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Creating a single perceptron for training

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5

learning how perceptron works and attempted to created a function out of it.

I recently watched a video in youtube as an introduction to the said topic.

Right now, I tried to mimic his function and I would like to try applying it in a sample dataset:

# x1 x2 y
data = [ [3.5, 1.5, 1],
 [2.0, 1.0, 0],
 [4.0, 1.5, 1],
 [3.0, 1.0, 0],
 [3.5, 0.5, 1],
 [2.0, 0.5, 0],
 [5.5, 1.0, 1],
 [1.0, 1.0, 0],
 [4.5, 1.0, 1] ]

data = pd.DataFrame(data, columns = ["Length", "Width", "Class"])

Sigmoid function:

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

Perceptron function:

w1 = np.random.randn()
w2 = np.random.randn()
b = np.random.randn()

def perceptron(x1,x2, w1, w2, b):

 z = (w1 * x1) + (w2 * x2) + b

 return sigmoid(z)

My question here is how can I add the cost function inside the Perceptron and loop it n times based from a parameter to adjust the weights using the cost function?

def get_cost_slope(b,a):
 """
 b = predicted value
 a = actual value
 """

 sqrerror = (b - a) ** 2
 slope = 2 * (b-a)

 return sqrerror, slope

python python-3.x pandas neural-network jupyter-notebook

share|improve this question

edited Mar 28 at 22:03

Sid

asked Mar 28 at 21:52

SidSid

4344 bronze badges

add a comment
 | 

5

learning how perceptron works and attempted to created a function out of it.

I recently watched a video in youtube as an introduction to the said topic.

Right now, I tried to mimic his function and I would like to try applying it in a sample dataset:

# x1 x2 y
data = [ [3.5, 1.5, 1],
 [2.0, 1.0, 0],
 [4.0, 1.5, 1],
 [3.0, 1.0, 0],
 [3.5, 0.5, 1],
 [2.0, 0.5, 0],
 [5.5, 1.0, 1],
 [1.0, 1.0, 0],
 [4.5, 1.0, 1] ]

data = pd.DataFrame(data, columns = ["Length", "Width", "Class"])

Sigmoid function:

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

Perceptron function:

w1 = np.random.randn()
w2 = np.random.randn()
b = np.random.randn()

def perceptron(x1,x2, w1, w2, b):

 z = (w1 * x1) + (w2 * x2) + b

 return sigmoid(z)

My question here is how can I add the cost function inside the Perceptron and loop it n times based from a parameter to adjust the weights using the cost function?

def get_cost_slope(b,a):
 """
 b = predicted value
 a = actual value
 """

 sqrerror = (b - a) ** 2
 slope = 2 * (b-a)

 return sqrerror, slope

python python-3.x pandas neural-network jupyter-notebook

share|improve this question

edited Mar 28 at 22:03

Sid

asked Mar 28 at 21:52

SidSid

4344 bronze badges

add a comment
 | 

learning how perceptron works and attempted to created a function out of it.

I recently watched a video in youtube as an introduction to the said topic.

Right now, I tried to mimic his function and I would like to try applying it in a sample dataset:

# x1 x2 y
data = [ [3.5, 1.5, 1],
 [2.0, 1.0, 0],
 [4.0, 1.5, 1],
 [3.0, 1.0, 0],
 [3.5, 0.5, 1],
 [2.0, 0.5, 0],
 [5.5, 1.0, 1],
 [1.0, 1.0, 0],
 [4.5, 1.0, 1] ]

data = pd.DataFrame(data, columns = ["Length", "Width", "Class"])

Sigmoid function:

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

Perceptron function:

w1 = np.random.randn()
w2 = np.random.randn()
b = np.random.randn()

def perceptron(x1,x2, w1, w2, b):

 z = (w1 * x1) + (w2 * x2) + b

 return sigmoid(z)

My question here is how can I add the cost function inside the Perceptron and loop it n times based from a parameter to adjust the weights using the cost function?

def get_cost_slope(b,a):
 """
 b = predicted value
 a = actual value
 """

 sqrerror = (b - a) ** 2
 slope = 2 * (b-a)

 return sqrerror, slope

python python-3.x pandas neural-network jupyter-notebook

share|improve this question

edited Mar 28 at 22:03

Sid

asked Mar 28 at 21:52

SidSid

4344 bronze badges

# x1 x2 y
data = [ [3.5, 1.5, 1],
 [2.0, 1.0, 0],
 [4.0, 1.5, 1],
 [3.0, 1.0, 0],
 [3.5, 0.5, 1],
 [2.0, 0.5, 0],
 [5.5, 1.0, 1],
 [1.0, 1.0, 0],
 [4.5, 1.0, 1] ]

data = pd.DataFrame(data, columns = ["Length", "Width", "Class"])

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

w1 = np.random.randn()
w2 = np.random.randn()
b = np.random.randn()

def perceptron(x1,x2, w1, w2, b):

 z = (w1 * x1) + (w2 * x2) + b

 return sigmoid(z)

def get_cost_slope(b,a):
 """
 b = predicted value
 a = actual value
 """

 sqrerror = (b - a) ** 2
 slope = 2 * (b-a)

 return sqrerror, slope

share|improve this question

edited Mar 28 at 22:03

Sid

asked Mar 28 at 21:52

SidSid

4344 bronze badges

share|improve this question

edited Mar 28 at 22:03

Sid

asked Mar 28 at 21:52

SidSid

4344 bronze badges

asked Mar 28 at 21:52

SidSid

4344 bronze badges

asked Mar 28 at 21:52

SidSid

4344 bronze badges

1 Answer
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2

You need to create a method which would backpropagate through the perceptron and optimize the weights.

def optimize( a , b ):

 sqrerror = (b - a) ** 2
 cost_deriv = 2 * (b-a)

 sigmoid_deriv = z * ( 1 - z ) # derivative of sigmoid function

 learning_rate = 0.001 # Used to scale the gradients

 w1 -= ( cost_deriv * sigmoid_deriv * x1 ) * learning_rate # Gradient Descent update rule
 w2 -= ( cost_deriv * sigmoid_deriv * x2 ) * learning_rate
 b -= ( cost_deriv * sigmoid_deriv ) * learning_rate

Since ,

Where $J$ is the cost function.

share|improve this answer

answered Mar 29 at 4:02

Shubham PanchalShubham Panchal

1,76222 gold badges22 silver badges1717 bronze badges

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Awesome! That explains a lot :) thank you!
  
  – Sid
  Mar 29 at 11:02
  

  
  
  
  

add a comment
 | 

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2

You need to create a method which would backpropagate through the perceptron and optimize the weights.

def optimize( a , b ):

 sqrerror = (b - a) ** 2
 cost_deriv = 2 * (b-a)

 sigmoid_deriv = z * ( 1 - z ) # derivative of sigmoid function

 learning_rate = 0.001 # Used to scale the gradients

 w1 -= ( cost_deriv * sigmoid_deriv * x1 ) * learning_rate # Gradient Descent update rule
 w2 -= ( cost_deriv * sigmoid_deriv * x2 ) * learning_rate
 b -= ( cost_deriv * sigmoid_deriv ) * learning_rate

Since ,

Where $J$ is the cost function.

share|improve this answer

answered Mar 29 at 4:02

Shubham PanchalShubham Panchal

1,76222 gold badges22 silver badges1717 bronze badges

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Awesome! That explains a lot :) thank you!
  
  – Sid
  Mar 29 at 11:02
  

  
  
  
  

add a comment
 | 

2

You need to create a method which would backpropagate through the perceptron and optimize the weights.

def optimize( a , b ):

 sqrerror = (b - a) ** 2
 cost_deriv = 2 * (b-a)

 sigmoid_deriv = z * ( 1 - z ) # derivative of sigmoid function

 learning_rate = 0.001 # Used to scale the gradients

 w1 -= ( cost_deriv * sigmoid_deriv * x1 ) * learning_rate # Gradient Descent update rule
 w2 -= ( cost_deriv * sigmoid_deriv * x2 ) * learning_rate
 b -= ( cost_deriv * sigmoid_deriv ) * learning_rate

Since ,

Where $J$ is the cost function.

share|improve this answer

answered Mar 29 at 4:02

Shubham PanchalShubham Panchal

1,76222 gold badges22 silver badges1717 bronze badges

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Awesome! That explains a lot :) thank you!
  
  – Sid
  Mar 29 at 11:02
  

  
  
  
  

add a comment
 | 

You need to create a method which would backpropagate through the perceptron and optimize the weights.

def optimize( a , b ):

 sqrerror = (b - a) ** 2
 cost_deriv = 2 * (b-a)

 sigmoid_deriv = z * ( 1 - z ) # derivative of sigmoid function

 learning_rate = 0.001 # Used to scale the gradients

 w1 -= ( cost_deriv * sigmoid_deriv * x1 ) * learning_rate # Gradient Descent update rule
 w2 -= ( cost_deriv * sigmoid_deriv * x2 ) * learning_rate
 b -= ( cost_deriv * sigmoid_deriv ) * learning_rate

Since ,

Where $J$ is the cost function.

share|improve this answer

answered Mar 29 at 4:02

Shubham PanchalShubham Panchal

1,76222 gold badges22 silver badges1717 bronze badges

def optimize( a , b ):

 sqrerror = (b - a) ** 2
 cost_deriv = 2 * (b-a)

 sigmoid_deriv = z * ( 1 - z ) # derivative of sigmoid function

 learning_rate = 0.001 # Used to scale the gradients

 w1 -= ( cost_deriv * sigmoid_deriv * x1 ) * learning_rate # Gradient Descent update rule
 w2 -= ( cost_deriv * sigmoid_deriv * x2 ) * learning_rate
 b -= ( cost_deriv * sigmoid_deriv ) * learning_rate

share|improve this answer

answered Mar 29 at 4:02

Shubham PanchalShubham Panchal

1,76222 gold badges22 silver badges1717 bronze badges

answered Mar 29 at 4:02

Shubham PanchalShubham Panchal

1,76222 gold badges22 silver badges1717 bronze badges

answered Mar 29 at 4:02

Shubham PanchalShubham Panchal

1,76222 gold badges22 silver badges1717 bronze badges