Artificial Neural Network 简明教程

Brain-State-in-a-Box Network

脑状态神经网络 (BSB) 是一种非线性自关联神经网络，可以扩展到具有两层或更多层的异关联。它也类似于霍普菲尔德网络。它是由 J.A. 安德森、J.W. 西尔弗斯坦、S.A. 里茨和 R.S. 琼斯于 1977 年提出的。

The Brain-State-in-a-Box (BSB) neural network is a nonlinear auto-associative neural network and can be extended to hetero-association with two or more layers. It is also similar to Hopfield network. It was proposed by J.A. Anderson, J.W. Silverstein, S.A. Ritz and R.S. Jones in 1977.

关于 BSB 网络需要注意的一些要点 -

Some important points to remember about BSB Network −

  1. It is a fully connected network with the maximum number of nodes depending upon the dimensionality n of the input space.

  2. All the neurons are updated simultaneously.

  3. Neurons take values between -1 to +1.

Mathematical Formulations

BSB 网络中使用的节点函数是一个坡道函数，可定义如下 −

The node function used in BSB network is a ramp function, which can be defined as follows −

f(net)\:=\:min(1,\:max(-1,\:net))

该坡道函数是有界的，且是连续的。

This ramp function is bounded and continuous.

我们知道每个节点都会改变其状态，这可以通过以下数学关系来完成 −

As we know that each node would change its state, it can be done with the help of the following mathematical relation −

x_{t}(t\:+\:1)\:=\:f\left(\begin{array}{c}\displaystyle\sum\limits_{j=1}^n w_{i,j}x_{j}(t)\end{array}\right)

此处， xi(t) 是 ith 节点在时间 t 的状态。

Here, xi(t) is the state of the ith node at time t.

ith 节点到 jth 节点的权重可以通过以下关系测量 −

Weights from ith node to jth node can be measured with the following relation −

w_{ij}\:=\:\frac{1}{P}\displaystyle\sum\limits_{p=1}^P (v_{p,i}\:v_{p,j})

此处， P 是训练模式的数量，它们是双极性的。

Here, P is the number of training patterns, which are bipolar.