머신러닝 - Deep Learning from scratch2019년 3월 14일

M.L (p.112)

import numpy as np

y = [0.1, 0.05, 0.6, 0.0, 0.05, 0.1, 0.0, 0.1, 0.0, 0.0]
t = [0,0,1,0,0,0,0,0,0,0]

def mean_squared_error(y,t):
    return 0.5 * np.sum((y - t) ** 2)

print(mean_squared_error(np.array(y),np.array(t)))

y = [0.1, 0.05, 0.1, 0.0, 0.05, 0.1, 0.0, 0.6, 0.0, 0.0]

print(mean_squared_error(np.array(y),np.array(t)))

import numpy as np

y = [0.1, 0.05, 0.6, 0.0, 0.05, 0.1, 0.0, 0.1, 0.0, 0.0]

t = [0,0,1,0,0,0,0,0,0,0]

def mean_squared_error(y,t):

return 0.5 * np.sum((y - t) ** 2)

print(mean_squared_error(np.array(y),np.array(t)))

y = [0.1, 0.05, 0.1, 0.0, 0.05, 0.1, 0.0, 0.6, 0.0, 0.0]

print(mean_squared_error(np.array(y),np.array(t)))

mean squared error로 신경망을 학습시키는 방법으로 그 값이 작을수록 Error가 적다는 뜻으로 해석할 수 있다.

import numpy as np

def cross_entropy_error(y,t):
    delta = 1e-7
    return -np.sum(t * np.log(y+delta))

t = [0,0,1,0,0,0,0,0,0,0]
y = [0.1, 0.05, 0.6, 0.0, 0.05, 0.1, 0.0, 0.1, 0.0, 0.0]
d = cross_entropy_error(np.array(y),np.array(t))
print(d)

y = [0.1, 0.05, 0.1, 0.0, 0.05, 0.1, 0.0, 0.6, 0.0, 0.0]
d = cross_entropy_error(np.array(y),np.array(t))
print(d)

import numpy as np

def cross_entropy_error(y,t):

delta = 1e-7

return -np.sum(t * np.log(y+delta))

t = [0,0,1,0,0,0,0,0,0,0]

y = [0.1, 0.05, 0.6, 0.0, 0.05, 0.1, 0.0, 0.1, 0.0, 0.0]

d = cross_entropy_error(np.array(y),np.array(t))

print(d)

y = [0.1, 0.05, 0.1, 0.0, 0.05, 0.1, 0.0, 0.6, 0.0, 0.0]

d = cross_entropy_error(np.array(y),np.array(t))

print(d)

다음 코드는 cross entropy error로 위의 함수이며 p(x)…

머신러닝 - Deep Learning from scratch2019년 3월 14일

M.L (p.105)

import numpy as np

x = np.array([[0.1, 0.8, 0.4], [0.3, 0.1, 0.6],
              [0.2, 0.5, 0.3], [0.8, 0.1, 0.1]])
print(x)
print(x.shape)
y = np.argmax(x, axis=1)
print(y)
y = np.argmax(x, axis=0)
print(y)

import numpy as np

x = np.array([[0.1, 0.8, 0.4], [0.3, 0.1, 0.6],

[0.2, 0.5, 0.3], [0.8, 0.1, 0.1]])

print(x)

print(x.shape)

y = np.argmax(x, axis=1)

print(y)

y = np.argmax(x, axis=0)

print(y)

np.argmax() 함수는 axis = 값에 따라 그 차원에 해당하는 값 중 최고 값을 return 하는 함수로 신경망에서는 softmax에서 가장 확률이 높은 값이 어떤 건지…

머신러닝 - Deep Learning from scratch2019년 3월 14일

M.L code(p.96) forward neural network

import sys,os
sys.path.append(os.pardir)
import numpy as np
from mnist import load_mnist
from PIL import Image
import matplotlib.pyplot as plt
from p88func import *
import pickle

(x_train, t_train), (x_test, t_test) = load_mnist(flatten=True, normalize=False)

def get_data():
    (x_train, t_train),(x_test,t_test) = load_mnist(normalize=True, flatten=True, one_hot_label = False)
    return x_test, t_test

def init_network():
    with open("sample_weight.pkl",'rb') as f:
        network = pickle.load(f)

    return network

def predict(network,x):
    W1,W2,W3 = network['W1'],network['W2'],network['W3']
    b1,b2,b3 = network['b1'],network['b2'],network['b3']

    a1 = np.dot(x,W1) + b1
    z1 = sigmoid(a1)
    a2 = np.dot(z1,W2) + b2
    z2 = sigmoid(a2)
    a3 = np.dot(z2,W3) + b3
    y = softmax(a3)

    return y

x,t = get_data()
network = init_network()

accuracy_cnt = 0
for i in range(len(x)):
    y = predict(network, x[i])
    p = np.argmax(y)
    if p == t[i]:
        accuracy_cnt += 1

print("Accuracy : " + str(float(accuracy_cnt) / len(x)))

import sys,os

sys.path.append(os.pardir)

import numpy as np

from mnist import load_mnist

from PIL import Image

import matplotlib.pyplot as plt

from p88func import *

import pickle

(x_train, t_train), (x_test, t_test) = load_mnist(flatten=True, normalize=False)

def get_data():

(x_train, t_train),(x_test,t_test) = load_mnist(normalize=True, flatten=True, one_hot_label = False)

return x_test, t_test

def init_network():

with open("sample_weight.pkl",'rb') as f:

network = pickle.load(f)

return network

def predict(network,x):

W1,W2,W3 = network['W1'],network['W2'],network['W3']

b1,b2,b3 = network['b1'],network['b2'],network['b3']

a1 = np.dot(x,W1) + b1

z1 = sigmoid(a1)

a2 = np.dot(z1,W2) + b2

z2 = sigmoid(a2)

a3 = np.dot(z2,W3) + b3

y = softmax(a3)

return y

x,t = get_data()

network = init_network()

accuracy_cnt = 0

for i in range(len(x)):

y = predict(network, x[i])

p = np.argmax(y)

if p == t[i]:

accuracy_cnt += 1

print("Accuracy : " + str(float(accuracy_cnt) / len(x)))

third layer을 통해 약 93%의 정확도를 내고 있다.

머신러닝 - Deep Learning from scratch2019년 3월 14일

M.L code(p.92)

softmax function 분모의 지수함수들을 더한 값들과 분자의 특정 지수함수의 값으로 나타내는 함수이며 그 합이 1인 확률함수적인 성질을 가져서 신경망의 답을 구현해낼때 많이 사용하는 함수다.

import numpy as np

def softmax(a):
    exp_a = np.exp(a)
    sum_exp_a = np.sum(exp_a)
    y = exp_a / sum_exp_a
    return y

a = np.array([[0.3, 2.9, 4.0]])
y = softmax(a)
print(y)

import numpy as np

def softmax(a):

exp_a = np.exp(a)

sum_exp_a = np.sum(exp_a)

y = exp_a / sum_exp_a

return y

a = np.array([[0.3, 2.9, 4.0]])

y = softmax(a)

print(y)

…

머신러닝 - Deep Learning from scratch2019년 3월 13일

M.L code(p.89)

import numpy as np
from p88func import *

def init_network():
    network = {}
    network['W1'] = np.array([[0.1,0.3,0.5], [0.2,0.4,0.6]])
    network['b1'] = np.array([0.1,0.2,0.3])
    network['W2'] = np.array([[0.1,0.4], [0.2,0.5], [0.3,0.6]])
    network['b2'] = np.array([0.1,0.2])
    network['W3'] = np.array([[0.1,0.3],[0.2,0.4]])
    network['b3'] = np.array([0.1,0.2])

    return network

def forward(network, x):
    W1,W2,W3 = network['W1'], network['W2'], network['W3']
    b1,b2,b3 = network['b1'], network['b2'], network['b3']

    a1 = np.dot(x,W1) + b1
    z1 = sigmoid(a1)
    a2 = np.dot(z1,W2) + b2
    z2 = sigmoid(a2)
    a3 = np.dot(z2,W3) + b3
    y = identity_function(a3)

    return y

network = init_network()
x = np.array([1.0, 0.5])
y = forward(network,x)
print(y)

import numpy as np

from p88func import *

def init_network():

network = {}

network['W1'] = np.array([[0.1,0.3,0.5], [0.2,0.4,0.6]])

network['b1'] = np.array([0.1,0.2,0.3])

network['W2'] = np.array([[0.1,0.4], [0.2,0.5], [0.3,0.6]])

network['b2'] = np.array([0.1,0.2])

network['W3'] = np.array([[0.1,0.3],[0.2,0.4]])

network['b3'] = np.array([0.1,0.2])

return network

def forward(network, x):

W1,W2,W3 = network['W1'], network['W2'], network['W3']

b1,b2,b3 = network['b1'], network['b2'], network['b3']

a1 = np.dot(x,W1) + b1

z1 = sigmoid(a1)

a2 = np.dot(z1,W2) + b2

z2 = sigmoid(a2)

a3 = np.dot(z2,W3) + b3

y = identity_function(a3)

return y

network = init_network()

x = np.array([1.0, 0.5])

y = forward(network,x)

print(y)

third layer 구현 정리

머신러닝 - Deep Learning from scratch2019년 3월 13일

M.L code(p.85)

#p85 - p88
import numpy as np
from p69 import sigmoid
#identity function def
def identity_function(x):
    return x

# first layer
X = np.array([1.0, 0.5])
W1 = np.array([[0.1, 0.3, 0.5], [0.2,0.4,0.6]])
B1 = np.array([0.1, 0.2, 0.3])

print(X.shape)
print(W1.shape)
print(B1.shape)

A1 = np.dot(X,W1) + B1
print(A1)
Z1 = sigmoid(A1)
print(Z1)

# second layer
W2 = np.array([[0.1,0.4], [0.2,0.5], [0.3,0.6]])
B2 = np.array([0.1, 0.2])

print(Z1.shape)
print(W2.shape)
print(B2.shape)

A2 = np.dot(Z1,W2) + B2
print(A2)
Z2 = sigmoid(A2)
print(Z2)

W3 = np.array([[0.1, 0.3], [0.2,0.4]])
B3 = np.array([0.1,0.2])

A3 = np.dot(Z2,W3) + B3
print(identity_function(A3))

#p85 - p88

import numpy as np

from p69 import sigmoid

#identity function def

def identity_function(x):

return x

# first layer

X = np.array([1.0, 0.5])

W1 = np.array([[0.1, 0.3, 0.5], [0.2,0.4,0.6]])

B1 = np.array([0.1, 0.2, 0.3])

print(X.shape)

print(W1.shape)

print(B1.shape)

A1 = np.dot(X,W1) + B1

print(A1)

Z1 = sigmoid(A1)

print(Z1)

# second layer

W2 = np.array([[0.1,0.4], [0.2,0.5], [0.3,0.6]])

B2 = np.array([0.1, 0.2])

print(Z1.shape)

print(W2.shape)

print(B2.shape)

A2 = np.dot(Z1,W2) + B2

print(A2)

Z2 = sigmoid(A2)

print(Z2)

W3 = np.array([[0.1, 0.3], [0.2,0.4]])

B3 = np.array([0.1,0.2])

A3 = np.dot(Z2,W3) + B3

print(identity_function(A3))

third layer neural networks

머신러닝 - Deep Learning from scratch2019년 3월 13일

M.L code(p.77)

#p77 - p82
import numpy as np

A = np.array([1,2,3,4])
print(A)
print(np.ndim(A))
print(np.shape(A))
print(A.shape[0])

B = np.array([[1,2], [3,4], [5,6]])
print(B)
print(np.ndim(B))
print(np.shape(B))

A = np.array([[1,2], [3,4]])
print(A.shape)
B = np.array([[5,6], [7,8]])
print(B.shape)
print(np.dot(A,B))

A = np.array([[1,2,3], [4,5,6]])
print(A.shape)
B = np.array([[1,2], [3,4], [5,6]])
print(B.shape)
print(np.dot(A,B))

A = np.array([[1,2], [3,4], [5,6]])
print(A.shape)
B = np.array([7,8])
print(B.shape)
print(np.dot(A,B))

# 신경망행렬곱

X = np.array([1,2])
print(X.shape)

W = np.array([[1,3,5],[2,4,6]])
print(W.shape)
Y = np.dot(X,W)
print(Y)
print(Y.shape)

#p77 - p82

import numpy as np

A = np.array([1,2,3,4])

print(A)

print(np.ndim(A))

print(np.shape(A))

print(A.shape[0])

B = np.array([[1,2], [3,4], [5,6]])

print(B)

print(np.ndim(B))

print(np.shape(B))

A = np.array([[1,2], [3,4]])

print(A.shape)

B = np.array([[5,6], [7,8]])

print(B.shape)

print(np.dot(A,B))

A = np.array([[1,2,3], [4,5,6]])

print(A.shape)

B = np.array([[1,2], [3,4], [5,6]])

print(B.shape)

print(np.dot(A,B))

A = np.array([[1,2], [3,4], [5,6]])

print(A.shape)

B = np.array([7,8])

print(B.shape)

print(np.dot(A,B))

# 신경망행렬곱

X = np.array([1,2])

print(X.shape)

W = np.array([[1,3,5],[2,4,6]])

print(W.shape)

Y = np.dot(X,W)

print(Y)

print(Y.shape)

머신러닝 - Deep Learning from scratch2019년 3월 13일

M.L code(p.69)

import numpy as np
import matplotlib.pyplot as plt

def step_function(x):
    return np.array(x > 0, dtype=np.int)

x = np.array([-1.0, 1.0, 2.0])
print(x)
y = x > 0
print(y)
y = y.astype(np.int)
print(y)

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

x = np.array([-1.0,1.0,2.0])
print(sigmoid(x))

def relu(x):
    return np.maximum(0,x)

x = np.arange(-5.0,5.0,0.1)
y = relu(x)
plt.plot(x,y)
plt.ylim(-0.1,1.1)
plt.show()

import numpy as np

import matplotlib.pyplot as plt

def step_function(x):

return np.array(x > 0, dtype=np.int)

x = np.array([-1.0, 1.0, 2.0])

print(x)

y = x > 0

print(y)

y = y.astype(np.int)

print(y)

def sigmoid(x):

return 1 / (1 + np.exp(-x))

x = np.array([-1.0,1.0,2.0])

print(sigmoid(x))

def relu(x):

return np.maximum(0,x)

x = np.arange(-5.0,5.0,0.1)

y = relu(x)

plt.plot(x,y)

plt.ylim(-0.1,1.1)

plt.show()

step function 그래프sigmoid function 그래프 Relu function 그래프

머신러닝 - Deep Learning from scratch2019년 3월 13일

M.L code(p.53)

# p51 ~ p59

import numpy as np
import  matplotlib.pyplot as plt

def AND(x1,x2):
    x = np.array([x1,x2])
    w = np.array([0.5,0.5])
    b = -0.7
    tmp = np.sum(w*x) + b
    if tmp <= 0:
        return 0
    elif tmp > 0:
        return 1

def NAND(x1,x2):
    x = np.array([x1,x2])
    w = np.array([-0.5,-0.5])
    b = 0.7
    tmp = np.sum(w*x) + b
    if tmp <= 0:
        return 0
    elif tmp > 0:
        return 1

def OR(x1,x2):
    x = np.array([x1,x2])
    w = np.array([0.5,0.5])
    b = -0.3
    tmp = np.sum(w*x) + b
    if tmp <= 0:
        return 0
    elif tmp > 0:
        return 1

def XOR(x1,x2):
    s1 = NAND(x1,x2)
    s2 = OR(x1,x2)
    y = AND(s1,s2)
    return y

print(XOR(0,0))
print(XOR(1,0))
print(XOR(0,1))
print(XOR(1,1))

# p51 ~ p59

import numpy as np

import matplotlib.pyplot as plt

def AND(x1,x2):

x = np.array([x1,x2])

w = np.array([0.5,0.5])

b = -0.7

tmp = np.sum(w*x) + b

if tmp <= 0:

return 0

elif tmp > 0:

return 1

def NAND(x1,x2):

x = np.array([x1,x2])

w = np.array([-0.5,-0.5])

b = 0.7

tmp = np.sum(w*x) + b

if tmp <= 0:

return 0

elif tmp > 0:

return 1

def OR(x1,x2):

x = np.array([x1,x2])

w = np.array([0.5,0.5])

b = -0.3

tmp = np.sum(w*x) + b

if tmp <= 0:

return 0

elif tmp > 0:

return 1

def XOR(x1,x2):

s1 = NAND(x1,x2)

s2 = OR(x1,x2)

y = AND(s1,s2)

return y

print(XOR(0,0))

print(XOR(1,0))

print(XOR(0,1))

print(XOR(1,1))

단층 퍼셉트론과 다층 퍼셉트론 (XOR 연산자)