Diffusion Map

Authors

[Editor] Hu Zheng;

[Contributors]

Diffusion Map is a nonlinear dimensionality reduction algorithm that can be used to visualize developmental trajectories.

Setup

  • System Requirements: Cross-platform (Linux/MacOS/Windows)

  • Programming language: R

  • Dependent packages: destiny; ggplotify; scatterplot3d; ggpubr

# Install packages
if (!requireNamespace("destiny", quietly = TRUE)) {
  install_github("theislab/destiny")
}
if (!requireNamespace("ggplotify", quietly = TRUE)) {
  install.packages("ggplotify")
}
if (!requireNamespace("scatterplot3d", quietly = TRUE)) {
  install.packages("scatterplot3d")
}
if (!requireNamespace("ggpubr", quietly = TRUE)) {
  install.packages("ggpubr")
}

# Load packages
library(destiny)
library(ggplotify)
library(scatterplot3d)
library(ggpubr)

Data Preparation

# Load data
data1 <- read.delim("files/Hiplot/042-diffusion-map-data1.txt", header = T)
data2 <- read.delim("files/Hiplot/042-diffusion-map-data2.txt", header = T)

# convert data structure
sample.info <- data2
rownames(data1) <- data1[, 1]
data1 <- as.matrix(data1[, -1])
## tsne
set.seed(123)
dm_info <- DiffusionMap(t(data1))
dm_info <- cbind(DC1 = dm_info$DC1, DC2 = dm_info$DC2, DC3 = dm_info$DC3)
dm_data <- data.frame(
  sample = colnames(data1),
  dm_info
)

colorBy <- sample.info[match(colnames(data1), sample.info[, 1]), "Group"]
colorBy <- factor(colorBy, level = colorBy[!duplicated(colorBy)])
dm_data$colorBy = colorBy

# View data
head(dm_data)
   sample        DC1        DC2         DC3 colorBy
M1     M1 0.05059918 0.15203860 -0.06533168      G1
M2     M2 0.05030863 0.14435034 -0.06044277      G1
M3     M3 0.04271398 0.09273382 -0.02730427      G1
M4     M4 0.04680742 0.10425273 -0.03789962      G1
M5     M5 0.04971521 0.12786900 -0.05608321      G1
M6     M6 0.04840072 0.12728303 -0.05256815      G1

Visualization

1. 2D

# 2D Diffusion Map
p <- ggscatter(data = dm_data,  x = "DC1", y = "DC2", color = "colorBy",
               size = 2, palette = "lancet", alpha = 1) +
  labs(color = "Group") +
  ggtitle("Diffusion Map") +
  scale_color_manual(values = c("#3B4992FF","#EE0000FF","#008B45FF")) +
  theme_classic() +
  theme(text = element_text(family = "Arial"),
        plot.title = element_text(size = 12,hjust = 0.5),
        axis.title = element_text(size = 12),
        axis.text = element_text(size = 10),
        axis.text.x = element_text(angle = 0, hjust = 0.5,vjust = 1),
        legend.position = "right",
        legend.direction = "vertical",
        legend.title = element_text(size = 10),
        legend.text = element_text(size = 10))

p
FigureΒ 1: 2D Diffusion Map

2. 3D

# 3D Diffusion Map
group.color <- c("#3B4992FF","#EE0000FF","#008B45FF")
names(group.color) <- unique(dm_data$colorBy)
group.color <- group.color[!is.na(names(group.color))]
if (length(group.color) == 0) {
  group.color <- c(Default="black")
  dm_data$colorBy <- "Default"
}
p <- as.ggplot(function(){
  scatterplot3d(x = dm_data$DC1, y = dm_data$DC2, z = dm_data$DC3,
                color =  alpha(group.color[dm_data$colorBy], 1),
                xlim=c(min(dm_data$DC1), max(dm_data$DC1)),
                ylim=c(min(dm_data$DC2), max(dm_data$DC2)),
                zlim=c(min(dm_data$DC3), max(dm_data$DC3)),
                pch = 16, cex.symbols  = 0.6,
                scale.y = 0.8,
                xlab = "DC1", ylab = "DC2", zlab = "DC3",
                angle = 40,
                main = "Diffusion Map",
                col.axis = "#444444", col.grid = "#CCCCCC")
  legend("right", legend = names(group.color),
         col = alpha(group.color, 0.8), pch = 16)
    })
p <- p + theme_classic()

p
FigureΒ 2: 3D Diffusion Map