Sep 062007
This demo was written by me about three months ago when I was illustrating the algorithm of “Gradient Descent” in the class of “Data Mining & Machine Learning”. I like to combine iterations (or loopings) with animated pictures, because it’s simple and heuristic, and of course, it’s easy in R: just use Sys.sleep() to control the time of steps of your demonstration and some low-level graphics functions such as lines(), points(), rect(), polygon() and segments(), etc to illustrate the process of your algorithm. To understand the figure below, you need to be clear about what’s contour plot.
The code for the above example is as follows:
Downdload the file hereop = par(pty = "s", mar = c(2, 1, 2, 0), cex.axis = 0.75,
cex.main = 0.85)
x2 = x1 = seq(-2 * pi, 2 * pi, 0.1)
f = function(x, y) x^2 + 3 * sin(y)
contour(x1, x2, outer(x1, x2, f), col = "red", main = "")
mtext(side = 3, expression(z == x[1]^2 + 3 * sin(x[2])))
for (i in 1:3) {
x = unlist(locator(1))
s = 0.05
newx = x - s * c(2 * x[1], 3 * cos(x[2]))
eps = 0.001
gap = abs(f(newx[1], newx[2]) - f(x[1], x[2]))
while (gap > eps) {
arrows(x[1], x[2], newx[1], newx[2], length = 0.075,
col = "blue")
x = newx
newx = x - s * c(2 * x[1], 3 * cos(x[2]))
gap = abs(f(newx[1], newx[2]) - f(x[1], x[2]))
Sys.sleep(gap/3)
}
}
par(op)
Nothing special, huh?
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2 Responses to “Process of Minimization by Gradient Descent (2D)”
Comments (2)
刚好在看最速下降法，谢谢
Hi, I have rewritten the code and summarized it in the function
grad.desc()in the R package 'animation'.