CNN

2019-08-31 이민예

CNN을 Numpy로 구현

CNN

import numpy as np
from scipy import signal

def tanh(x):
    return np.tanh(x)
def d_tanh(x):
    return 1 - np.tanh(x) ** 2

def log(x):
    return 1/(1 + np.exp(-1*x))
def d_log(x):
    return log(x) * ( 1 - log(x) )

np.random.seed(598765)

#4개의 입력층 
x1 = np.array([[0,0,0],[0,0,0],[0,0,0]])
x2 = np.array([[1,1,1],[0,0,0],[0,0,0]])
x3 = np.array([[0,0,0],[1,1,1],[1,1,1]])
x4 = np.array([ [1,1,1],[1,1,1],[1,1,1]])
X = [x1,x2,x3,x4]
Y = np.array([
    [0.53],
    [0.77],
    [0.88],
    [1.1]
])

# 0. Declare Weights
w1 = np.random.randn(2,2) * 4 # 컨볼루션 필터 
w2 = np.random.randn(4,1) * 4

# 1. Declare hyper Parameters
num_epoch = 1000
learning_rate = 0.7

cost_before_train = 0
cost_after_train = 0
final_out,start_out =np.array([[]]),np.array([[]])

# ---- Cost before training ------
for i in range(len(X)):
    
    layer_1 = signal.convolve2d(X[i],w1,'valid')
    layer_1_act = tanh(layer_1) #2*2
    
    # -1 은 배열을 쭉 펴지게함. 
    layer_1_act_vec = np.expand_dims(np.reshape(layer_1_act,-1),axis=0) #1*4  
    layer_2 = layer_1_act_vec.dot(w2)
    layer_2_act = log(layer_2)   
    cost = np.square(layer_2_act- Y[i]).sum() * 0.5
    cost_before_train = cost_before_train + cost
    start_out = np.append(start_out,layer_2_act)
    
# ----- TRAINING -------
for iter in range(num_epoch):
    
    for i in range(len(X)):
    
        layer_1 = signal.convolve2d(X[i],w1,'valid')
        layer_1_act = tanh(layer_1) #2*2

        layer_1_act_vec = np.expand_dims(np.reshape(layer_1_act,-1),axis=0)
        layer_2 = layer_1_act_vec.dot(w2)
        layer_2_act = log(layer_2)

        cost = np.square(layer_2_act- Y[i]).sum() * 0.5
        #print("Current iter : ",iter , " Current train: ",i, " Current cost: ",cost,end="\r")

        grad_2_part_1 = layer_2_act- Y[i]
        grad_2_part_2 = d_log(layer_2)
        grad_2_part_3 = layer_1_act_vec
        grad_2 =   grad_2_part_3.T.dot(grad_2_part_1*grad_2_part_2)      

        grad_1_part_1 = (grad_2_part_1*grad_2_part_2).dot(w2.T)
        grad_1_part_2 = d_tanh(layer_1)
        grad_1_part_3 = X[i]

        grad_1_part_1_reshape = np.reshape(grad_1_part_1,(2,2))
        grad_1_temp_1 = grad_1_part_1_reshape * grad_1_part_2
    
        grad_1 = np.rot90(
          signal.convolve2d(grad_1_part_3, np.rot90(grad_1_temp_1, 2),'valid'),
          2)

        w2 = w2 - grad_2 * learning_rate
        w1 = w1 - grad_1 * learning_rate
        
# ---- Cost after training ------
for i in range(len(X)):
    
    layer_1 = signal.convolve2d(X[i],w1,'valid')
    layer_1_act = tanh(layer_1)

    layer_1_act_vec = np.expand_dims(np.reshape(layer_1_act,-1),axis=0)
    layer_2 = layer_1_act_vec.dot(w2)
    layer_2_act = log(layer_2)   
    cost = np.square(layer_2_act- Y[i]).sum() * 0.5
    cost_after_train = cost_after_train + cost
    final_out = np.append(final_out,layer_2_act)

    
# ----- Print Results ---
print("\nW1 :",w1, "\n\nw2 :", w2)
print("----------------")
print("Cost before Training: ",cost_before_train)
print("Cost after Training: ",cost_after_train)
print("----------------")
print("Start Out put : ", start_out)
print("Final Out put : ", final_out)
print("Ground Truth  : ", Y.T)




# -- end code --

• 왜 로테이션하는지 모르겠음 : 컨볼루션의 미분

• 학습속도 곱하는 것 : 개념 이해

• 시그모이드 미분

• 탄젠트 미분 -> 비선형함수 공부 (소프트맥스, 렐루...)

[ Reference ]

https://becominghuman.ai/only-numpy-implementing-convolutional-neural-network-using-numpy-deriving-forward-feed-and-back-458a5250d6e4

Learning Rate

http://www.ishenping.com/ArtInfo/145116.html