感知器中的阈值有什么意义? [英] What's the point of the threshold in a perceptron?

问题描述

我无法看到阈值在单层感知器中的实际作用.无论阈值是多少，数据通常都是分开的.似乎较低的阈值可以更平等地划分数据；这是它的用途吗?

I'm having trouble seeing what the threshold actually does in a single-layer perceptron. The data is usually separated no matter what the value of the threshold is. It seems a lower threshold divides the data more equally; is this what it is used for?

推荐答案

实际上，您只需在不使用偏差时设置阈值即可.否则，阈值为 0.

Actually, you'll just set threshold when you aren't using bias. Otherwise, the threshold is 0.

请记住，单个神经元用超平面划分您的输入空间.好吗?

Remember that, a single neuron divides your input space with a hyperplane. Ok?

现在想象一个有 2 个输入 X=[x1, x2]、2 个权重 W=[w1, w2] 和阈值 TH 的神经元>.该等式显示了该神经元的工作原理:

Now imagine a neuron with 2 inputs X=[x1, x2], 2 weights W=[w1, w2] and threshold TH. The equation shows how this neuron works:

x1.w1 + x2.w2 = TH

这等于:

x1.w1 + x2.w2 - 1.TH = 0

即，这是您的超平面方程，它将划分输入空间.

I.e., this is your hyperplane equation that will divides the input space.

请注意，如果您手动设置阈值，这个神经元就会起作用.解决方案是将 TH 更改为另一个权重，因此:

Notice that, this neuron just work if you set manually the threshold. The solution is change TH to another weight, so:

x1.w1 + x2.w2 - 1.w0 = 0

其中术语 1.w0 是您的 BIAS.现在您仍然可以在输入空间中绘制平面而无需手动设置阈值(即阈值始终为 0).但是，如果您将阈值设置为其他值，权重将自行调整以调整方程，即权重(包括偏差)吸收阈值效应.

Where the term 1.w0 is your BIAS. Now you still can draw a plane in your input space without set manually a threshold (i.e, threshold is always 0). But, in case you set the threshold to another value, the weights will just adapt themselves to adjust equation, i.e., weights (INCLUDING BIAS) absorves the threshold effects.

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