Machine Learning - Neural Networks Examples and Intuitions
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This series of articles are the study notes of " Machine Learning ", by Prof. Andrew Ng., Stanford University. This article is the notes of week 4. It contains topics about Neural Networks examples and intuitions.
Neural Networks Examples and Intuitions
1. Neural Networks Examples and intuitions I
Non-linear classification example: XOR/XNOR
Consider the following problem where we have features X1 and X2 that are binary values. So, either 0 or 1. So, X1 and X2 can each take on only one of two possible values. In this example, I've drawn only two positive examples and two negative examples. That you can think of this as a simplified version of a more complex learning problem where we may have a bunch of positive examples in the upper right and lower left and a bunch of negative examples denoted by the circles. And what we'd like to do is learn a non-linear division of boundary that may need to separate the positive and negative examples.
x1,x2 are binary (0 or 1).
y = x1 XOR x2
x1 XNOR x2 = NOT(x1 XOR x2)
Example: AND
x1, x2 ∈{0,1}
y = x1 AND x2
Let's look at what this little single neuron network will compute. Just to remind you the sigmoid activation function g(z) looks like this. It starts from 0 rises smoothly crosses 0.5 and then it asymptotic as 1 and to give you some landmarks, if the horizontal axis value z is equal to 4.6 then the sigmoid function is equal to 0.99. This is very close to 1 and kind of symmetrically, if it's -4.6 then the sigmoid function there is 0.01 which is very close to 0.
Let's look at the four possible input values for x1 and x2 and look at what the hypotheses will output in that case.
Example: OR
So, hopefully with this you now understand how single neurons in a neural network can be used to compute logical functions like AND and OR and so on. In the next video we'll continue building on these examples and work through a more complex example. We'll get to show you how a neural network now with multiple layers of units can be used to compute more complex functions like the XOR function or the XNOR function.
2. Neural Networks Examples and intuitions II
Negation:
Not x
Putting it together: x1 XNOR x2
We end up with a nonlinear decision boundary that computes this XNOR function.
Neural Network intuition
intuition about why neural networks can compute pretty complicated functions
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