Let's learn perceptron the noob way

Posted on October 31, 2017
Tags: programming machine-learning perceptron

Perceptron is the building block for a larger network (which is called neural network to be taught later). It is a blackbox that accepts inputs, processes them and gives out outputs (actually tries to predict them). A perceptron, in fact, is just a crude way to simulate a single biological neuron. We know, a neuron fires (or does not fire) based on its input stimuli. So, a perceptron is like that:

input ---> process ---> output (prediction)

How does it work?

A perceptron is a decision maker. It outputs certain number which can be interpreted as yes/no or 0/1 or similar range of decision.

For example, the prediction of a house cost depends on various input factors like area, resident type, popularity, number of rooms, etc. These inputs can be modeled as variables.

So,

|   x1  |
|   x2  |   ---> |process|  --->    |z|
|   x3  |

This is the overall blackbox model for a perceptron. It takes x1, x2, x3 inputs go into the process. Does some mathe-magic. And, gives output.

But wait a sec

Not all the inputs have influence over the final output/result. This is analogous to the biological neuron where some stimulus have greater influence on the resposne of the neuron.

For example, to buy the house the weather doesn’t really affect the pricing.

So, the inputs are prioritized accordingly. These priorities are called weights in perceptron.

|   x1, w1  |
|   x2, w2  |   ---> |process|  --->    |z|
|   x3, w3  |

Process

The process is nothing but weighted sum of inputs.

    x1*w1 + x2*w2 + x3*w3

In general sense,

    summation(xi, wi)

Vectoricallly,

    dot_product(X, W)

But, the summation doesn’t tell us about decision because there has to be some conditions for decision making.
Like: if output/y is more than some threshold, the perceptron fires. This very idea of threshold gives rise to some kind of so-called activation shit which we machine learning freak call activation function.

So, what really happens is

    dot_product(X, W)   --->    y   ---> activation  --->    output(z)

The activation function accepts the weighted sum (which is a single value for given inputs) and performs some conditions to fire up the neuron (or not to fire the neuron)

Normally, only simple conditions are used

    if y >= 0.6,    z = 1
    if y < 0.6,    z = 0

Or you can use already available activation function like sigmoid This activation gives you the output in the range 0 to 1. If this output is high around 1, it means perceptron has fired.

Output

Strictly, perceptron outputs boolean value : 0/1 or False/True. If you are using some kinda activation, the perceptron outputs some real numbers. But it isn’t perceptron really. It is an artificial neural network.

The difference between a neuron and perceptron is that a perceptron outputs boolean value while a neuron outputs a real number.

For simplicity, I will consider both perceptron and a neuron as being same; used synonymously.


Let’s build a perceptron

We will be using python3 and numpy. Other libraries/modules can be installed accordingly from pip3.

Import numpy

Numpy is a python library for performing vector (matrix) operations efficiently.

import numpy as np

Training Inputs

The inputs are numpy arrays

X_train = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])

Training Outputs

Let’s try an OR gate. So, training output will be:

>> Y_train = np.array([[0, 1, 1, 1]]).T

Weights/Synapses

>> synapses = np.array([ [ 2.45685895, 2.56862029] ]).T

This weight is actually obtained after training the perceptron. The above is what I have obtained after training for 100 iterations.

Sigmoid

def sigmoid(x):
    return 1 / (1 + np.exp(-x))

Prediction

>> y = np.dot(X_train, synapses)
array([[ 0.        ],
       [ 2.56862029],
       [ 2.45685895],
       [ 5.02547924]])
>> z = sigmoid(y)
array([[ 0.5       ],
       [ 0.92881453],
       [ 0.92106159],
       [ 0.99347442]])

So, OR Gate is working nicely. The perceptron is giving us the output very high for any input that contains a 1.

Hence, perceptron is all about finding the real values of the weights.

Training

Since, we have used already solved weights, we haven’t trained the perceptron in the tutorial. We will do the perceptron learning/training process in the next part.