머신러닝 - Deep Learning from scratch2019년 3월 17일

M.L (p.134)

import numpy as np
from p88func import *

class simpleNet:
    def __init__(self):
        self.W = np.random.randn(2,3)

    def predict(self,x):
        return np.dot(x,self.W)

    def loss(self,x,t):
        z = self.predict(x)
        y = softmax(z)
        loss = cross_entropy_error(y,t)

        return loss
net = simpleNet()
print(net.W)
x = np.array([0.6,0.9])
p = net.predict(x)
print(p)
print(np.argmax(p))
t= np.array([0,0,1])
d = net.loss(x,t)
print(d)

def f(W):
    return net.loss(x,t)

dW = numerical_gradient(f,net.W)
print(dW)

import numpy as np

from p88func import *

class simpleNet:

def __init__(self):

self.W = np.random.randn(2,3)

def predict(self,x):

return np.dot(x,self.W)

def loss(self,x,t):

z = self.predict(x)

y = softmax(z)

loss = cross_entropy_error(y,t)

return loss

net = simpleNet()

print(net.W)

x = np.array([0.6,0.9])

p = net.predict(x)

print(p)

print(np.argmax(p))

t= np.array([0,0,1])

d = net.loss(x,t)

print(d)

def f(W):

return net.loss(x,t)

dW = numerical_gradient(f,net.W)

print(dW)

(2,3) 같은 다차원배열일 경우의 기울기를 구한다. simpleNet은 입력 값 x와 normal distribution로 초기화한 W 값(가중치) 를 행렬곱하여 (xW) 그 값을 softmax 값으로 변환하고 정답레이블(t)와…

머신러닝 - Deep Learning from scratch2019년 3월 17일

M.L (p.131)

import numpy as np
from p88func import *

def gradient_descent(f, init_x, lr=0.01, step_num=100):
    x = init_x

    for i in range(step_num):
        grad = numerical_gradient(f,x)
        x -= lr * grad

    return x

def function_2(x):
    return x[0]**2 + x[1]**2

init_x = np.array([-3.0,4.0])
d = gradient_descent(function_2,init_x=init_x,lr=0.1,step_num=100)
print(d)

init_x = np.array([-3.0,4.0])
print(gradient_descent(function_2,init_x=init_x, lr = 10.0, step_num=100))
init_x = np.array([-3.0,4.0])
print(gradient_descent(function_2,init_x=init_x, lr = 1e-10, step_num=100))

import numpy as np

from p88func import *

def gradient_descent(f, init_x, lr=0.01, step_num=100):

x = init_x

for i in range(step_num):

grad = numerical_gradient(f,x)

x -= lr * grad

return x

def function_2(x):

return x[0]**2 + x[1]**2

init_x = np.array([-3.0,4.0])

d = gradient_descent(function_2,init_x=init_x,lr=0.1,step_num=100)

print(d)

init_x = np.array([-3.0,4.0])

print(gradient_descent(function_2,init_x=init_x, lr = 10.0, step_num=100))

init_x = np.array([-3.0,4.0])

print(gradient_descent(function_2,init_x=init_x, lr = 1e-10, step_num=100))

gradient_descent method 로 경사법 수식 , (eta) 는 갱신하는 양을 나타내고 신경망에서는 이를 학습률(learning rate)라 부른다. 이 parameter는 사용자가 정의하며 learning rate * 편미분…

머신러닝 - Deep Learning from scratch2019년 3월 16일

M.L (p.127)

import numpy as np

def function_2(x):
    return x[0] ** 2 + x[1] ** 2
    # return np.sum(x**2)

def numerical_gradient(f,x):
    h = 1e-4
    grad = np.zeros_like(x)

    for idx in range(x.size):
        tmp_val = x[idx]
        x[idx] = tmp_val + h
        fxh1 = f(x)

        x[idx] = tmp_val - h
        fxh2 = f(x)

        grad[idx] = (fxh1 - fxh2) / (2*h)
        x[idx] = tmp_val
    return grad

print(numerical_gradient(function_2, np.array([3.0,4.0])))
print(numerical_gradient(function_2, np.array([0.0,2.0])))

import numpy as np

def function_2(x):

return x[0] ** 2 + x[1] ** 2

# return np.sum(x**2)

def numerical_gradient(f,x):

h = 1e-4

grad = np.zeros_like(x)

for idx in range(x.size):

tmp_val = x[idx]

x[idx] = tmp_val + h

fxh1 = f(x)

x[idx] = tmp_val - h

fxh2 = f(x)

grad[idx] = (fxh1 - fxh2) / (2*h)

x[idx] = tmp_val

return grad

print(numerical_gradient(function_2, np.array([3.0,4.0])))

print(numerical_gradient(function_2, np.array([0.0,2.0])))

편미분을 간단히 하나의 함수로 나타내기 위한 코드 function_2 = x[0]^2 + x[1]^2 식을 가지고 있고, numerical_gradient 를 보면 for문을 이용해 각 인덱스의 중앙차분을 구하여…

머신러닝 - Deep Learning from scratch2019년 3월 16일

M.L (p.125)

import numpy as np

def numerical_diff(f,x):
    h = 1e-4
    return (f(x+h) - f(x-h)) / (2*h)

def function_2(x):
    return x[0] ** 2 + x[1] ** 2
    # return np.sum(x**2)


def function_tmp1(x0):
    return x0 * x0 + 4.0 ** 2.0

A = numerical_diff(function_tmp1, 3.0)
print(A)

def function_tmp2(x1):
    return 3.0 ** 2.0 + x1 * x1

B = numerical_diff(function_tmp2,4.0)
print(B)

import numpy as np

def numerical_diff(f,x):

h = 1e-4

return (f(x+h) - f(x-h)) / (2*h)

def function_2(x):

return x[0] ** 2 + x[1] ** 2

# return np.sum(x**2)

def function_tmp1(x0):

return x0 * x0 + 4.0 ** 2.0

A = numerical_diff(function_tmp1, 3.0)

print(A)

def function_tmp2(x1):

return 3.0 ** 2.0 + x1 * x1

B = numerical_diff(function_tmp2,4.0)

print(B)

편미분 (둘 이상의 변수) 식 f(x0,x1) = x0^2 + x1^2 같은 간단한 식 구현 편미분을 구할 때는 구하려는 변수 외의 다른 변수 값은 상수로…

머신러닝 - Deep Learning from scratch2019년 3월 16일

M.L (p.121)

import numpy as np
import matplotlib.pyplot as plt

def numerical_diff(f,x):
    h = 1e-4
    return (f(x+h) - f(x-h)) / (2*h)

def function_1(x):
    return 0.01*x**2 + 0.1*x

x = np.arange(0.0, 20.0, 0.1)
y = function_1(x)
plt.xlabel("x")
plt.ylabel("f(x)")
plt.plot(x,y)
plt.show()

print(numerical_diff(function_1,5))
print(numerical_diff(function_1,10))

import numpy as np

import matplotlib.pyplot as plt

def numerical_diff(f,x):

h = 1e-4

return (f(x+h) - f(x-h)) / (2*h)

def function_1(x):

return 0.01*x**2 + 0.1*x

x = np.arange(0.0, 20.0, 0.1)

y = function_1(x)

plt.xlabel("x")

plt.ylabel("f(x)")

plt.plot(x,y)

plt.show()

print(numerical_diff(function_1,5))

print(numerical_diff(function_1,10))

경사법에서는 기울기 값을 기준으로 나아갈 방향을 정하는데 기울기 값을 미분으로 구할 수 있다. (기울기 값이 0에 가까워지는 지점이 최적 값을 나타내기때문에 ) 하지만 컴퓨터…

머신러닝 - Deep Learning from scratch2019년 3월 15일

M.L (p.116)

import sys,os
import numpy as np
sys.path.append(os.pardir)
from mnist import load_mnist

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

train_size = x_train.shape[0]
batch_size = 10
a = batch_mask = np.random.choice(train_size, batch_size)
x_batch = x_train[batch_mask]
t_batch = t_train[batch_mask]
print(a)

import sys,os

import numpy as np

sys.path.append(os.pardir)

from mnist import load_mnist

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

train_size = x_train.shape[0]

batch_size = 10

a = batch_mask = np.random.choice(train_size, batch_size)

x_batch = x_train[batch_mask]

t_batch = t_train[batch_mask]

print(a)

mini batch : 거대한 데이터셋을 다 계산해보는 건 시간적, 비용적으로 부담이 크기 때문에 적절히 어느정도 양의 데이터를 골라 그 값을 이용해 근사치를 구한다. 예를…

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)

…