softmax及python实现过程解析

相对于自适应神经网络、感知器，softmax巧妙低使用简单的方法来实现多分类问题。功能上

相对于自适应神经网络、感知器，softmax巧妙低使用简单的方法来实现多分类问题。

• 功能上，完成从N维向量到M维向量的映射
• 输出的结果范围是[0, 1]，对于一个sample的结果所有输出总和等于1
• 输出结果，可以隐含地表达该类别的概率

softmax的损失函数是采用了多分类问题中常见的交叉熵，注意经常有2个表达的形式

• 经典的交叉熵形式：L=-sum(y_right * log(y_pred))， 具体
• 简单版本是: L = -Log(y_pred),具体

这两个版本在求导过程有点不同，但是结果都是一样的，同时损失表达的意思也是相同的，因为在第一种表达形式中，当y不是

正确分类时,y_right等于0，当y是正确分类时,y_right等于1。

下面基于mnist数据做了一个多分类的实验，整体能达到85%的精度。

'''
softmax classifier for mnist 

created on 2019.9.28
author: vince
'''
import math
import logging
import numpy 
import random
import matplotlib.pyplot as plt
from tensorflow.contrib.learn.python.learn.datasets.mnist import read_data_sets
from sklearn.metrics import accuracy_score

def loss_max_right_class_prob(predictions, y):
	return -predictions[numpy.argmax(y)];

def loss_cross_entropy(predictions, y):
	return -numpy.dot(y, numpy.log(predictions));
	
'''
Softmax classifier
linear classifier 
'''
class Softmax:

	def __init__(self, iter_num = 100000, batch_size = 1):
 self.__iter_num = iter_num;
 self.__batch_size = batch_size;
	
	def train(self, train_X, train_Y):
 X = numpy.c_[train_X, numpy.ones(train_X.shape[0])];
 Y = numpy.copy(train_Y);

 self.L = [];

 #initialize parameters
 self.__weight = numpy.random.rand(X.shape[1], 10) * 2 - 1.0;
 self.__step_len = 1e-3; 

 logging.info("weight:%s" % (self.__weight));

 for iter_index in range(self.__iter_num):
 if iter_index % 1000 == 0:
 logging.info("-----iter:%s-----" % (iter_index));
 if iter_index % 100 == 0:
 l = 0;
 for i in range(0, len(X), 100):
 predictions = self.forward_pass(X[i]);
 #l += loss_max_right_class_prob(predictions, Y[i]); 
 l += loss_cross_entropy(predictions, Y[i]); 
 l /= len(X);
 self.L.append(l);

 sample_index = random.randint(0, len(X) - 1);
 logging.debug("-----select sample %s-----" % (sample_index));

 z = numpy.dot(X[sample_index], self.__weight);
 z = z - numpy.max(z);
 predictions = numpy.exp(z) / numpy.sum(numpy.exp(z));
 dw = self.__step_len * X[sample_index].reshape(-1, 1).dot((predictions - Y[sample_index]).reshape(1, -1));
# dw = self.__step_len * X[sample_index].reshape(-1, 1).dot(predictions.reshape(1, -1)); 
# dw[range(X.shape[1]), numpy.argmax(Y[sample_index])] -= X[sample_index] * self.__step_len;

 self.__weight -= dw;

 logging.debug("weight:%s" % (self.__weight));
 logging.debug("loss:%s" % (l));
 logging.info("weight:%s" % (self.__weight));
 logging.info("L:%s" % (self.L));
	
	def forward_pass(self, x):
 net = numpy.dot(x, self.__weight);
 net = net - numpy.max(net);
 net = numpy.exp(net) / numpy.sum(numpy.exp(net)); 
 return net;

	def predict(self, x):
 x = numpy.append(x, 1.0);
 return self.forward_pass(x);


def main():
	logging.basicConfig(level = logging.INFO,
 format = '%(asctime)s %(filename)s[line:%(lineno)d] %(levelname)s %(message)s',
 datefmt = '%a, %d %b %Y %H:%M:%S');
 
	logging.info("trainning begin.");

	mnist = read_data_sets('../data/MNIST',one_hot=True) # MNIST_data指的是存放数据的文件夹路径，one_hot=True 为采用one_hot的编码方式编码标签

	#load data
	train_X = mnist.train.images #训练集样本
	validation_X = mnist.validation.images #验证集样本
	test_X = mnist.test.images #测试集样本
	#labels
	train_Y = mnist.train.labels #训练集标签
	validation_Y = mnist.validation.labels #验证集标签
	test_Y = mnist.test.labels #测试集标签

	classifier = Softmax();
	classifier.train(train_X, train_Y);

	logging.info("trainning end. predict begin.");

	test_predict = numpy.array([]);
	test_right = numpy.array([]);
	for i in range(len(test_X)):
 predict_label = numpy.argmax(classifier.predict(test_X[i]));
 test_predict = numpy.append(test_predict, predict_label);
 right_label = numpy.argmax(test_Y[i]);
 test_right = numpy.append(test_right, right_label);

	logging.info("right:%s, predict:%s" % (test_right, test_predict));
	score = accuracy_score(test_right, test_predict);
	logging.info("The accruacy score is: %s "% (str(score)));


	plt.plot(classifier.L)
	plt.show();

if __name__ == "__main__":
	main();

损失函数收敛情况

Sun, 29 Sep 2019 18:08:08 softmax.py[line:104] INFO trainning end. predict begin.
Sun, 29 Sep 2019 18:08:08 softmax.py[line:114] INFO right:[7. 2. 1. ... 4. 5. 6.], predict:[7. 2. 1. ... 4. 8. 6.]
Sun, 29 Sep 2019 18:08:08 softmax.py[line:116] INFO The accruacy score is: 0.8486 

以上就是本文的全部内容，希望对大家的学习有所帮助，也希望大家多多支持脚本之家。

softmax python 实现