softmax及python实现过程解析

'''softmax classifier for mnist created on 2019.9.28author: vince'''import mathimport loggingimport numpy import randomimport matplotlib.pyplot as pltfrom tensorflow.contrib.learn.python.learn.datasets.mnist import read_data_setsfrom sklearn.metrics import accuracy_scoredef 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 classifierlinear 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();

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