tSNE Parameter Tuning in R

Introduction

Welcome! Today's focus is on t-SNE parameter tuning using R and the Rtsne package . This lesson covers an understanding of critical t-SNE parameters, the practice of parameter tuning, and its impact on data visualization outcomes in R.

Preparing the data

Before delving into parameter tuning, let's quickly set up the dataset: Here's a basic setup in R: R # Load required libraries library(ggplot2) # Generate a non-linearly separable dataset (two circles) like sklearn.make_circles set.seed(42) n_samples <- 500 factor <- 0.3 noise <- 0.1 half <- n_samples / 2 theta_outer <- runif(half, 0, 2*pi) theta_inner <- runif(half, 0, 2*pi) r_outer <- 1 + rnorm(half, sd = noise) r_inner <- factor + rnorm(half, sd = noise) X <- rbind(cbind(r_outer * cos(theta_outer), r_outer * sin(theta_outer)), cbind(r_inner * cos(theta_inner), r_inner * sin(theta_inner))) X <- as.data.frame(X) colnames(X) <- c("x1", "x2") y <- as.factor(c(rep(0, half), rep(1, half))) # Plot the dataset plot <- ggplot(X, aes(x = x1, y = x2, color = y)) + geom_point(size = 2) + labs(title = "Original Data", color = "Class") + theme_minimal() + theme( panel.background = element_rect(fill = "white", color = NA), plot.background = element_rect(fill = "white", color = NA) ) + coord_equal() # Load required libraries library(ggplot2) # Generate a non-linearly separable dataset (two circles) like sklearn.make_circles set.seed(42) n_samples <- 500 factor <- 0.3 noise <- 0.1 half <- n_samples / 2 theta_outer <- runif(half, 0, 2*pi) theta_inner <- runif(half, 0, 2*pi) r_outer <- 1 + rnorm(half, sd = noise) r_inner <- factor + rnorm(half, sd = noise) X <- rbind(cbind(r_outer * cos(theta_outer), r_outer * sin(theta_outer)), cbind(r_inner * cos(theta_inner), r_inner * sin(theta_inner))) X <- as.data.frame(X) colnames(X) <- c("x1", "x2") y <- as.factor(c(rep(0, half), rep(1, half))) # Plot the dataset plot <- ggplot(X, aes(x = x1, y = x2, color = y)) + geom_point(size = 2) + labs(title = "Original Data", color = "Class") + theme_minimal() + theme( panel.background = element_rect(fill = "white", color = NA), plot.background = element_rect(fill = "white", color = NA) ) + coord_equal()

Understanding t-SNE Parameters: Perplexity

We will now delve into the key parameters in R's t-SNE implementation (Rtsne). The first one is perplexity, which is loosely determined by the number of effective nearest neighbors. It strikes a balance between preserving the local and global data structure.

Understanding t-SNE Parameters: Early Exaggeration

The next parameter is exaggeration_factor (in Rtsne, this replaces early_exaggeration). It governs how tight natural clusters are in the embedded space. High values tend to make clusters denser.

Understanding t-SNE Parameters: Learning Rate

The final parameter, eta, modulates the step size for the gradient during the optimization process.

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# Load required libraries
library(ggplot2)

# Generate a non-linearly separable dataset (two circles) like sklearn.make_circles
set.seed(42)
n_samples <- 500
factor <- 0.3
noise  <- 0.1

half <- n_samples / 2
theta_outer <- runif(half, 0, 2*pi)
theta_inner <- runif(half, 0, 2*pi)

r_outer <- 1 + rnorm(half, sd = noise)
r_inner <- factor + rnorm(half, sd = noise)

X <- rbind(
  cbind(r_outer * cos(theta_outer), r_outer * sin(theta_outer)),
  cbind(r_inner * cos(theta_inner), r_inner * sin(theta_inner))
)
X <- as.data.frame(X)
colnames(X) <- c("x1", "x2")
y <- as.factor(c(rep(0, half), rep(1, half)))

# Plot the dataset
plot <- ggplot(X, aes(x = x1, y = x2, color = y)) +
  geom_point(size = 2) +
  labs(title = "Original Data", color = "Class") +
  theme_minimal() + theme( panel.background = element_rect(fill = "white", color = NA), plot.background = element_rect(fill = "white", color = NA) )  + coord_equal()

library(Rtsne)
library(ggplot2)

# t-SNE with default-like parameters (no scaling; pca=FALSE to mirror sklearn behavior)
set.seed(42)
tsne_1 <- Rtsne(
  as.matrix(X),
  dims = 2,
  perplexity = 30,
  exaggeration_factor = 12,
  eta = 200,
  pca = FALSE,
  check_duplicates = FALSE,
  verbose = FALSE
)
tsne_transformed_1 <- as.data.frame(tsne_1$Y)
colnames(tsne_transformed_1) <- c("tsne1", "tsne2")
tsne_transformed_1$class <- y
tsne_transformed_1$method <- "Default parameters"

# t-SNE with custom (more aggressive) parameters
set.seed(42)
tsne_2 <- Rtsne(
  as.matrix(X),
  dims = 2,
  perplexity = 50,
  exaggeration_factor = 20,
  eta = 500,
  pca = FALSE,
  check_duplicates = FALSE,
  verbose = FALSE
)
tsne_transformed_2 <- as.data.frame(tsne_2$Y)
colnames(tsne_transformed_2) <- c("tsne1", "tsne2")
tsne_transformed_2$class <- y
tsne_transformed_2$method <- "Aggressive tuning"

# Combine results for faceted plotting
all_tsne <- rbind(tsne_transformed_1, tsne_transformed_2)

# Plot using facets in ggplot2
tsne_plot <- ggplot(all_tsne, aes(x = tsne1, y = tsne2, color = class)) +
  geom_point(size = 2) +
  facet_wrap(~ method, nrow = 1) +
  labs(
    title = "t-SNE Parameter Tuning in R",
    subtitle = "Comparison of Default vs Custom Parameters",
    x = "t-SNE 1", y = "t-SNE 2", color = "Class"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    panel.background = element_rect(fill = "white", color = NA),
    plot.background = element_rect(fill = "white", color = NA),
    strip.background = element_rect(fill = "white", color = NA),
    strip.text = element_text(face = "bold", size = 15),
    plot.title = element_text(face = "bold", size = 18, hjust = 0.5),
    plot.subtitle = element_text(size = 13, hjust = 0.5),
    legend.position = "right"
  )

library(Rtsne)
library(ggplot2)

# t-SNE with default-like parameters (no scaling; pca=FALSE to mirror sklearn behavior)
set.seed(42)
tsne_1 <- Rtsne(
  as.matrix(X),
  dims = 2,
  perplexity = 30,
  exaggeration_factor = 12,
  eta = 200,
  pca = FALSE,
  check_duplicates = FALSE,
  verbose = FALSE
)
tsne_transformed_1 <- as.data.frame(tsne_1$Y)
colnames(tsne_transformed_1) <- c("tsne1", "tsne2")
tsne_transformed_1$class <- y
tsne_transformed_1$method <- "Default parameters"

# t-SNE with custom (more aggressive) parameters
set.seed(42)
tsne_2 <- Rtsne(
  as.matrix(X),
  dims = 2,
  perplexity = 50,
  exaggeration_factor = 20,
  eta = 500,
  pca = FALSE,
  check_duplicates = FALSE,
  verbose = FALSE
)
tsne_transformed_2 <- as.data.frame(tsne_2$Y)
colnames(tsne_transformed_2) <- c("tsne1", "tsne2")
tsne_transformed_2$class <- y
tsne_transformed_2$method <- "Aggressive tuning"

# Combine results for faceted plotting
all_tsne <- rbind(tsne_transformed_1, tsne_transformed_2)

# Plot using facets in ggplot2
tsne_plot <- ggplot(all_tsne, aes(x = tsne1, y = tsne2, color = class)) +
  geom_point(size = 2) +
  facet_wrap(~ method, nrow = 1) +
  labs(
    title = "t-SNE Parameter Tuning in R",
    subtitle = "Comparison of Default vs Custom Parameters",
    x = "t-SNE 1", y = "t-SNE 2", color = "Class"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    panel.background = element_rect(fill = "white", color = NA),
    plot.background = element_rect(fill = "white", color = NA),
    strip.background = element_rect(fill = "white", color = NA),
    strip.text = element_text(face = "bold", size = 15),
    plot.title = element_text(face = "bold", size = 18, hjust = 0.5),
    plot.subtitle = element_text(size = 13, hjust = 0.5),
    legend.position = "right"
  )

library(Rtsne)
library(ggplot2)

# t-SNE with default-like parameters (no scaling; pca=FALSE to mirror sklearn behavior)
set.seed(42)
tsne_1 <- Rtsne(
  as.matrix(X),
  dims = 2,
  perplexity = 30,
  exaggeration_factor = 12,
  eta = 200,
  pca = FALSE,
  check_duplicates = FALSE,
  verbose = FALSE
)
tsne_transformed_1 <- as.data.frame(tsne_1$Y)
colnames(tsne_transformed_1) <- c("tsne1", "tsne2")
tsne_transformed_1$class <- y
tsne_transformed_1$method <- "Default parameters"

# t-SNE with custom (more aggressive) parameters
set.seed(42)
tsne_2 <- Rtsne(
  as.matrix(X),
  dims = 2,
  perplexity = 50,
  exaggeration_factor = 20,
  eta = 500,
  pca = FALSE,
  check_duplicates = FALSE,
  verbose = FALSE
)
tsne_transformed_2 <- as.data.frame(tsne_2$Y)
colnames(tsne_transformed_2) <- c("tsne1", "tsne2")
tsne_transformed_2$class <- y
tsne_transformed_2$method <- "Aggressive tuning"

# Combine results for faceted plotting
all_tsne <- rbind(tsne_transformed_1, tsne_transformed_2)

# Plot using facets in ggplot2
tsne_plot <- ggplot(all_tsne, aes(x = tsne1, y = tsne2, color = class)) +
  geom_point(size = 2) +
  facet_wrap(~ method, nrow = 1) +
  labs(
    title = "t-SNE Parameter Tuning in R",
    subtitle = "Comparison of Default vs Custom Parameters",
    x = "t-SNE 1", y = "t-SNE 2", color = "Class"
  ) +
  theme_minimal(base_size = 14) +
  theme(
    panel.background = element_rect(fill = "white", color = NA),
    plot.background = element_rect(fill = "white", color = NA),
    strip.background = element_rect(fill = "white", color = NA),
    strip.text = element_text(face = "bold", size = 15),
    plot.title = element_text(face = "bold", size = 18, hjust = 0.5),
    plot.subtitle = element_text(size = 13, hjust = 0.5),
    legend.position = "right"
  )

Introduction

Preparing the data

Understanding t-SNE Parameters: Perplexity

Understanding t-SNE Parameters: Early Exaggeration

Understanding t-SNE Parameters: Learning Rate

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Parameter Tuning Practice

Conclusion and Practice