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<LI><A HREF="#name">NAME</A></LI>
<LI><A HREF="#synopsis">SYNOPSIS</A></LI>
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<LI><A HREF="#description">DESCRIPTION</A></LI>
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<LI><A HREF="#methods">METHODS</A></LI>
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<LI><A HREF="#notes">NOTES</A></LI>
<LI><A HREF="#other included packages">OTHER INCLUDED PACKAGES</A></LI>
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<P>
<H1><A NAME="name">NAME</A></H1>
<P>AI::NeuralNet::BackProp - A simple back-prop neural net that uses Delta's and Hebbs' rule.</P>
<P>
<HR>
<H1><A NAME="synopsis">SYNOPSIS</A></H1>
<P>use AI::NeuralNet::BackProp;
</P>
<PRE>
# Create a new network with 1 layer, 5 inputs, and 5 outputs.
my $net = new AI::NeuralNet::BackProp(1,5,5);</PRE>
<PRE>
# Add a small amount of randomness to the network
$net->random(0.001);</PRE>
<PRE>
# Demonstrate a simple learn() call
my @inputs = ( 0,0,1,1,1 );
my @ouputs = ( 1,0,1,0,1 );
</PRE>
<PRE>
print $net->learn(\@inputs, \@outputs),"\n";</PRE>
<PRE>
# Create a data set to learn
my @set = (
[ 2,2,3,4,1 ], [ 1,1,1,1,1 ],
[ 1,1,1,1,1 ], [ 0,0,0,0,0 ],
[ 1,1,1,0,0 ], [ 0,0,0,1,1 ]
);
</PRE>
<PRE>
# Demo learn_set()
my $f = $net->learn_set(\@set);
print "Forgetfulness: $f unit\n";</PRE>
<PRE>
# Crunch a bunch of strings and return array refs
my $phrase1 = $net->crunch("I love neural networks!");
my $phrase2 = $net->crunch("Jay Lenno is wierd.");
my $phrase3 = $net->crunch("The rain in spain...");
my $phrase4 = $net->crunch("Tired of word crunching yet?");</PRE>
<PRE>
# Make a data set from the array refs
my @phrases = (
$phrase1, $phrase2,
$phrase3, $phrase4
);</PRE>
<PRE>
# Learn the data set
$net->learn_set(\@phrases);
</PRE>
<PRE>
# Run a test phrase through the network
my $test_phrase = $net->crunch("I love neural networking!");
my $result = $net->run($test_phrase);</PRE>
<PRE>
# Get this, it prints "Jay Leno is networking!" ... LOL!
print $net->uncrunch($result),"\n";</PRE>
<P>
<HR>
<H1><A NAME="updates">UPDATES</A></H1>
<P>This is version 0.77, a complete internal upgrade from version 0.42. A new feature
is the introduction of a randomness factor in the network, optional to disable. The
restriction on 0s are removed, so you can run any network you like. See NOTES on using 0s with
randomness disabled, below. Included is an improved <A HREF="#item_learn"><CODE>learn()</CODE></A> function, and a much more accurate
internal fixed-point system for learning. Also included is automated learning of input sets. See
<A HREF="#item_learn_set"><CODE>learn_set()</CODE></A> and <CODE>learn_rand_set()</CODE></P>
<P>
<HR>
<H1><A NAME="description">DESCRIPTION</A></H1>
<P>AI::NeuralNet::BackProp is the flagship package for this file.
It implements a nerual network similar to a feed-foward,
back-propagtion network; learning via a mix of a generalization
of the Delta rule and a disection of Hebbs rule. The actual
neruons of the network are implemented via the AI::NeuralNet::BackProp::neuron package.
</P>
<PRE>
You constuct a new network via the new constructor:</PRE>
<PRE>
my $net = new AI::NeuralNet::BackProp(2,3,1);</PRE>
<P>The <CODE>new()</CODE> constructor accepts two arguments and one optional argument, $layers, $size,
and $outputs is optional (in this example, $layers is 2, $size is 3, and $outputs is 1).</P>
<P>$layers specifies the number of layers, including the input
and the output layer, to use in each neural grouping. A new
neural grouping is created for each pattern learned. Layers
is typically set to 2. Each layer has $size neurons in it.
Each neuron's output is connected to one input of every neuron
in the layer below it.
</P>
<PRE>
This diagram illustrates a simple network, created with a call
to "new AI::NeuralNet::BackProp(2,2)" (2 layers, 2 neurons/layer).</PRE>
<PRE>
input
/ \
O O
|\ /|
| \/ |
| /\ |
|/ \|
O O
\ /
mapper</PRE>
<P>In this diagram, each neuron is connected to one input of every
neuron in the layer below it, but there are not connections
between neurons in the same layer. Weights of the connection
are controlled by the neuron it is connected to, not the connecting
neuron. (E.g. the connecting neuron has no idea how much weight
its output has when it sends it, it just sends its output and the
weighting is taken care of by the receiving neuron.) This is the
method used to connect cells in every network built by this package.</P>
<P>Input is fed into the network via a call like this:</P>
<PRE>
use AI;
my $net = new AI::NeuralNet::BackProp(2,2);
</PRE>
<PRE>
my @map = (0,1);</PRE>
<PRE>
my $result = $net->run(\@map);</PRE>
<P>Now, this call would probably not give what you want, because
the network hasn't ``learned'' any patterns yet. But this
illustrates the call. Run expects an array refrence, and
run gets mad if you don't give it what it wants. So be nice.</P>
<P>Run returns a refrence with $size elements (Remember $size? $size
is what you passed as the second argument to the network
constructor.) This array contains the results of the mapping. If
you ran the example exactly as shown above, $result would contain
(1,1) as its elements.</P>
<P>To make the network learn a new pattern, you simply call the learn
method with a sample input and the desired result, both array
refrences of $size length. Example:</P>
<PRE>
use AI;
my $net = new AI::NeuralNet::BackProp(2,2);
</PRE>
<PRE>
my @map = (0,1);
my @res = (1,0);</PRE>
<PRE>
$net->learn(\@map,\@res);</PRE>
<PRE>
my $result = $net->run(\@map);</PRE>
<P>Now $result will conain (1,0), effectivly flipping the input pattern
around. Obviously, the larger $size is, the longer it will take
to learn a pattern. <CODE>Learn()</CODE> returns a string in the form of</P>
<PRE>
Learning took X loops and X wallclock seconds (X.XXX usr + X.XXX sys = X.XXX CPU).</PRE>
<P>With the X's replaced by time or loop values for that loop call. So,
to view the learning stats for every learn call, you can just:
</P>
<PRE>
print $net->learn(\@map,\@res);</PRE>
<P>If you call ``$net->debug(4)'' with $net being the
refrence returned by the <CODE>new()</CODE> constructor, you will get benchmarking
information for the learn function, as well as plenty of other information output.
See notes on <A HREF="#item_debug"><CODE>debug()</CODE></A> , in METHODS, below.</P>
<P>If you do call $net->debug(1), it is a good
idea to point STDIO of your script to a file, as a lot of information is output. I often
use this command line:</P>
<PRE>
$ perl some_script.pl > .out</PRE>
<P>Then I can simply go and use emacs or any other text editor and read the output at my leisure,
rather than have to wait or use some 'more' as it comes by on the screen.</P>
<P>This system was originally created to be a type of content-addressable-memory
system. As such, it implements ``groups'' for storing patterns and
maps. After the network has learned the patterns you want, then you
can call run with a pattern it has never seen before, and it will
decide which of the stored patterns best fit the new pattern, returning
the results the same as the above examples (as an array ref from $net->run()).</P>
<P>
<H2><A NAME="methods">METHODS</A></H2>
<DL>
<DT><STRONG><A NAME="item_BackProp">new AI::NeuralNet::BackProp($layers, $size [, $outputs])</A></STRONG><BR>
<DD>
Returns a newly created neural network from an <CODE>AI::NeuralNet::BackProp</CODE>
object. Each group of this network will have <CODE>$layers</CODE> number layers in it
and each layer will have <CODE>$size</CODE> number of neurons in that layer.
<P>There is an optional parameter of $outputs, which specifies the number
of output neurons to provide. If $outputs is not specified, $outputs
defaults to equal $size. $outputs may not exceed $size. If $outputs
exceeds $size, the <CODE>new()</CODE> constructor will return undef.</P>
<P>Before you can really do anything useful with your new neural network
object, you need to teach it some patterns. See the <A HREF="#item_learn"><CODE>learn()</CODE></A> method, below.</P>
<P></P>
<DT><STRONG><A NAME="item_learn">$net->learn($input_map_ref, $desired_result_ref [, options ]);</A></STRONG><BR>
<DD>
This will 'teach' a network to associate an new input map with a desired resuly.
It will return a string containg benchmarking information. You can retrieve the
pattern index that the network stored the new input map in after <A HREF="#item_learn"><CODE>learn()</CODE></A> is complete
with the <CODE>pattern()</CODE> method, below.
<P>The first two arguments must be array refs, and they may be of different lengths.</P>
<P>Options should be written on hash form. There are three options:
</P>
<PRE>
inc => $learning_gradient
max => $maximum_iterations
error => $maximum_allowable_percentage_of_error</PRE>
<P>$learning_gradient is an optional value used to adjust the weights of the internal
connections. If $learning_gradient is ommitted, it defaults to 0.20.
</P>
<PRE>
$maximum_iterations is the maximum numbers of iteration the loop should do.
It defaults to 1024. Set it to 0 if you never want the loop to quit before
the pattern is perfectly learned.</PRE>
<P>$maximum_allowable_percentage_of_error is the maximum allowable error to have. If
this is set, then <A HREF="#item_learn"><CODE>learn()</CODE></A> will return when the perecentage difference between the
actual results and desired results falls below $maximum_allowable_percentage_of_error.
If you do not include 'error', or $maximum_allowable_percentage_of_error is set to -1,
then <A HREF="#item_learn"><CODE>learn()</CODE></A> will not return until it gets an exact match for the desired result OR it
reaches $maximum_iterations.</P>
<P></P>
<DT><STRONG><A NAME="item_learn_set">$net->learn_set(\@set, [ options ]);</A></STRONG><BR>
<DD>
This takes the same options as <A HREF="#item_learn"><CODE>learn()</CODE></A> and allows you to specify a set to learn, rather
than individual patterns. <A HREF="#item_learn_set"><CODE>learn_set()</CODE></A> will return an integer specifying the amount of forgetfulness
when all the patterns are learned. If the learn_set()-specific option 'p' is set true, as in
'p => 1' in the hash of options, then it will return a percentage represting the amount of forgetfullness,
rather than an integer.
<P>NOTE: I have disabled percentage returns, so it will always return a integer, for now. I disabled
it because I found there is a problem with the array refs and percentages when I was writing
the new synopsis, so for now it returns intergers, no matter what the 'p' option is.</P>
<P>Example:</P>
<PRE>
# Data from 1989 (as far as I know..this is taken from example data on BrainMaker)
my @data = (
# Mo CPI CPI-1 CPI-3 Oil Oil-1 Oil-3 Dow Dow-1 Dow-3 Dow Ave (output)
[ 1, 229, 220, 146, 20.0, 21.9, 19.5, 2645, 2652, 2597], [ 2647 ],
[ 2, 235, 226, 155, 19.8, 20.0, 18.3, 2633, 2645, 2585], [ 2637 ],
[ 3, 244, 235, 164, 19.6, 19.8, 18.1, 2627, 2633, 2579], [ 2630 ],
[ 4, 261, 244, 181, 19.6, 19.6, 18.1, 2611, 2627, 2563], [ 2620 ],
[ 5, 276, 261, 196, 19.5, 19.6, 18.0, 2630, 2611, 2582], [ 2638 ],
[ 6, 287, 276, 207, 19.5, 19.5, 18.0, 2637, 2630, 2589], [ 2635 ],
[ 7, 296, 287, 212, 19.3, 19.5, 17.8, 2640, 2637, 2592], [ 2641 ]
);
</PRE>
<PRE>
# Learn the set
my $f = learn_set(\@data,
inc => 0.1,
max => 500,
p => 1
);</PRE>
<PRE>
# Print it
print "Forgetfullness: $f%";</PRE>
<P></P>
<PRE>
This is a snippet from the example script examples/finance.pl, which demonstrates DOW average
prediction for the next month. A more simple set defenition would be as such:</PRE>
<PRE>
my @data = (
[ 0,1 ], [ 1 ],
[ 1,0 ], [ 0 ]
);
</PRE>
<PRE>
$net->learn_set(\@data);</PRE>
<PRE>
Same effect as above, but not the same data (obviously).</PRE>
<P></P>
<DT><STRONG><A NAME="item_learn_set_rand">$net->learn_set_rand(\@set, [ options ]);</A></STRONG><BR>
<DD>
This takes the same options as <A HREF="#item_learn"><CODE>learn()</CODE></A> and allows you to specify a set to learn, rather
than individual patterns.
<P><A HREF="#item_learn_set_rand"><CODE>learn_set_rand()</CODE></A> differs from <A HREF="#item_learn_set"><CODE>learn_set()</CODE></A> in that it learns the patterns in a random order,
each pattern once, rather than in the order that they are in the array. This returns a true
value (1) instead of a forgetfullnes factor.</P>
<P>Example:</P>
<PRE>
my @data = (
[ 0,1 ], [ 1 ],
[ 1,0 ], [ 0 ]
);
</PRE>
<PRE>
$net->learn_set_rand(\@data);</PRE>
<P></P>
<DT><STRONG><A NAME="item_run">$net->run($input_map_ref);</A></STRONG><BR>
<DD>
This method will apply the given array ref at the input layer of the neural network.
<P>It will return undef on an error. An error is caused by one of two events.</P>
<P>The first is the possibility that the argument passed is not an array ref. If it
is not an array ref, it returns silently a value of undef.</P>
<P>UPDATED: You can now run maps with a 0 value. Beware though, it may not <A HREF="#item_learn"><CODE>learn()</CODE></A> a 0 value
in the input map if you have randomness disabled. See NOTES on using a 0 value with randomness
disabled.</P>
<P></P>
<DT><STRONG><A NAME="item_benchmarked">$net->benchmarked();</A></STRONG><BR>
<DD>
This returns a benchmark info string for the last <A HREF="#item_learn"><CODE>learn()</CODE></A> or the last <A HREF="#item_run"><CODE>run()</CODE></A> call,
whichever occured later. It is easily printed as a string,
as following:
<PRE>
print $net->benchmarked() . "\n";</PRE>
<P></P>
<DT><STRONG><A NAME="item_debug">$net-><CODE>debug($level)</CODE></A></STRONG><BR>
<DD>
Toggles debugging off if called with $level = 0 or no arguments. There are four levels
of debugging.
<P>Level 0 ($level = 0) : Default, no debugging information printed, except for the 'Cannot run
0 value.' error message. Other than that one message, all printing is left to calling script.</P>
<P>Level 1 ($level = 1) : This causes ALL debugging information for the network to be dumped
as the network runs. In this mode, it is a good idea to pipe your STDIO to a file, especially
for large programs.</P>
<P>Level 2 ($level = 2) : A slightly-less verbose form of debugging, not as many internal
data dumps.</P>
<P>Level 3 ($level = 3) : JUST prints weight mapping as weights change.</P>
<P>Level 4 ($level = 4) : JUST prints the benchmark info for EACH learn loop iteteration, not just
learning as a whole. Also prints the percentage difference for each loop between current network
results and desired results, as well as learning gradient ('incremenet').</P>
<P>Level 4 is useful for seeing if you need to give a smaller learning incrememnt to <A HREF="#item_learn"><CODE>learn()</CODE></A> .
I used level 4 debugging quite often in creating the letters.pl example script and the small_1.pl
example script.</P>
<P>Toggles debuging off when called with no arguments.</P>
<P></P>
<DT><STRONG><A NAME="item_save">$net->save($filename);</A></STRONG><BR>
<DD>
This will save the complete state of the network to disk, including all weights and any
words crunched with <A HREF="#item_crunch"><CODE>crunch()</CODE></A> .
<P></P>
<DT><STRONG><A NAME="item_load">$net->load($filename);</A></STRONG><BR>
<DD>
This will load from disk any network saved by <A HREF="#item_save"><CODE>save()</CODE></A> and completly restore the internal
state at the point it was <A HREF="#item_save"><CODE>save()</CODE></A> was called at.
<P></P>
<DT><STRONG><A NAME="item_join_cols">$net->join_cols($array_ref,$row_length_in_elements,$high_state_character,$low_state_character);</A></STRONG><BR>
<DD>
This is more of a utility function than any real necessary function of the package.
Instead of joining all the elements of the array together in one long string, like <CODE>join()</CODE> ,
it prints the elements of $array_ref to STDIO, adding a newline (\n) after every $row_length_in_elements
number of elements has passed. Additionally, if you include a $high_state_character and a $low_state_character,
it will print the $high_state_character (can be more than one character) for every element that
has a true value, and the $low_state_character for every element that has a false value.
If you do not supply a $high_state_character, or the $high_state_character is a null or empty or
undefined string, it <A HREF="#item_join_cols"><CODE>join_cols()</CODE></A> will just print the numerical value of each element seperated
by a null character (\0). <A HREF="#item_join_cols"><CODE>join_cols()</CODE></A> defaults to the latter behaviour.
<P></P>
<DT><STRONG><A NAME="item_pdiff">$net->pdiff($array_ref_A, $array_ref_B);</A></STRONG><BR>
<DD>
This function is used VERY heavily internally to calculate the difference in percent
between elements of the two array refs passed. It returns a %.02f (sprintf-format)
percent sting.
<P></P>
<DT><STRONG><A NAME="item_p">$net->p($a,$b);</A></STRONG><BR>
<DD>
Returns a floating point number which represents $a as a percentage of $b.
<P></P>
<DT><STRONG><A NAME="item_intr">$net->intr($float);</A></STRONG><BR>
<DD>
Rounds a floating-point number rounded to an integer using <CODE>sprintf()</CODE> and <CODE>int()</CODE> , Provides
better rounding than just calling <CODE>int()</CODE> on the float. Also used very heavily internally.
<P></P>
<DT><STRONG><A NAME="item_high">$net->high($array_ref);</A></STRONG><BR>
<DD>
Returns the index of the element in array REF passed with the highest comparative value.
<P></P>
<DT><STRONG><A NAME="item_low">$net->low($array_ref);</A></STRONG><BR>
<DD>
Returns the index of the element in array REF passed with the lowest comparative value.
<P></P>
<DT><STRONG><A NAME="item_show">$net->show();</A></STRONG><BR>
<DD>
This will dump a simple listing of all the weights of all the connections of every neuron
in the network to STDIO.
<P></P>
<DT><STRONG><A NAME="item_crunch">$net->crunch($string);</A></STRONG><BR>
<DD>
UPDATE: Now you can use a variabled instead of using qw(). Strings will be split internally.
Do not use <CODE>qw()</CODE> to pass strings to crunch.
<P>This splits a string passed with /[\s\t]/ into an array ref containing unique indexes
to the words. The words are stored in an intenal array and preserved across <A HREF="#item_load"><CODE>load()</CODE></A> and <A HREF="#item_save"><CODE>save()</CODE></A>
calls. This is designed to be used to generate unique maps sutible for passing to <A HREF="#item_learn"><CODE>learn()</CODE></A> and
<A HREF="#item_run"><CODE>run()</CODE></A> directly. It returns an array ref.</P>
<P>The words are not duplicated internally. For example:</P>
<PRE>
$net->crunch("How are you?");</PRE>
<P>Will probably return an array ref containing 1,2,3. A subsequent call of:</P>
<PRE>
$net->crunch("How is Jane?");</PRE>
<P>Will probably return an array ref containing 1,4,5. Notice, the first element stayed
the same. That is because it already stored the word ``How''. So, each word is stored
only once internally and the returned array ref reflects that.</P>
<P></P>
<DT><STRONG><A NAME="item_uncrunch">$net->uncrunch($array_ref);</A></STRONG><BR>
<DD>
Uncrunches a map (array ref) into an array of words (not an array ref) and returns array.
This is ment to be used as a counterpart to the <A HREF="#item_crunch"><CODE>crunch()</CODE></A> method, above, possibly to <A HREF="#item_uncrunch"><CODE>uncrunch()</CODE></A>
the output of a <A HREF="#item_run"><CODE>run()</CODE></A> call. Consider the below code (also in ./examples/ex1.pl):
<PRE>
use AI::NeuralNet::BackProp;
my $net = AI::NeuralNet::BackProp->new(2,3);</PRE>
<PRE>
for (0..3) {
$net->learn($net->crunch("I love chips."), $net->crunch(qw(That's Junk Food!"));
$net->learn($net->crunch("I love apples."), $net->crunch("Good, Healthy Food."));
$net->learn($net->crunch("I love pop."), $net->crunch("That's Junk Food!"));
$net->learn($net->crunch("I love oranges."),$net->crunch("Good, Healthy Food."));
}</PRE>
<PRE>
my $response = $net->run($net->crunch("I love corn."));</PRE>
<PRE>
print join(' ',$net->uncrunch($response));</PRE>
<P>On my system, this responds with, ``Good, Healthy Food.'' If you try to run <A HREF="#item_crunch"><CODE>crunch()</CODE></A> with
``I love pop.'', though, you will probably get ``Food! apples. apples.'' (At least it returns
that on my system.) As you can see, the associations are not yet perfect, but it can make
for some interesting demos!</P>
<P></P>
<DT><STRONG><A NAME="item_crunched">$net->crunched($word);</A></STRONG><BR>
<DD>
This will return undef if the word is not in the internal crunch list, or it will return the
index of the word if it exists in the crunch list.
<P></P>
<DT><STRONG><A NAME="item_col_width">$net->col_width($width);</A></STRONG><BR>
<DD>
This is useful for formating the debugging output of Level 4 if you are learning simple
bitmaps. This will set the debugger to automatically insert a line break after that many
elements in the map output when dumping the currently run map during a learn loop.
<P>It will return the current width when called with a 0 or undef value.</P>
<P></P>
<DT><STRONG><A NAME="item_random">$net->random($rand);</A></STRONG><BR>
<DD>
This will set the randomness factor from the network. Default is 0.001. When called
with no arguments, or an undef value, it will return current randomness value. When
called with a 0 value, it will disable randomness in the network. See NOTES on learning
a 0 value in the input map with randomness disabled.
<P></P>
<DT><STRONG><A NAME="item_load_pcx">$net->load_pcx($filename);</A></STRONG><BR>
<DD>
Oh heres a treat... this routine will load a PCX-format file (yah, I know ... ancient format ... but
it is the only one I could find specs for to write it in Perl. If anyone can get specs for
any other formats, or could write a loader for them, I would be very grateful!) Anyways, a PCX-format
file that is exactly 320x200 with 8 bits per pixel, with pure Perl. It returns a blessed refrence to
a AI::NeuralNet::BackProp::PCX object, which supports the following routinges/members. See example
files pcx.pl and pcx2.pl in the ./examples/ directory.
<P></P>
<DT><STRONG><A NAME="item_%24pcx%2D%3E%7Bimage%7D">$pcx->{image}</A></STRONG><BR>
<DD>
This is an array refrence to the entire image. The array containes exactly 64000 elements, each
element contains a number corresponding into an index of the palette array, details below.
<P></P>
<DT><STRONG><A NAME="item_%24pcx%2D%3E%7Bpalette%7D">$pcx->{palette}</A></STRONG><BR>
<DD>
This is an array ref to an AoH (array of hashes). Each element has the following three keys:
<PRE>
$pcx->{palette}->[0]->{red};
$pcx->{palette}->[0]->{green};
$pcx->{palette}->[0]->{blue};</PRE>
<P>Each is in the range of 0..63, corresponding to their named color component.</P>
<P></P>
<DT><STRONG><A NAME="item_get_block">$pcx->get_block($array_ref);</A></STRONG><BR>
<DD>
Returns a rectangular block defined by an array ref in the form of:
<PRE>
[$left,$top,$right,$bottom]</PRE>
<P>These must be in the range of 0..319 for $left and $right, and the range of 0..199 for
$top and $bottom. The block is returned as an array ref with horizontal lines in sequental order.
I.e. to get a pixel from [2,5] in the block, and $left-$right was 20, then the element in
the array ref containing the contents of coordinates [2,5] would be found by [5*20+2] ($y*$width+$x).
</P>
<PRE>
print (@{$pcx->get_block(0,0,20,50)})[5*20+2];</PRE>
<P>This would print the contents of the element at block coords [2,5].</P>
<P></P>
<DT><STRONG><A NAME="item_get">$pcx->get($x,$y);</A></STRONG><BR>
<DD>
Returns the value of pixel at image coordinates $x,$y.
$x must be in the range of 0..319 and $y must be in the range of 0..199.
<P></P>
<DT><STRONG><A NAME="item_rgb">$pcx->rgb($index);</A></STRONG><BR>
<DD>
Returns a 3-element array (not array ref) with each element corresponding to the red, green, or
blue color components, respecitvely.
<P></P>
<DT><STRONG><A NAME="item_avg">$pcx->avg($index);</A></STRONG><BR>
<DD>
Returns the mean value of the red, green, and blue values at the palette index in $index.
<P></P></DL>
<P>
<HR>
<H1><A NAME="notes">NOTES</A></H1>
<DL>
<DT><STRONG><A NAME="item_Learning_0s_With_Randomness_Disabled">Learning 0s With Randomness Disabled</A></STRONG><BR>
<DD>
You can now use 0 values in any input maps. This is a good improvement over versions 0.40
and 0.42, where no 0s were allowed because the learning would never finish learning completly
with a 0 in the input.
<P>Yet with the allowance of 0s, it requires one of two factors to learn correctly. Either you
must enable randomness with $net-><A HREF="#item_random"><CODE>random(0.0001)</CODE></A> (Other valuse work, see <A HREF="#item_random"><CODE>random()</CODE></A> ), or you
must set an error-minum with the 'error => 5' option (you can use some other error value as well).</P>
<P>When randomness is enabled (that is, when you call <A HREF="#item_random"><CODE>random()</CODE></A> with a value other than 0), it interjects
a bit of randomness into the output of every neuron in the network, except for the input and output
neurons. The randomness is interjected with rand()*$rand, where $rand is the value that was
passed to <A HREF="#item_random"><CODE>random()</CODE></A> call. This assures the network that it will never have a pure 0 internally. It is
bad to have a pure 0 internally because the weights cannot change a 0 when multiplied by a 0, the
product stays a 0. Yet when a weight is multiplied by 0.00001, eventually with enough weight, it will
be able to learn. With a 0 value instead of 0.00001 or whatever, then it would never be able
to add enough weight to get anything other than a 0.</P>
<P>The second option to allow for 0s is to enable a maximum error with the 'error' option in
<A HREF="#item_learn"><CODE>learn()</CODE></A> , <A HREF="#item_learn_set"><CODE>learn_set()</CODE></A> , and <A HREF="#item_learn_set_rand"><CODE>learn_set_rand()</CODE></A> . This allows the network to not worry about
learning an output perfectly.</P>
<P>For accuracy reasons, it is recomended that you work with 0s using the <A HREF="#item_random"><CODE>random()</CODE></A> method.</P>
<P>If anyone has any thoughts/arguments/suggestions for using 0s in the network, let me know
at <A HREF="mailto:jdb@wcoil.com.">jdb@wcoil.com.</A></P>
<P></P></DL>
<P>
<HR>
<H1><A NAME="other included packages">OTHER INCLUDED PACKAGES</A></H1>
<DL>
<DT><STRONG><A NAME="item_AI%3A%3ANeuralNet%3A%3ABackProp%3A%3AFile">AI::NeuralNet::BackProp::File</A></STRONG><BR>
<DD>
<A HREF="#item_AI%3A%3ANeuralNet%3A%3ABackProp%3A%3AFile"><CODE>AI::NeuralNet::BackProp::File</CODE></A> implements a simple 'relational'-style
database system. It is used internally by <CODE>AI::NeuralNet::BackProp</CODE> for
storage and retrival of network states. It can also be used independently
of <CODE>AI::NeuralNet::BackProp</CODE>. PODs are not yet included for this package, I hope
to include documentation for this package in future releases.
<P><A HREF="#item_AI%3A%3ANeuralNet%3A%3ABackProp%3A%3AFile"><CODE>AI::NeuralNet::BackProp::File</CODE></A> depends on <CODE>Storable</CODE>, version 0.611 for low-
level disk access. This dependency is noted in Makefile.PL, and should be handled
automatically when you installe this <CODE>AI::NeuralNet::BackProp</CODE>.</P>
<P></P>
<DT><STRONG><A NAME="item_AI%3A%3ANeuralNet%3A%3ABackProp%3A%3Aneuron">AI::NeuralNet::BackProp::neuron</A></STRONG><BR>
<DD>
AI::NeuralNet::BackProp::neuron is the worker package for AI::NeuralNet::BackProp.
It implements the actual neurons of the nerual network.
AI::NeuralNet::BackProp::neuron is not designed to be created directly, as
it is used internally by AI::NeuralNet::BackProp.
<P></P>
<DT><STRONG><A NAME="item_AI%3A%3ANeuralNet%3A%3ABackProp%3A%3A_run">AI::NeuralNet::BackProp::_run</A></STRONG><BR>
<DD>
<DT><STRONG><A NAME="item_AI%3A%3ANeuralNet%3A%3ABackProp%3A%3A_map">AI::NeuralNet::BackProp::_map</A></STRONG><BR>
<DD>
These two packages, _run and _map are used to insert data into
the network and used to get data from the network. The _run and _map packages
are connected to the neurons so that the neurons think that the IO packages are
just another neuron, sending data on. But the IO packs. are special packages designed
with the same methods as neurons, just meant for specific IO purposes. You will
never need to call any of the IO packs. directly. Instead, they are called whenever
you use the <A HREF="#item_run"><CODE>run()</CODE></A> or <A HREF="#item_learn"><CODE>learn()</CODE></A> methods of your network.
<P></P></DL>
<P>
<HR>
<H1><A NAME="bugs">BUGS</A></H1>
<P>This is the beta release of <CODE>AI::NeuralNet::BackProp</CODE>, and that holding true, I am sure
there are probably bugs in here which I just have not found yet. If you find bugs in this module, I would
appreciate it greatly if you could report them to me at <EM><<A HREF="mailto:jdb@wcoil.com">jdb@wcoil.com</A>></EM>,
or, even better, try to patch them yourself and figure out why the bug is being buggy, and
send me the patched code, again at <EM><<A HREF="mailto:jdb@wcoil.com">jdb@wcoil.com</A>></EM>.</P>
<P>
<HR>
<H1><A NAME="author">AUTHOR</A></H1>
<P>Josiah Bryan <EM><<A HREF="mailto:jdb@wcoil.com">jdb@wcoil.com</A>></EM></P>
<P>Copyright (c) 2000 Josiah Bryan. All rights reserved. This program is free software;
you can redistribute it and/or modify it under the same terms as Perl itself.</P>
<P>The <CODE>AI::NeuralNet::BackProp</CODE> and related modules are free software. THEY COME WITHOUT WARRANTY OF ANY KIND.
</P>
<PRE>
=head1 THANX</PRE>
<P>Below is a list of people that have helped, made suggestions, patches, etc. No particular order.</P>
<PRE>
Tobias Bronx, F<E<lt>tobiasb@odin.funcom.comE<gt>>
Pat Trainor, F<E<lt>ptrainor@title14.comE<gt>>
Steve Purkis, F<E<lt>spurkis@epn.nuE<gt>>
Rodin Porrata, F<E<lt>rodin@ursa.llnl.govE<gt>></PRE>
<P>Tobias was a great help with the initial releases, and helped with learning options and a great
many helpful suggestions. Rodin has gave me some great ideas for the new internals. Steve is
the author of AI::Perceptron, and gave some good suggestions for weighting the neurons. Pat
has been a great help for running the module through the works. Pat is the author of the new Inter
game, a in-depth strategy game. He is using a group of neural networks internally which provides
a good test bed for coming up with new ideas for the network. Thankyou for all of your help, everybody.</P>
<P>
<HR>
<H1><A NAME="download">DOWNLOAD</A></H1>
<P>You can always download the latest copy of AI::NeuralNet::BackProp
from <A HREF="http://www.josiah.countystart.com/modules/AI/cgi-bin/rec.pl">http://www.josiah.countystart.com/modules/AI/cgi-bin/rec.pl</A></P>
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