Simple Neural Network Python Code

Nov 16, 20151 like1,357 views

Here, we have a simple neural network described in my slides about neural networks... It is using simple concepts from linear algebra to encapsulate the complexities (This makes possible to even use parallel matrix multiplication and some other algorithms to make everything faster) and making everything more modular and compact. The data sets are coming from http://yann.lecun.com/exdb/mnist/.

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)

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

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]))

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The document discusses square matrices and determinants. It begins by noting that square matrices are the only matrices that can have inverses. It then presents an algorithm for calculating the inverse of a square matrix A by forming the partitioned matrix (A|I) and applying Gauss-Jordan reduction. The document also discusses determinants, defining them recursively as the sum of products of diagonal entries with signs depending on row/column position, for matrices larger than 1x1. Complexity increases exponentially with matrix size.

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This document provides an introduction to systems of linear equations and matrix operations. It defines key concepts such as matrices, matrix addition and multiplication, and transitions between different bases. It presents an example of multiplying two matrices using NumPy. The document outlines how systems of linear equations can be represented using matrices and discusses solving systems using techniques like Gauss-Jordan elimination and elementary row operations. It also introduces the concepts of homogeneous and inhomogeneous systems.

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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]))

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