11 january 2017, 00:55
3.9. Neural network Hopfield
and its application.
The revival of interest in neural networks related to the work of Hopfield, 1982..
This work has shed light on the fact that borrowed from nature
network of neuronopathic elements can be used to compute
goals. Researchers from many areas of knowledge was an incentive for further
studies of those networks with the double purpose of a better understanding of
how the brain works apply mothodologie properties of these networks to solve problems
which are not amenable to solution by traditional methods.
3.9.1. The idea of recurrently.
Neural Hopfield network is an example network which can be defined as dynamic
system running in which the output of one fully direct operation serves as the entrance
the next operation of the network as shown in Fig.1
Figure 1. A binary Hopfield network.
Network which work as a feedback are called recurrent networks. Each video operation network is called an iteration. Recurrent network as with any other nonlinear dynamic systems able to show a whole variety of different behaviors. In particular, one possible pattern of behavior is that the system can be sustainable i.e. it can converge to the only fixed fixed point. When the stationary point is the input to this dynamic system, the output will have the same point. Therefore, the system remains fixed in the same condition. There are periodic cycles or chaotic behavior.
It has been shown that a Hopfield network is stable. In the General case may be more
one fixed point. Then such a fixed point will converge the network
depends on the initial point chosen for the initial iteration.
The fixed points are called attractors. Many
of vector points which are attracted to a specific attractor in the process
iterations the network is called the region of attraction of this attractor. Many
fixed points of the Hopfield network is its memory. In this case, the network can
to act as an associative memory. Those input vectors that fall into
the sphere of attraction of the attractor the individual are associated associated
For example, the attractor may be a certain desired way. The region of attraction
can consist of noisy or incomplete versions of this image. There is hope
the images that vaguely resemble the desired image will be remembered by the network as
associated with a given image.
3.9.2. Binary Hopfield networks.
In Fig. 1 shows a binary Hopfield network. Input and
the output vectors consist of 1 and +1 instead of 1 can be used
0 A symmetric weight matrix consisting of integers with zeros
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