In our previous lecture, we discussed the perceptron, a fundamental concept in machine learning. Today, let's take it one step further and explore how we can extend its capabilities to handle real-valued inputs.
Why go beyond binary?
The initial design of the perceptron limited its input values to 1 and 0 (binary). However, there is no logical reason to restrict ourselves to such a narrow range. By allowing real numbers as input values, we can represent a wider spectrum of information.
Adjusting the Perceptron Equation
To achieve this, we'll make some minor adjustments to the perceptron equation:z = w1x1 + w2x2 + ... + wnxn + bHere,brepresents a constant bias term often referred to as thebias. By moving the threshold to the left and introducing this new term, we have a more general representation of the perceptron.
Graphical Representation
Let's examine the graphical representation of this function. The following equation is what determines the output:f(z) = 1 if z > 0, else 0In this case, a valuezless than zero results in an output of zero, while a value greater than or equal to zero yields an output of one. This function is known as thestep functionand serves as an activation function.
The Sigmoid Function: A Smoother Alternative
The step function presents some challenges when training our perceptron using historical data, especially when dealing with classification problems like the MNIST dataset. The sigmoid function offers a smoother and more manageable alternative. With the sigmoid function, changes are gradual, making it easier to control the behavior of the model.
By replacing the step function with a sigmoid activation function, we create what's known as asigmoid neuronorlogistic neuron. This new cell formula looks like:f(z) = 1 / (1 + e^-z)With this modification, our artificial neural cell can now accept any number of real-valued inputs and produce an output between 0 and 1.
Next Time on Machine Learning Basics
In our next lecture, we'll explore how to create an artificial neural network using these individual cells. Stay tuned for more insights into the world of machine learning!
Let's discuss your project and find the best solution for your business.
