[R] Backpropagation to adjust weights in a neural net when receiving new training examples

Fri May 29 16:24:14 CEST 2009

You can figure out which weights go with which connections with the
function summary(nnet.object) and nnet.object$wts. Sample code from
Venables and Ripley is below:

# Neural Network model in Modern Applied Statistics with S, Venables and
Ripley, pages 246 and 247

> library(nnet)

> attach(rock)

> dim(rock)

[1] 48  4

> area1 <- area/10000; peri1 <- peri/10000

> rock1 <- data.frame(perm, area = area1, peri = peri1, shape)

> dim(rock1)

[1] 48  4

> head(rock1)

  perm   area     peri     shape

1  6.3 0.4990 0.279190 0.0903296

2  6.3 0.7002 0.389260 0.1486220

3  6.3 0.7558 0.393066 0.1833120

4  6.3 0.7352 0.386932 0.1170630

5 17.1 0.7943 0.394854 0.1224170

6 17.1 0.7979 0.401015 0.1670450

> rock.nn <- nnet(log(perm) ~ area + peri + shape, rock1, size=3,
decay=1e-3, linout=T, skip=T, maxit=1000, Hess=T)

# weights:  19

initial  value 1196.787489 

iter  10 value 32.400984

iter  20 value 31.664545

...

iter 280 value 14.230077

iter 290 value 14.229809

final  value 14.229785 

converged

> summary(rock.nn)

a 3-3-1 network with 19 weights

options were - skip-layer connections  linear output units  decay=0.001

 b->h1 i1->h1 i2->h1 i3->h1 

 -0.51  -9.33  14.59   3.85 

 b->h2 i1->h2 i2->h2 i3->h2 

  0.93   3.35   6.09  -5.86 

 b->h3 i1->h3 i2->h3 i3->h3 

  0.80 -10.93  -4.58   9.53 

  b->o  h1->o  h2->o  h3->o  i1->o  i2->o  i3->o 

  1.89 -14.62   7.35   8.77  -3.00  -4.25   4.44 

> sum((log(perm) - predict(rock.nn))^2)

[1] 13.20451

> rock.nn$wts

 [1]  -0.5064848  -9.3288410  14.5859255   3.8521844   0.9266730
3.3524267   6.0900909  -5.8628448   0.8026366 -10.9345352  -4.5783516
9.5311123

[13]   1.8866734 -14.6181959   7.3466236   8.7655882  -2.9988287
-4.2508948   4.4397158

> 

In the output from summary(rock.nn), b is the bias or intercept, h1 is
the 1st hidden neuron, i1 is the first input (peri) and o is the
(linear) output. So b->h1 is the bias or intercept to the first hidden
neuron, i1->h1 is the 1st input (peri) to the first hidden neuron (there
are 3 hidden neurons in this example), h1->o is the 1st hidden neuron to
the first output, and i1->o is the first input to the output (since
skip=T - this is a skip layer network). The weights are below (b->h1 ..)
but are rounded. But rock.nn$wts gives you the un-rounded weights. If
you compare the output from summary(rock.nn) and rock.nn$wts you will
see that the first row of weights from summary() is listed first in
rock.nn$wts, followed by the 2nd row of weights from summary() and so
on.

You can construct the neural network equations manually (this is not in
the Venables Ripley book) and check the results against the predict()
function to verify that the weights are listed in the order I described.
The code to do this is:

# manually calculate the neural network predictions based on the neural
network equations

rock1$h1 <- -0.5064848 -9.3288410 * rock1$area + 14.5859255 * rock1$peri
+ 3.8521844 * rock1$shape

rock1$logistic_h1 <- exp(rock1$h1) / (1 + exp(rock1$h1))

rock1$h2 <- 0.9266730 + 3.3524267 * rock1$area + 6.0900909 * rock1$peri
-5.8628448 * rock1$shape

rock1$logistic_h2 <- exp(rock1$h2) / (1 + exp(rock1$h2))

rock1$h3 <- 0.8026366 - 10.9345352 * rock1$area - 4.5783516 * rock1$peri
+ 9.5311123 * rock1$shape

rock1$logistic_h3 <- exp(rock1$h3) / (1 + exp(rock1$h3))

rock1$pred1 <- (1.8866734 - 14.6181959 * rock1$logistic_h1 + 7.3466236 *
rock1$logistic_h2 + 

                8.7655882 * rock1$logistic_h3 - 2.9988287 * rock1$area -
4.2508948 * rock1$peri + 

                4.4397158 * rock1$shape)

rock1$nn.pred <- predict(rock.nn)

head(rock1)      

  perm   area     peri     shape         h1 logistic_h1       h2
logistic_h2        h3  logistic_h3    pred1  nn.pred

1  6.3 0.4990 0.279190 0.0903296 -0.7413656   0.3227056 3.770238
0.9774726 -5.070985 0.0062370903 2.122910 2.122910

2  6.3 0.7002 0.389260 0.1486220 -0.7883026   0.3125333 4.773323
0.9916186 -7.219361 0.0007317343 1.514820 1.514820

3  6.3 0.7558 0.393066 0.1833120 -1.1178398   0.2464122 4.779515
0.9916699 -7.514112 0.0005450367 2.451231 2.451231

4  6.3 0.7352 0.386932 0.1170630 -1.2703391   0.2191992 5.061506
0.9937039 -7.892204 0.0003735057 2.656199 2.656199

5 17.1 0.7943 0.394854 0.1224170 -1.6854993   0.1563686 5.276490
0.9949156 -8.523675 0.0001986684 3.394902 3.394902

6 17.1 0.7979 0.401015 0.1670450 -1.4573040   0.1888800 5.064433
0.9937222 -8.165892 0.0002841023 3.072776 3.072776

The first 6 records show that the numbers from the manual equations and
the predict() function are the same (the last 2 columns). As VR point
out in their book, there are several solutions and a random starting
point and if you run the same example your results may differ.

Hope this helps.

Jude Ryan

Filipe Rocha wrote:

I want to create a neural network, and then everytime it receives new
data,

instead of  creating a new nnet, i want to use a backpropagation
algorithm

to adjust the weights in the already created nn.

I'm using nnet package, I know that nn$wts gives the weights,  but I
cant

find out which weights belong to which conections so I could implement
the

backpropagation algorithm myself.

But if anyone knows some function to  do this, it would be even better.

In anycase, thank you!

Filipe Rocha

___________________________________________
Jude Ryan
Director, Client Analytical Services
Strategy & Business Development
UBS Financial Services Inc.
1200 Harbor Boulevard, 4th Floor
Weehawken, NJ 07086-6791
Tel. 201-352-1935
Fax 201-272-2914
Email: jude.ryan at ubs.com

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