File:Gradient descent.svg
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Original file (SVG file, nominally 512 × 549 pixels, file size: 56 KB)
This file is from Wikimedia Commons and may be used by other projects. The description on its file description page there is shown below.
Summary
DescriptionGradient descent.svg | An illustration of the gradient descent method. I graphed this with Matlab |
Date | (UTC) |
Source |
This file was derived from: Gradient descent.png: |
Author |
|
This is a retouched picture, which means that it has been digitally altered from its original version. Modifications: Vector version. The original can be viewed here: Gradient descent.png: . Modifications made by Zerodamage.
|
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
Public domainPublic domainfalsefalse |
I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |
Source code
% Illustration of gradient descent
function main()
% the ploting window
figure(1);
clf; hold on;
set(gcf, 'color', 'white');
set(gcf, 'InvertHardCopy', 'off');
axis equal; axis off;
% the box
Lx1=-2; Lx2=2; Ly1=-2; Ly2=2;
% the function whose contours will be plotted
N=60; h=1/N;
XX=Lx1:h:Lx2;
YY=Ly1:h:Ly2;
[X, Y]=meshgrid(XX, YY);
f=inline('-((y+1).^4/25+(x-1).^4/10+x.^2+y.^2-1)');
Z=f(X, Y);
% the contours
h=0.3; l0=-1; l1=20;
l0=h*floor(l0/h);
l1=h*floor(l1/h);
v=[l0:1.5*h:0 0:h:l1 0.8 0.888];
[c,h] = contour(X, Y, Z, v, 'b');
% graphing settings
small=0.08;
small_rad = 0.01;
thickness=1; arrowsize=0.06; arrow_type=2;
fontsize=13;
red = [1, 0, 0];
white = 0.99*[1, 1, 1];
% initial guess for gradient descent
x=-0.6498; y=-1.0212;
% run several iterations of gradient descent
for i=0:4
H=text(x-1.5*small, y+small/2, sprintf('x_%d', i));
set(H, 'fontsize', fontsize, 'color', 0*[1 1 1]);
% the derivatives in x and in y, the step size
u=-2/5*(x-1)^3-2*x;
v=-4/25*(y+1)^3-2*y;
alpha=0.11;
if i< 4
plot([x, x+alpha*u], [y, y+alpha*v]);
arrow([x, y], [x, y]+alpha*[u, v], thickness, arrowsize, pi/8, ...
arrow_type, [1, 0, 0])
x=x+alpha*u; y=y+alpha*v;
end
end
% some dummy text, to expand the saving window a bit
text(-0.9721, -1.5101, '*', 'color', white);
text(1.5235, 1.1824, '*', 'color', white);
% save to eps
saveas(gcf, 'Gradient_descent.eps', 'psc2')
function arrow(start, stop, thickness, arrow_size, sharpness, arrow_type, color)
% Function arguments:
% start, stop: start and end coordinates of arrow, vectors of size 2
% thickness: thickness of arrow stick
% arrow_size: the size of the two sides of the angle in this picture ->
% sharpness: angle between the arrow stick and arrow side, in radians
% arrow_type: 1 for filled arrow, otherwise the arrow will be just two segments
% color: arrow color, a vector of length three with values in [0, 1]
% convert to complex numbers
i=sqrt(-1);
start=start(1)+i*start(2); stop=stop(1)+i*stop(2);
rotate_angle=exp(i*sharpness);
% points making up the arrow tip (besides the "stop" point)
point1 = stop - (arrow_size*rotate_angle)*(stop-start)/abs(stop-start);
point2 = stop - (arrow_size/rotate_angle)*(stop-start)/abs(stop-start);
if arrow_type==1 % filled arrow
% plot the stick, but not till the end, looks bad
t=0.5*arrow_size*cos(sharpness)/abs(stop-start); stop1=t*start+(1-t)*stop;
plot(real([start, stop1]), imag([start, stop1]), 'LineWidth', thickness, 'Color', color);
% fill the arrow
H=fill(real([stop, point1, point2]), imag([stop, point1, point2]), color);
set(H, 'EdgeColor', 'none')
else % two-segment arrow
plot(real([start, stop]), imag([start, stop]), 'LineWidth', thickness, 'Color', color);
plot(real([stop, point1]), imag([stop, point1]), 'LineWidth', thickness, 'Color', color);
plot(real([stop, point2]), imag([stop, point2]), 'LineWidth', thickness, 'Color', color);
end
function ball(x, y, r, color)
Theta=0:0.1:2*pi;
X=r*cos(Theta)+x;
Y=r*sin(Theta)+y;
H=fill(X, Y, color);
set(H, 'EdgeColor', 'none');
%plot2svg must be retrieved from http://www.zhinst.com/blogs/schwizer/
plot2svg;
Original upload log
This image is a derivative work of the following images:
- File:Gradient_descent.png licensed with PD-self
- 2007-06-23T03:33:09Z Oleg Alexandrov 482x529 (25564 Bytes) {{Information |Description=An illustration of the gradient descent method. I graphed this with Matlab |Source=Originally from [http://en.wikipedia.org en.wikipedia]; description page is/was [http://en.wikipedia.org/w/index.ph
Uploaded with derivativeFX
Items portrayed in this file
depicts
7 August 2012
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 21:04, 7 August 2012 | 512 × 549 (56 KB) | wikimediacommons>Zerodamage | == {{int:filedesc}} == {{Information |Description=An illustration of the gradient descent method. I graphed this with Matlab |Source={{Derived from|Gradient_descent.png|display=50}} |Date=2012-08-07 19:02 (UTC) |Author=*File:Gradient_descent.png:... |
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