Simple Neural Network Python Code
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This document contains a Python implementation of a simple neural network that utilizes sigmoid activation and trains on binary classification data (digits 0 and 1). It includes methods for initializing weights, forward propagation, and weight updates using backpropagation. Additionally, it handles data preprocessing, such as loading images and labels, and generates a confusion matrix to evaluate the model's performance.
![File: /home/andres/Dropbox/Classes/…es/Data/SimpleNeuralNetwork.py Page 1 of 3
import matplotlib.pyplot as plt
import numpy as np
from scipy.special import expit
def sigmoid(eval):
return expit(eval)
def Neural_Training(Y01, Labels01 , eta , Epochs):
d,samplenumb = Y01.shape
# Random [-1,1] init from Haykin
WIH = 2*np.mat(np.random.rand(2*d,d)) -1.0
WHO = 2*np.mat(np.random.rand(1,2*d)) -1.0
difft = Labels01.astype(np.float64)
for i in xrange(1,Epochs):
#Get the input to the output layer
y_j_temp = sigmoid(WIH*Y01)
netk = WHO*y_j_temp
zk = sigmoid(netk)
# Creating Delta Wk
diff1 = difft - zk
tDeltaWk = eta*np.multiply(diff1,np.multiply(sigmoid(netk),1.0-sigmoid(netk)))
tDeltaWk = np.tile(tDeltaWk,(2*d,1))
DeltaWk = np.multiply( y_j_temp,tDeltaWk)
DeltaWk = np.transpose(np.sum(DeltaWk,1))
# New Weights
WHO = WHO + DeltaWk
#Creating Delta Wj
dnetj = np.multiply(y_j_temp,1.0-y_j_temp)
tprodsumk = np.multiply(np.transpose(DeltaWk),np.transpose(WHO))
tprodsumk = np.tile(tprodsumk, (1,samplenumb) )
tprodsumk = eta*np.multiply(tprodsumk,dnetj)
DeltaWj = tprodsumk * np.transpose(Y01)
# New Weights
WIH = WIH + DeltaWj
return WIH, WHO
# Number of samples
N= 60000
#Number of Epochs
Epochs = 20
#Learning Rate
eta = 0.001
# opening images for [r]eading as [b]inary
in_file = open("train-images.idx3-ubyte", "rb")
in_file.read(16)
Data = in_file.read()
in_file.close()
# Transform the data stream
X = np.fromstring(Data, dtype=np.uint8)
X = X.astype(np.float64)
X = np.mat(X)](https://image.slidesharecdn.com/simpleneuralnetwork-151116193731-lva1-app6892/85/Simple-Neural-Network-Python-Code-1-320.jpg)
![File: /home/andres/Dropbox/Classes/…es/Data/SimpleNeuralNetwork.py Page 2 of 3
X = X.reshape(N,784)
X = np.transpose(X)
# Now the labels:
in_file = open("train-labels.idx1-ubyte", "rb")
in_file.read(8)
DLabel = in_file.read()
in_file.close()
# Transform the label
Labels = np.fromstring(DLabel, dtype=np.uint8)
Labels01 = Labels[ np.logical_or(Labels[:]==0 , Labels[:]==1) ]
#Extract Data 01
X01 = X[:, Labels[ np.logical_or(Labels[:]==0 , Labels[:]==1) ] ]
dummy, N1 = X01.shape
#Mean Creation
Xmean= X01.sum(axis=1)
Xmean = (1.0/(N1*1.0))*Xmean
# Thus we create data with zero mean
X01= X01-Xmean
#Covariance
C_X = (1.0/(N1*1.0-1.0))*(X01*np.transpose(X01))
D, E = np.linalg.eigh(C_X)
idx = D.argsort()[::-1]
D = D[idx]
E = E[:,idx]
P = np.transpose(E[:,0:100])
Y01 = P*X01
# Run the Training
WIH, WHO = Neural_Training(Y01, Labels01 , eta, Epochs)
# Create the results
Results = sigmoid(WHO*sigmoid(WIH*Y01))
# Find the decisions
d,samplenumb = Y01.shape
index = np.ones(samplenumb)
Results = np.asarray(Results).reshape(-1)
# Generate the Confusion Matrix using a hard threshold half of minimum and maximum
t1 = np.max(Results[Labels01[:]==0])
t2 = np.max(Results[Labels01[:]==1])
tr = (t2-t1)/2.0
# print threshold
print tr
R11 = np.sum(index[ np.logical_and(Results[:]<tr, Labels01[:]==0 )])
R22 = np.sum(index[ np.logical_and(Results[:]>tr, Labels01[:]==1 )])
R12 = np.sum(index[ np.logical_and(Results[:]>=tr, Labels01[:]==0 ) ])
R21 = np.sum(index[ np.logical_and(Results[:]<=tr, Labels01[:]==1 ) ])
ConfusionMatrix = np.matrix([[R11 ,R12] , [R21 , R22]])
# Print the results
print "Confusion Matrix n", ConfusionMatrix](https://image.slidesharecdn.com/simpleneuralnetwork-151116193731-lva1-app6892/85/Simple-Neural-Network-Python-Code-2-320.jpg)
![File: /home/andres/Dropbox/Classes/…es/Data/SimpleNeuralNetwork.py Page 3 of 3
# Print some Labels
for i in xrange(0,15):
print("Gen Label {} = {} Real Label {}".format(i , round(Results[i],2), Labels01[i]))](https://image.slidesharecdn.com/simpleneuralnetwork-151116193731-lva1-app6892/85/Simple-Neural-Network-Python-Code-3-320.jpg)
Simple Neural Network Python Code
- 1. File: /home/andres/Dropbox/Classes/…es/Data/SimpleNeuralNetwork.py Page 1 of 3 import matplotlib.pyplot as plt import numpy as np from scipy.special import expit def sigmoid(eval): return expit(eval) def Neural_Training(Y01, Labels01 , eta , Epochs): d,samplenumb = Y01.shape # Random [-1,1] init from Haykin WIH = 2*np.mat(np.random.rand(2*d,d)) -1.0 WHO = 2*np.mat(np.random.rand(1,2*d)) -1.0 difft = Labels01.astype(np.float64) for i in xrange(1,Epochs): #Get the input to the output layer y_j_temp = sigmoid(WIH*Y01) netk = WHO*y_j_temp zk = sigmoid(netk) # Creating Delta Wk diff1 = difft - zk tDeltaWk = eta*np.multiply(diff1,np.multiply(sigmoid(netk),1.0-sigmoid(netk))) tDeltaWk = np.tile(tDeltaWk,(2*d,1)) DeltaWk = np.multiply( y_j_temp,tDeltaWk) DeltaWk = np.transpose(np.sum(DeltaWk,1)) # New Weights WHO = WHO + DeltaWk #Creating Delta Wj dnetj = np.multiply(y_j_temp,1.0-y_j_temp) tprodsumk = np.multiply(np.transpose(DeltaWk),np.transpose(WHO)) tprodsumk = np.tile(tprodsumk, (1,samplenumb) ) tprodsumk = eta*np.multiply(tprodsumk,dnetj) DeltaWj = tprodsumk * np.transpose(Y01) # New Weights WIH = WIH + DeltaWj return WIH, WHO # Number of samples N= 60000 #Number of Epochs Epochs = 20 #Learning Rate eta = 0.001 # opening images for [r]eading as [b]inary in_file = open("train-images.idx3-ubyte", "rb") in_file.read(16) Data = in_file.read() in_file.close() # Transform the data stream X = np.fromstring(Data, dtype=np.uint8) X = X.astype(np.float64) X = np.mat(X)
- 2. File: /home/andres/Dropbox/Classes/…es/Data/SimpleNeuralNetwork.py Page 2 of 3 X = X.reshape(N,784) X = np.transpose(X) # Now the labels: in_file = open("train-labels.idx1-ubyte", "rb") in_file.read(8) DLabel = in_file.read() in_file.close() # Transform the label Labels = np.fromstring(DLabel, dtype=np.uint8) Labels01 = Labels[ np.logical_or(Labels[:]==0 , Labels[:]==1) ] #Extract Data 01 X01 = X[:, Labels[ np.logical_or(Labels[:]==0 , Labels[:]==1) ] ] dummy, N1 = X01.shape #Mean Creation Xmean= X01.sum(axis=1) Xmean = (1.0/(N1*1.0))*Xmean # Thus we create data with zero mean X01= X01-Xmean #Covariance C_X = (1.0/(N1*1.0-1.0))*(X01*np.transpose(X01)) D, E = np.linalg.eigh(C_X) idx = D.argsort()[::-1] D = D[idx] E = E[:,idx] P = np.transpose(E[:,0:100]) Y01 = P*X01 # Run the Training WIH, WHO = Neural_Training(Y01, Labels01 , eta, Epochs) # Create the results Results = sigmoid(WHO*sigmoid(WIH*Y01)) # Find the decisions d,samplenumb = Y01.shape index = np.ones(samplenumb) Results = np.asarray(Results).reshape(-1) # Generate the Confusion Matrix using a hard threshold half of minimum and maximum t1 = np.max(Results[Labels01[:]==0]) t2 = np.max(Results[Labels01[:]==1]) tr = (t2-t1)/2.0 # print threshold print tr R11 = np.sum(index[ np.logical_and(Results[:]<tr, Labels01[:]==0 )]) R22 = np.sum(index[ np.logical_and(Results[:]>tr, Labels01[:]==1 )]) R12 = np.sum(index[ np.logical_and(Results[:]>=tr, Labels01[:]==0 ) ]) R21 = np.sum(index[ np.logical_and(Results[:]<=tr, Labels01[:]==1 ) ]) ConfusionMatrix = np.matrix([[R11 ,R12] , [R21 , R22]]) # Print the results print "Confusion Matrix n", ConfusionMatrix
- 3. File: /home/andres/Dropbox/Classes/…es/Data/SimpleNeuralNetwork.py Page 3 of 3 # Print some Labels for i in xrange(0,15): print("Gen Label {} = {} Real Label {}".format(i , round(Results[i],2), Labels01[i]))