【python實現卷積神經網絡】損失函數的定義（均方誤差損失、交叉熵損失）

代碼來源：https://github.com/eriklindernoren/ML-From-Scratch

卷積神經網絡中卷積層Conv2D（帶stride、padding）的具體實現：https://www.cnblogs.com/xiximayou/p/12706576.html

激活函數的實現（sigmoid、softmax、tanh、relu、leakyrelu、elu、selu、softplus）：https://www.cnblogs.com/xiximayou/p/12713081.html

 

這節講解兩個基礎的損失函數的實現：

from __future__ import division
import numpy as np
from mlfromscratch.utils import accuracy_score
from mlfromscratch.deep_learning.activation_functions import Sigmoid

class Loss(object):
    def loss(self, y_true, y_pred):
        return NotImplementedError()

    def gradient(self, y, y_pred):
        raise NotImplementedError()

    def acc(self, y, y_pred):
        return 0

class SquareLoss(Loss):
    def __init__(self): pass

    def loss(self, y, y_pred):
        return 0.5 * np.power((y - y_pred), 2)

    def gradient(self, y, y_pred):
        return -(y - y_pred)

class CrossEntropy(Loss):
    def __init__(self): pass

    def loss(self, y, p):
        # Avoid division by zero
        p = np.clip(p, 1e-15, 1 - 1e-15)
        return - y * np.log(p) - (1 - y) * np.log(1 - p)

    def acc(self, y, p):
        return accuracy_score(np.argmax(y, axis=1), np.argmax(p, axis=1))

    def gradient(self, y, p):
        # Avoid division by zero
        p = np.clip(p, 1e-15, 1 - 1e-15)
        return - (y / p) + (1 - y) / (1 - p)

其中y是真實值對應的標簽，p是預測值對應的標簽。

補充：

• numpy.clip()：看個例子

  import numpy as np
  x=np.array([1,2,3,5,6,7,8,9])
  np.clip(x,3,8)
  array([3, 3, 3, 5, 6, 7, 8, 8])

這里使用到了mlfromscrach/utils/data_operation.py中的：

def accuracy_score(y_true, y_pred):
    """ Compare y_true to y_pred and return the accuracy """
    accuracy = np.sum(y_true == y_pred, axis=0) / len(y_true)
    return accuracy

用於計算准確率。