<s>
The	O
generalized	B-Algorithm
Hebbian	I-Algorithm
algorithm	I-Algorithm
(	O
GHA	O
)	O
,	O
also	O
known	O
in	O
the	O
literature	O
as	O
Sanger	B-Algorithm
's	I-Algorithm
rule	I-Algorithm
,	O
is	O
a	O
linear	O
feedforward	B-Algorithm
neural	I-Algorithm
network	I-Algorithm
model	O
for	O
unsupervised	B-General_Concept
learning	I-General_Concept
with	O
applications	O
primarily	O
in	O
principal	B-Application
components	I-Application
analysis	I-Application
.	O
</s>
<s>
First	O
defined	O
in	O
1989	O
,	O
it	O
is	O
similar	O
to	O
Oja	B-Algorithm
's	I-Algorithm
rule	I-Algorithm
in	O
its	O
formulation	O
and	O
stability	O
,	O
except	O
it	O
can	O
be	O
applied	O
to	O
networks	O
with	O
multiple	O
outputs	O
.	O
</s>
<s>
where	O
defines	O
the	O
synaptic	B-Algorithm
weight	I-Algorithm
or	O
connection	O
strength	O
between	O
the	O
th	O
input	O
and	O
th	O
output	O
neurons	O
,	O
and	O
are	O
the	O
input	O
and	O
output	O
vectors	O
,	O
respectively	O
,	O
and	O
is	O
the	O
learning	B-General_Concept
rate	I-General_Concept
parameter	O
.	O
</s>
<s>
where	O
is	O
any	O
matrix	O
,	O
in	O
this	O
case	O
representing	O
synaptic	B-Algorithm
weights	I-Algorithm
,	O
is	O
the	O
autocorrelation	O
matrix	O
,	O
simply	O
the	O
outer	O
product	O
of	O
inputs	O
,	O
is	O
the	O
function	O
that	O
diagonalizes	O
a	O
matrix	O
,	O
and	O
is	O
the	O
function	O
that	O
sets	O
all	O
matrix	O
elements	O
on	O
or	O
above	O
the	O
diagonal	O
equal	O
to	O
0	O
.	O
</s>
<s>
The	O
GHA	O
is	O
used	O
in	O
applications	O
where	O
a	O
self-organizing	B-Algorithm
map	I-Algorithm
is	O
necessary	O
,	O
or	O
where	O
a	O
feature	O
or	O
principal	B-Application
components	I-Application
analysis	I-Application
can	O
be	O
used	O
.	O
</s>
<s>
Examples	O
of	O
such	O
cases	O
include	O
artificial	B-Application
intelligence	I-Application
and	O
speech	O
and	O
image	O
processing	O
.	O
</s>
<s>
Its	O
importance	O
comes	O
from	O
the	O
fact	O
that	O
learning	O
is	O
a	O
single-layer	O
process	O
—	O
that	O
is	O
,	O
a	O
synaptic	B-Algorithm
weight	I-Algorithm
changes	O
only	O
depending	O
on	O
the	O
response	O
of	O
the	O
inputs	O
and	O
outputs	O
of	O
that	O
layer	O
,	O
thus	O
avoiding	O
the	O
multi-layer	O
dependence	O
associated	O
with	O
the	O
backpropagation	B-Algorithm
algorithm	O
.	O
</s>
<s>
It	O
also	O
has	O
a	O
simple	O
and	O
predictable	O
trade-off	O
between	O
learning	O
speed	O
and	O
accuracy	O
of	O
convergence	O
as	O
set	O
by	O
the	O
learning	B-General_Concept
rate	I-General_Concept
parameter	O
.	O
</s>
