Predict method of the perceptron algorithm

Question

Can someone explain to me how the predict method of the perceptron algorithm works?

def predict(self, pattern):
    activation = np.dot(self.w, pattern) + self.b
    if activation > 0:
        return 1
    else:
        return -1

In this example b stands for bias.

def train(self, pattern, label, step = 0.01):
    out_label = self.predict(pattern)
    if out_label == label:
        return True
    self.w += step * (label - out_label) * pattern
    self.b += step * (label - out_label)
    return False

This is the train method. But as far as I understand in out_label there will only be either 1 or -1. How could this be possibly equal to label? If we would return activation I (think) I would understand it.

Answer 1

Here is how the code appears to break down:

method parameters:

The train(...) method takes an input vector called pattern along with the target output called label and a weight update coefficient (learning rate) called step.

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method execution:

1. train(...) first passes the input vector through our neuron using the predict(...) method.
2. The result of predict(...) is stored in a variable named out_label.
3. The out_label variable is either 1 or -1.
4. Depending on the pattern that we provide we want the target output (label) to be either 1 or -1.
5. If out_label is equal to label (1 == 1 or -1 == -1), then we return True
6. Otherwise, the neuron outputted a value we do not want (-1 != 1 or 1 != -1), so we update the weights accordingly, then return False

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example where the neuron is correct:

Let's say we have the following parameters:

input vector (pattern) = [-5,2,8]

target output (label) = 1

The train(...) method executes as follows:

1. we call the predict(...) which does the following:

   • passes our vector [-5,2,8] through the neuron using the function np.dot(self.w, pattern) + self.b

   • stores the result of the above function in a variable called activation (let's say activation = 0.23)

   • returns 1 because activation > 0

2. we store the result of predict(...) in the variable out_label, which is 1 in this example

3. because our target output (label = 1), is equal to the actual output (out_label = 1) of the neuron, we return True and consider the neuron output correct.

---

example where the neuron is incorrect:

Let's say we have the following parameters:

input vector (pattern) = [-1,-5,3]

target output (label) = 1

The train(...) method executes as follows:

1. we call the predict(...) which does the following:

   • passes our vector [-1,-5,3] through the neuron using the function np.dot(self.w, pattern) + self.b

   • stores the result of the above function in a variable called activation (let's say activation = -0.65)

   • returns -1 because activation <= 0

2. we store the result of predict(...) in the variable out_label, which is -1 in this example

3. because our target output (label = 1), is not equal to the actual output (out_label = -1) of the neuron, we update the weights using:
   self.w += step * (label - out_label) * pattern self.b += step * (label - out_label)
4. we then return False because the neuron was incorrect