In the field of Machine Learning, the Perceptron is a Supervised Learning Algorithm for binary classifiers. The Perceptron Model implements the following function:
![\[ \begin{array}{c} \hat{y}=\Theta\left(w_{1} x_{1}+w_{2} x_{2}+\ldots+w_{n} x_{n}+b\right) \\ =\Theta(\mathbf{w} \cdot \mathbf{x}+b) \\ \text { where } \Theta(v)=\left\{\begin{array}{cc} 1 & \text { if } v \geqslant 0 \\ 0 & \text { otherwise } \end{array}\right. \end{array} \]](https://neveropen.co.za/wp-content/uploads/2023/10/quicklatex.com-f98cbf4744582c2b3309f1b0ceb8a313_l3-4.png "Rendered by QuickLaTeX.com")
For a particular choice of the weight vector 
and bias parameter 
, the model predicts output 
for the corresponding input vector 
.
NOT logical function truth table is of only 1-bit binary input (0 or 1), i.e, the input vector and the corresponding output 
–
|
|
|---|---|
| 0 | 1 |
| 1 | 0 |
Now for the corresponding weight vector of the input vector , the associated Perceptron Function can be defined as:
![\[$\boldsymbol{\hat{y}} = \Theta\left(w x+b\right)$\]](https://neveropen.co.za/wp-content/uploads/2023/10/quicklatex.com-ffc911fc71ed0749b941afac38e76081_l3-1.png "Rendered by QuickLaTeX.com")
For the implementation, considered weight parameter is 
and the bias parameter is 
.
Python Implementation:
# importing Python library import numpy as np # define Unit Step Function def unitStep(v): if v >= 0: return 1 else: return 0 # design Perceptron Model def perceptronModel(x, w, b): v = np.dot(w, x) + b y = unitStep(v) return y # NOT Logic Function # w = -1, b = 0.5 def NOT_logicFunction(x): w = -1 b = 0.5 return perceptronModel(x, w, b) # testing the Perceptron Model test1 = np.array(1) test2 = np.array(0) print("NOT({}) = {}".format(1, NOT_logicFunction(test1))) print("NOT({}) = {}".format(0, NOT_logicFunction(test2))) |
NOT(1) = 0 NOT(0) = 1
Here, the model predicted output () for each of the test inputs are exactly matched with the NOT logic gate conventional output () according to the truth table.
Hence, it is verified that the perceptron algorithm for NOT logic gate is correctly implemented.
