Created
March 17, 2019 17:55
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Gradient Descent Visualization with ggplot2
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library(Deriv) | |
library(tidyverse) | |
library(stringr) | |
library(latex2exp) | |
library(glue) | |
# test function | |
f <- function(x) ((x^2-4*x+4)*(x^2+4*x+2)) | |
# plotting the test function | |
library(ggplot2) | |
p <- ggplot(data = data.frame(x = 0), mapping = aes(x = x)) | |
p + stat_function(fun = f) + | |
xlim(-4,4) | |
# derivative of the test function | |
f_prime <- Deriv(f) | |
# run a gradient descent | |
x = 0.35 | |
x_initial = x | |
x_updated_values <- numeric(0) | |
learning_rate = 0.001 | |
for (i in 1:240) { | |
if (i==1) {x_updated_values[i] = x} | |
if (i==1) {next} | |
x = x-learning_rate*f_prime(x) | |
x_updated_values[i] = x | |
} | |
df <- data_frame(x = x_updated_values, | |
y = f(x_updated_values)) | |
# plotting the parameter updates | |
x_on_iteration_i <- df$x[i] | |
y_on_iteration_i <- df$y[i] | |
p + stat_function(fun = f) + | |
xlim(-4,4)+ | |
geom_point(data = df, aes(x, y))+ | |
geom_point(x = x_on_iteration_i, y = y_on_iteration_i, color = 'blue', size = 4, alpha = 0.5)+ | |
theme(legend.position="none")+ | |
ylab("f(x)")+ | |
ggtitle(TeX('$f(x) = (x^2-4x+4)(x^2+4x+2)$'), | |
subtitle = glue("Gradient Descent with Learning Rate: {learning_rate}")) |
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