit, quietly = TRUE)) {
  mob_data <- partykit::glmtree(formula = y ~ x1 + x2 + x3 | x1 + x2 + x3, data = data, family = binomial)
  plot(mob_data)
  normalizedGini(test$y, predict(mob_data, test))
}

## [1] 0.4333233

`glmtree` approach

tree <- glmtree::glmtree(x = data[, c("x1", "x2", "x3")], y = data$y)

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plot(unlist(tree@performance$criterionEvolution), type = "l")

data$c_map <- factor(apply(predict(tree@best.tree$tree, data, type = "prob"), 1, function(p) names(which.max(p))))
test$c_map <- factor(apply(predict(tree@best.tree$tree, test, type = "prob"), 1, function(p) names(which.max(p))))

table(data$c, data$c_map)

##    
##      1  9
##   1 26 25
##   2 38 33
##   3 36 42

plot(data[, 1], data[, 2], pch = 2 + data[, 3], col = as.numeric(data$c_map), xlab = "First coordinate", ylab = "Second coordinate")

plot(tree@best.tree$tree)

pred <- matrix(0, nrow = 0.2 * 1000, ncol = 1)

for (j in 1:nlevels(data$c_map)) {
  pred[test$c_map == levels(data$c_map)[j]] <- predict(tree@best.tree$glms[[j]], test[test$c_map == levels(data$c_map)[j], ], type = "response")
}

normalizedGini(test$y, pred)

## [1] 0.4415985

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.

glmtree: logistic regression trees for efficient segmentation

Adrien Ehrhardt

2024-03-06

Segmentation

Three clusters, one predictive law

Simulation

PCA

MOB

glmtree approach

One “cluster”, three predictive laws

Simulation

PCA

MOB

glmtree approach

`glmtree`: logistic regression trees for efficient segmentation

`glmtree` approach

`glmtree` approach