softmax及python实现过程解析

Python  /  管理员 发布于 7年前   232

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 2019.9.28author: 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 parametersself.__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 datatrain_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#labelstrain_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 

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