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cnn_with_batch_norm.py
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#!/usr/bin/env python2
# -*- coding: utf-8 -*-
"""
Created on Mon Jun 11 16:35:19 2018
@author: alok
"""
#!/usr/bin/env python2
# -*- coding: utf-8 -*-
"""
Created on Sun Jun 10 21:37:02 2018
@author: alok
"""
#!/usr/bin/env python2
# -*- coding: utf-8 -*-
"""
Created on Sun Jun 10 18:42:01 2018
@author: alok
"""
from datetime import datetime
import numpy as np
import matplotlib.pyplot as plt
from tensorflow.examples.tutorials.mnist import input_data
mnist = input_data.read_data_sets("MNIST_data/")
train_x = mnist.train.images
train_y = mnist.train.labels
train_x = train_x.reshape(55000,28,28)
train_x = train_x.reshape((55000,28,28,1))
def zero_pad(X, pad):
X_pad = np.pad(X,((0,0),(pad,pad),(pad,pad),(0,0)),'constant',constant_values=(1,1))
return X_pad
def conv_single_step(a_slice_prev, W, b):
s = a_slice_prev*W
Z = np.sum(s)
Z = Z+b
return Z
def conv_forward(A_prev, W, b, hparameters):
(m, n_H_prev, n_W_prev, n_C_prev) = A_prev.shape
(f, f, n_C_prev, n_C) = W.shape
stride = hparameters['stride']
pad = hparameters['pad']
n_H =int((n_H_prev+2*pad -f)/stride + 1)
n_W = int((n_W_prev+2*pad-f)/stride + 1)
Z = np.zeros((m,n_H,n_W,n_C))
A_prev_pad = zero_pad(A_prev,pad)
for i in range(m): # loop over the batch of training examples
a_prev_pad = A_prev_pad[i]
for h in range(n_H): # loop over vertical axis of the output volume
for w in range(n_W): # loop over horizontal axis of the output volume
for c in range(n_C): # loop over channels (= #filters) of the output volume
# Find the corners of the current "slice"
vert_start = h*stride
vert_end = vert_start+f
horiz_start = w*stride
horiz_end = horiz_start+f
a_slice_prev = a_prev_pad[vert_start:vert_end,horiz_start:horiz_end,:]
Z[i, h, w, c] = conv_single_step(a_slice_prev,W[:,:,:,c],b[:,:,:,c])
assert(Z.shape == (m, n_H, n_W, n_C))
cache = (A_prev, W, b, hparameters)
return Z, cache
def pool_forward(A_prev, hparameters, mode = "max"):
(m, n_H_prev, n_W_prev, n_C_prev) = A_prev.shape
f = hparameters["f"]
stride = hparameters["stride"]
n_H = int(1 + (n_H_prev - f) / stride)
n_W = int(1 + (n_W_prev - f) / stride)
n_C = n_C_prev
A = np.zeros((m, n_H, n_W, n_C))
for i in range(m):
for h in range(n_H):
for w in range(n_W):
for c in range (n_C):
vert_start = h*stride
vert_end = vert_start+f
horiz_start = w*stride
horiz_end = horiz_start+f
a_prev_slice = A_prev[i,vert_start:vert_end,horiz_start:horiz_end,c]
if mode == "max":
A[i, h, w, c] = np.max(a_prev_slice)
elif mode == "average":
A[i, h, w, c] = np.mean(a_prev_slice)
cache = (A_prev, hparameters)
assert(A.shape == (m, n_H, n_W, n_C))
return A, cache
def batchnorm_forward(x, gamma, beta, eps):
N, D = x.shape
#step1: calculate mean
mu = 1./N * np.sum(x, axis = 0)
#step2: subtract mean vector of every trainings example
xmu = x - mu
#step3: following the lower branch - calculation denominator
sq = xmu ** 2
#step4: calculate variance
var = 1./N * np.sum(sq, axis = 0)
#step5: add eps for numerical stability, then sqrt
sqrtvar = np.sqrt(var + eps)
#step6: invert sqrtwar
ivar = 1./sqrtvar
#step7: execute normalization
xhat = xmu * ivar
#step8: Nor the two transformation steps
gammax = gamma * xhat
#step9
out = gammax + beta
#store intermediate
cache = (xhat,gamma,xmu,ivar,sqrtvar,var,eps)
return out, cache
def batchnorm_backward(dout, cache):
#unfold the variables stored in cache
xhat,gamma,xmu,ivar,sqrtvar,var,eps = cache
#get the dimensions of the input/output
N,D = dout.shape
#step9
dbeta = np.sum(dout, axis=0)
dgammax = dout
#step8
dgamma = np.sum(dgammax*xhat, axis=0)
dxhat = dgammax * gamma
#step7
divar = np.sum(dxhat*xmu, axis=0)
dxmu1 = dxhat * ivar
#step6
dsqrtvar = -1. /(sqrtvar**2) * divar
#step5
dvar = 0.5 * 1. /np.sqrt(var+eps) * dsqrtvar
#step4
dsq = 1. /N * np.ones((N,D)) * dvar
#step3
dxmu2 = 2 * xmu * dsq
#step2
dx1 = (dxmu1 + dxmu2)
dmu = -1 * np.sum(dxmu1+dxmu2, axis=0)
#step1
dx2 = 1. /N * np.ones((N,D)) * dmu
#step0
dx = dx1 + dx2
return dx, dgamma, dbeta
def conv_backward(dZ, cache):
(A_prev, W, b, hparameters) = cache
(m, n_H_prev, n_W_prev, n_C_prev) = A_prev.shape
(f, f, n_C_prev, n_C) = W.shape
stride = hparameters['stride']
pad = hparameters['pad']
(m, n_H, n_W, n_C) = dZ.shape
dA_prev = np.zeros_like(A_prev)
dW = np.zeros_like(W)
db = np.zeros_like(b)
A_prev_pad = zero_pad(A_prev,pad)
dA_prev_pad = zero_pad(dA_prev,pad)
for i in range(m):
a_prev_pad = A_prev_pad[i]
da_prev_pad = dA_prev_pad[i]
for h in range(n_H):
for w in range(n_W):
for c in range(n_C):
vert_start = h*stride
vert_end = vert_start+f
horiz_start = w*stride
horiz_end = horiz_start+f
a_slice = a_prev_pad[vert_start:vert_end,horiz_start:horiz_end,:]
da_prev_pad[vert_start:vert_end, horiz_start:horiz_end, :] += W[:,:,:,c] * dZ[i,h,w,c]
dW[:,:,:,c] += a_slice*dZ[i,h,w,c]
db[:,:,:,c] += dZ[i,h,w,c]
#dA_prev[i, :, :, :] = da_prev_pad[pad:-pad, pad:-pad, :]
assert(dA_prev.shape == (m, n_H_prev, n_W_prev, n_C_prev))
return dA_prev, dW, db
def create_mask_from_window(x):
mask = (x == np.max(x))
return mask
def distribute_value(dz, shape):
(n_H, n_W) = shape
average = dz
a = average*np.ones((n_H,n_W))/(n_H*n_W)
return a
def pool_backward(dA, cache, mode = "max"):
(A_prev, hparameters_pool) = cache
stride = hparameters_pool['stride']
f = hparameters_pool['f']
m, n_H_prev, n_W_prev, n_C_prev = A_prev.shape
m, n_H, n_W, n_C = dA.shape
dA_prev = np.zeros_like(A_prev)
for i in range(m): # loop over the training examples
a_prev = A_prev[i]
for h in range(n_H):
for w in range(n_W):
for c in range(n_C):
vert_start = h *stride
vert_end = vert_start + f
horiz_start = w*stride
horiz_end = horiz_start + f
if mode == "max":
a_prev_slice = a_prev[vert_start:vert_end, horiz_start:horiz_end, c]
mask = create_mask_from_window(a_prev_slice)
dA_prev[i, vert_start: vert_end, horiz_start: horiz_end, c] += mask * dA[i, h, w, c]
elif mode == "average":
da = dA[i,h,w,c]
shape = (f,f)
dA_prev[i, vert_start: vert_end, horiz_start: horiz_end, c] += distribute_value(da,shape)
assert(dA_prev.shape == A_prev.shape)
return dA_prev
A_prev = train_x[0:1000]
y = train_y[0:1000]
W = np.random.randn(3,3,1,3)/10
b = np.zeros((1,1,1,3))
W1 = np.random.randn(15,507)/10
b1 = np.zeros((15,1))
W2 = np.random.randn(10,15)/10
b2 = np.zeros((10,1))
l1,l2,l3,l4 = 0.001,0.001,0.001,0.001
loss= []
hparameters = {"pad" : 0,"stride": 1}
hparameters_pool = {"stride" : 2, "f": 2}
gamma = 1
beta = 0
eps = 0.0000001
iters = 10
for x in range(iters):
#first convoluted layer
Z, cache_conv = conv_forward(A_prev, W, b, hparameters)
zero_matrix = np.zeros_like(Z)
#apply relu activation
for i in range(len(Z)):
for j in range(len(Z[0])):
for k in range(len(Z[0][0])):
for c in range(len(Z[0][0][0])):
Z[i,j,k,c] = max(zero_matrix[i,j,k,c],Z[i,j,k,c])
#Z is activated matrix after 1st convolution
A = Z
#A_prev = A
A_pool, cache_pool = pool_forward(A, hparameters_pool,mode = 'max')
#fully connected layer
FC = A_pool.reshape((1000,A_pool[0].size))
batch_out, cache_batch = batchnorm_forward(FC,gamma,beta,eps)
Z1 = np.dot(batch_out,W1.T) + b1.T
A1 = 1/(1+np.exp(-Z1))
Z2 = np.dot(A1,W2.T) + b2.T
#A2 = 1/(1+np.exp(-Z2))
#softmax
Z2 = np.exp(Z2)
sums = np.sum(Z2,axis = 1)
sums = sums.reshape((1000,1))
A2 = Z2/sums
#one hot encoder
Y = np.eye(1000,10)[y.reshape(-1)]
loss.append(-sum(np.sum(Y*np.log(A2),axis = 1))/len(Y))
print(datetime.now().minute)
print(loss[x])
dZ2 = A2 - Y
dW2 = np.dot(dZ2.T , A1)
db2 = np.sum(dZ2,axis= 0,keepdims = True)
W2 = W2 - l3 * dW2
b2 = b2 - l3 * db2.T
dZ1 = np.dot(dZ2,W2) * ((1-A1)*A1)
dW1 = np.dot(dZ1.T , FC)
db1 = np.sum(dZ1,axis= 0,keepdims = True)
W1 = W1 - l2 * dW1
b1 = b1 - l2 * db1.T
dA0 = np.dot(dZ1,W1)
dA_batch, dgamma, dbeta = batchnorm_backward(dA0,cache_batch)
gamma = gamma - l4 * dgamma
beta = beta - l4 * dbeta
dA_batch = dA_batch.reshape((1000,13,13,3))
dA_conv = pool_backward(dA_batch ,cache_pool,mode = 'max')
dA_prev, dW, db = conv_backward(dA_conv,cache_conv)
W = W - l1 * dW
b = b - l1 * db
#calculation of accuracy
maxx = np.max(A2 ,axis=1).reshape(1000,1)
A2 = A2 - maxx
for i in range(1000):
for j in range(10):
if(A2[i][j] == 0):
A2[i][j] = 1
else:
A2[i][j] = 0
mat = np.arange(10).reshape(10,1)
p = np.dot(A2,mat)
cnt =0
for i in range(1000):
if((y[i]-p[i]) == 0):
cnt = cnt +1
acc = cnt/1000.0
print(acc)
plt.plot(np.arange(iters),loss)