LSTM拟合正弦曲线代码（转载）

于 2019-11-19 19:39:43 发布
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原文链接：https://www.cnblogs.com/pinking/p/9362966.html
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关于LSTM给大家推荐一篇讲解的十分好的博文：

难以置信！LSTM和GRU的解析从未如此清晰（动图+视频）

 https://blog.youkuaiyun.com/dQCFKyQDXYm3F8rB0/article/details/82922386

import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt
  
BATCH_START = 0 #建立 batch data 时候的 index
TIME_STEPS = 20 # backpropagation through time 的time_steps
BATCH_SIZE = 50
INPUT_SIZE = 1 # x数据输入size
OUTPUT_SIZE = 1 # cos数据输出 size
CELL_SIZE = 10 # RNN的 hidden unit size
LR = 0.006  # learning rate
  
# 定义一个生成数据的 get_batch function:
def get_batch():
    #global BATCH_START, TIME_STEPS
    # xs shape (50batch, 20steps)
    xs = np.arange(BATCH_START, BATCH_START+TIME_STEPS*BATCH_SIZE).reshape((BATCH_SIZE, TIME_STEPS)) / (10*np.pi)
    res = np.cos(xs)
    # returned  xs and res: shape (batch, step, input)
    return [xs[:, :, np.newaxis], res[:, :, np.newaxis]]
  
# 定义 LSTMRNN 的主体结构
class LSTMRNN(object):
    def __init__(self, n_steps, input_size, output_size, cell_size, batch_size):
        self.n_steps = n_steps
        self.input_size = input_size
        self.output_size = output_size
        self.cell_size = cell_size
        self.batch_size = batch_size
        with tf.name_scope('inputs'):
            self.xs = tf.placeholder(tf.float32, [None, n_steps, input_size], name='xs')
            self.ys = tf.placeholder(tf.float32, [None, n_steps, output_size], name='ys')
        with tf.variable_scope('in_hidden'):
            self.add_input_layer()
        with tf.variable_scope('LSTM_cell'):
            self.add_cell()
        with tf.variable_scope('out_hidden'):
            self.add_output_layer()
        with tf.name_scope('cost'):
            self.compute_cost()
        with tf.name_scope('train'):
            self.train_op = tf.train.AdamOptimizer(LR).minimize(self.cost)
  
    # 设置 add_input_layer 功能, 添加 input_layer:
    def add_input_layer(self, ):
        l_in_x = tf.reshape(self.xs, [-1, self.input_size], name='2_2D')  # (batch*n_step, in_size)
        # Ws (in_size, cell_size)
        Ws_in = self._weight_variable([self.input_size, self.cell_size])
        # bs (cell_size, )
        bs_in = self._bias_variable([self.cell_size, ])
        # l_in_y = (batch * n_steps, cell_size)
        with tf.name_scope('Wx_plus_b'):
            l_in_y = tf.matmul(l_in_x, Ws_in) + bs_in
        # reshape l_in_y ==> (batch, n_steps, cell_size)
        self.l_in_y = tf.reshape(l_in_y, [-1, self.n_steps, self.cell_size], name='2_3D')
  
    # 设置 add_cell 功能, 添加 cell, 注意这里的 self.cell_init_state,
    #  因为我们在 training 的时候, 这个地方要特别说明.
    def add_cell(self):
        lstm_cell = tf.contrib.rnn.BasicLSTMCell(self.cell_size, forget_bias=1.0, state_is_tuple=True)
        with tf.name_scope('initial_state'):
            self.cell_init_state = lstm_cell.zero_state(self.batch_size, dtype=tf.float32)
        self.cell_outputs, self.cell_final_state = tf.nn.dynamic_rnn(lstm_cell, 
                                                                     self.l_in_y,
                                                                     initial_state=self.cell_init_state,
                                                                     time_major=False)
  
    # 设置 add_output_layer 功能, 添加 output_layer:
    def add_output_layer(self):
        # shape = (batch * steps, cell_size)
        l_out_x = tf.reshape(self.cell_outputs, [-1, self.cell_size], name='2_2D')
        Ws_out = self._weight_variable([self.cell_size, self.output_size])
        bs_out = self._bias_variable([self.output_size, ])
        # shape = (batch * steps, output_size)
        with tf.name_scope('Wx_plus_b'):
            self.pred = tf.matmul(l_out_x, Ws_out) + bs_out
  
    # 添加 RNN 中剩下的部分:
    def compute_cost(self):
        losses = tf.contrib.legacy_seq2seq.sequence_loss_by_example(
            [tf.reshape(self.pred, [-1], name='reshape_pred')],
            [tf.reshape(self.ys, [-1], name='reshape_target')],
            [tf.ones([self.batch_size * self.n_steps], dtype=tf.float32)],
            average_across_timesteps=True,
            softmax_loss_function=self.ms_error,
            name='losses'
        )
        with tf.name_scope('average_cost'):
            self.cost = tf.div(
                tf.reduce_sum(losses, name='losses_sum'),
                self.batch_size,
                name='average_cost')
            tf.summary.scalar('cost', self.cost)
  
    def ms_error(self,labels, logits):
        return tf.square(tf.subtract(labels, logits))
  
    def _weight_variable(self, shape, name='weights'):
        initializer = tf.random_normal_initializer(mean=0., stddev=1., )
        return tf.get_variable(shape=shape, initializer=initializer, name=name)
  
    def _bias_variable(self, shape, name='biases'):
        initializer = tf.constant_initializer(0.1)
        return tf.get_variable(name=name, shape=shape, initializer=initializer)
  
  
# 训练 LSTMRNN
if __name__ == '__main__':
     
    # 搭建 LSTMRNN 模型
    model = LSTMRNN(TIME_STEPS, INPUT_SIZE, OUTPUT_SIZE, CELL_SIZE, BATCH_SIZE)
    sess = tf.Session()
    saver=tf.train.Saver(max_to_keep=3)
    sess.run(tf.global_variables_initializer())  
    t = 0   
    if(t == 1):
        model_file=tf.train.latest_checkpoint('model/')
        saver.restore(sess,model_file )
        xs, res = get_batch()  # 提取 batch data
        feed_dict = {model.xs: xs}
        pred = sess.run( model.pred,feed_dict=feed_dict)
        xs.shape = (-1,1)
        res.shape = (-1, 1)
        pred.shape = (-1, 1)
        print(xs.shape,res.shape,pred.shape)
        plt.figure()
        plt.plot(xs,res,'-r')
        plt.plot(xs,pred,'--g')        
        plt.show()
    else: 
        # matplotlib可视化
        plt.ion()  # 设置连续 plot
        plt.show()     
        # 训练多次
        for i in range(2500):
            xs, res = get_batch()  # 提取 batch data
            # 初始化 data
            feed_dict = {
                model.xs: xs,
                model.ys: res,
            }           
            # 训练
            _, cost, state, pred = sess.run(
                [model.train_op, model.cost, model.cell_final_state, model.pred],
                feed_dict=feed_dict)
      
            # plotting
            x = xs.reshape(-1,1)
            r = res.reshape(-1, 1)
            p = pred.reshape(-1, 1)
            plt.clf()
            plt.plot(x, r, 'r', x, p, 'b--')
            plt.ylim((-1.2, 1.2))
            plt.draw()
            plt.pause(0.3)  # 每 0.3 s 刷新一次
      
            # 打印 cost 结果
            if i % 20 == 0:
                saver.save(sess, "model/lstem_text.ckpt",global_step=i)#
                print('cost: ', round(cost, 4))

x值较小的点先收敛，x值大的收敛速度很慢。其原因主要是BPTT的求导过程，对于时间靠前的梯度下降快

将网络结构改为双向循环神经网络可以改善这个问题。

def add_cell(self):
        lstm_cell = tf.contrib.rnn.BasicLSTMCell(self.cell_size, forget_bias=1.0, state_is_tuple=True)
        lstm_cell = tf.contrib.rnn.MultiRNNCell([lstm_cell],1)
        with tf.name_scope('initial_state'):
            self.cell_init_state = lstm_cell.zero_state(self.batch_size, dtype=tf.float32)
        self.cell_outputs, self.cell_final_state = tf.nn.dynamic_rnn(lstm_cell, 
                                                                     self.l_in_y,
                                                                     initial_state=self.cell_init_state,
                                                                     time_major=False)

对于分类问题，其实和回归是一样的，假设在上面的正弦函数的基础上，若y大于0标记为1，y小于0标记为0，则输出变成了一个n_class（n个类别）的向量，本例中两个维度分别代表标记为0的概率和标记为1的概率。

需要修改的地方为：

首先是数据产生函数，添加一个打标签的过程：

# 定义一个生成数据的 get_batch function:
def get_batch():
    #global BATCH_START, TIME_STEPS
    # xs shape (50batch, 20steps)
    xs = np.arange(BATCH_START, BATCH_START+TIME_STEPS*BATCH_SIZE).reshape((BATCH_SIZE, TIME_STEPS)) / (200*np.pi)
    res = np.where(np.cos(4*xs)>=0,0,1).tolist()
    for i in range(BATCH_SIZE):
        for j in range(TIME_STEPS):           
            res[i][j] = [0,1] if res[i][j] == 1 else [1,0]
    # returned  xs and res: shape (batch, step, input/output)
    return [xs[:, :, np.newaxis], np.array(res)]

然后修改损失函数，回归问题就不能用最小二乘的损失了，可以采用交叉熵损失函数：

def compute_cost(self):
        self.cost = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(labels = self.ys,logits = self.pred))

 

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