$1$ Perceptron algorithm Classifier

The Perceptron algorithm, a fundamental concept in machine learning, serves as a building block for more complex models. It was initially proposed by Frank Rosenblatt in the late $1950$s and is widely used for binary classification tasks. The algorithm learns to classify input data points into two categories by adjusting its weights based on errors made during prediction. While relatively simple, the Perceptron algorithm forms the basis for neural networks and other sophisticated machine learning models. Its ability to learn from data and make decisions autonomously makes it a crucial tool in various fields, pattern recognition to natural language processing.

Forward propagation

In $[]$: $1$ import numpy $asnp$

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$4$ def forward$\_$propagation$(x,$ weights$)$:

Perform forward propagation for one perceptron.

Parameters:

x: Input data. $-$ weights: Weights matrix including the bais at weight $[0]$

Returns:

Returns: $-y$ : the prediction. Output of the perceptron $($either $0$ or $1).$ dotsn

# Write Your code here

return y

Use the following cell to test your solution in the previous cell. Here is a list of correct answers:

input data predicted label

$[0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}3],1$

Use the following cell to test your solution in the previous cell. Here is a list of correct answers:

Original weights Updated weights

$[0\mathrm{.}50\mathrm{.}30\mathrm{.}2][0\mathrm{.}2020\mathrm{.}50020\mathrm{.}30040\mathrm{.}2006]$

In $[1$: $1$ # Example usage

Training $($Forward & backward propagation$)$

In $[]$: $1$ import numpy $asnp$

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$3$ def $trai{n}_p$erceptron$(x,y,$ weights, $learnin{g}_r$ate, iterations$)$:

Train the perceptron with the given dataset and return the updated weights. This function should go over the then call the backward$\_$propagation$()$ function to update the weights. The function should go over the dataset Parameters:

$x$ : Input data, a $2$D array with $K$ rows and $n$ columns where $K$ is the number of datapoints in the dataset and $-$ weights: Weights matrix. A $1-$dimensional array of size $(n+1)$ where $n$ is the number of features, including $-$ learning$\_$rate: the learning rate used in the training $($alpha$)$

iterations: the number of iterations of the

Returns:

updated$\_$weights: Updated weights matrix.

# Write your code here

return weights

Use the following cell to test your solution in the previous cell. Here is a list of correct answers: $$

$\backslash$table$[[$Index of the example,Updated Weights$],[$Updated weights$[$datapoint$(1)],\left[\begin{array}{cccc}0\mathrm{.}5& 0\mathrm{.}3& 0\mathrm{.}2& 0\mathrm{.}1\end{array}\right]$