%?A?minimalistic?Echo?State?Networks?demo?with?Mackey-Glass?（delay?17）?data?
%?in?“plain“?Matlab.
%?by?Mantas?Lukosevicius?2012
%?http://minds.jacobs-university.de/mantas

%?load?the?data
trainLen?=?3000;
testLen?=?1000;
initLen?=?100;

data?=?load（‘MackeyGlass-t17.txt‘）;
load（‘signv.mat‘）;

%?plot?some?of?it
%?figure（10）;
%?plot（data（1:1000））;
%?title（‘A?sample?of?data‘）;

%?generate?the?ESN?reservoir
inSize?=?1;?outSize?=?1;
resSize?=?500;
a?=?0.3;?%?leaking?rate

signal?=?y（1:5001:2）;?%signal?of?W_in
%rand（?‘seed‘?42?）;
Win?=?（zeros（resSize1+inSize）+0.5）?.*?signal;?%r=0.5
W?=?eye（resSize）?*?0.8;
W?=?circshift（W[12]）;?%?generate?circle
W?=?reshape（W1resSize*resSize）;
step?=?10;
for?i=1:resSize
????if?mod（i?step）?==?1
????????W（i）?=?0.7;
????end
end
W?=?reshape（WresSizeresSize）
%?Option?1?-?direct?scaling?（quick&dirty?reservoir-specific）:
%?W?=?W?.*?0.13;
%?Option?2?-?normalizing?and?setting?spectral?radius?（correct?slower）:
disp?‘Computing?spectral?radius...‘;
opt.disp?=?0;
rhoW?=?abs（eigs（W1‘LM‘opt））;
disp?‘done.‘
W?=?W?.*?（?1.25?/rhoW）;

%?allocated?memory?for?the?design?（collected?states）?matrix
X?=?zeros（1+inSize+resSizetrainLen-initLen）;
%?set?the?corresponding?target?matrix?directly
Yt?=?data（initLen+2:trainLen+1）‘;

%?run?the?reservoir?with?the?data?and?collect?X
x?=?zeros（resSize1）;
for?t?=?1:trainLen
	u?=?data（t）;
	x?=?（1-a）*x?+?a*tanh（?Win*[1;u]?+?W*x?）;
	if?t?>?initLen
		X（:t-initLen）?=?[1;u;x];
	end
end

%?train?the?output
reg?=?1e-8;??%?regularization?coefficient
X_T?=?X‘;
%?Wout?=?Yt*X_T?*?inv（X*X_T?+?reg*eye（1+inSize+resSize））;
Wout?=?Yt*X_T?/?（X*X_T?+?reg*eye（1+inSize+resSize））;
%?Wout?=?Yt*pinv（X）;

%?run?the?trained?ESN?in?a?generative?mode.?no?need?to?initialize?here?
%?because?x?is?initialized?with?training?data?and?we?continue?from?there.
Y?=?zeros（outSizetestLen）;
u?=?data（trainLen+1）;
for?t?=?1:testLen?
	x?=?（1-a）*x?+?a*tanh（?Win*[1;u]?+?W*x?）;
	y?=?Wout*[1;u;x];
	Y（:t）?=?y;
	%?generative?mode:
	u?=?y;
	%?this?would?be?a?predictive?mode:
	u?=?data（trainLen+t+1）;
end

errorLen?=?1000;
mse?=?sum（（data（trainLen+2:trainLen+errorLen+1）‘-Y（11:errorLen））.^2）./errorLen;
disp（?[‘MSE?=?‘?num2str（?mse?）]?）;

%?plot?some?signals
figure（1）;
plot（?data（trainLen+2:trainLen+testLen+1）?‘color‘?[00.750]?）;
hold?on;
plot（?Y‘?‘b‘?）;
hold?off;
axis?tight;
title（‘Target?and?generated?signals?y（n）?starting?at?n=0‘）;
legend（‘Target?signal‘?‘Free-running?predicted?signal‘）;

figure（2）;
plot（?X（1:201:200）‘?）;
title（‘Some?reservoir?activations?x（n）‘）;

figure（3）;
bar（?Wout‘?）
title（‘Output?weights?W^{out}‘）;

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????文件????????2686??2018-05-19?15:27??minimalCRJ.m
?????文件????????2420??2018-05-19?15:00??minimalESN.m
?????文件????????2574??2015-12-10?00:33??signv.mat
?????文件??????265429??2016-11-21?18:13??MackeyGlass-t17.txt