Neural Nets
TUTORIAL ON MACHINE LEARNING AND NEURAL NETWORKS
Let's just dive right in... Below I've embedded a neural network classifier rendered using TensorflowPlayground. There are a variety of knobs and buttons on the interface; as we move along, more of these options will become available. Don't worry though, all these will be explained in detail, in due time. For now though, let's define our primary goal throughout this tutorial: categorization
Our primary task is to train neural nets to classify items into categories, based on some limited information. Like fruit or vegetable; or undergrad major; or Alzheimer's Disease patient (CASE) or control participant (CTRL). In the Tensorflow playground below, you can see a bunch of orange and blue dots. Instead of simply thinking about these as dots or arbitrary spatial coordinates, I think it will be helpful to think of these as representing people in a clinical study. Let's define the blue dots are patients from the CASE group, and orange dots are CTRL participants. Now what is our 'limited information' about them? Let's say we have collected information about their age and their score on a cognitive exam. So the first thing we'd probably want to do is make a scatter plot of these two variables. Let's define their respective dimensions on the plot axes as:
- x-axis | dim-1 | current age (AGE)
- y-axis | dim-2 | exam score (SCORE)
Notice that after plotting, the dots seem to form clusters. That very promising! If you were asked to draw a line on this plane, to separate these two clusters, it could be easily done. Our brain's neural nets have already solved the the spatial problem. Now let's see if an artificial neural net can solve the same problem.
Go ahead and click the blue start button below; let it run for about 500 epochs (~5 seconds), then click pause.
{{#widget:Tensorflow1}}
How'd it do? Does one neuron, with a single feature input (the value of each dot in the first dimension, the x-axis) perform well in the separation task? If it did well, an orange background should have formed behind the orange dots, and a blue background behind the blue dots.
The color gradient along the surface (under the dots) can be understood as the neural net's prediction 'confidence' at that given coordinate. More directly, it is the value spit-out by the activation function of the 'output layer'. Here, since we only have a single layer, our hidden 'hidden layer' and 'output layer' are one in the same. The output function of our neuron is known as the tanh function.
The tanh function is an extremely common choice for an output function in artificial neural network machine learning frameworks because it yields a nice sigmoid shape, and no matter the magnitude of its inputs, the output from the tanh function is bounded between { 0 : 1}. These are very desirable properties for neural net nodes. Here you see the tanh function evaluated across various x-dim inputs...
Tanh produces a sigmoid output over the range {-2 : 2}, and automatically evaluates to exact values when its argument is the natural logarithm. Speaking of the natural log, that is another very common choice of output function for the same reasons as tanh.
For now, let's not belabor the point that our neuron (and in going forward, all our neurons) are using the tanh function. Maybe just keep this in mind if you're wondering what sorts of numbers are travelling along the axons of these neurons, and ultimately those colored gradients underneath the dots.
This tutorial continues on the next page. Don't worry about playing around too much with the TensorFlow GUI, there will be plenty of that on the next page, and those that follow.