深度学习笔记之循环神经网络(十)基于循环神经网络模型的简单示例

引言

本节我们将前面介绍的几种循环神经网络——$\text{RNN,LSTM,GRU}$关于实例中的一个演示，但重点并不仅在于这些模型，这里以示例的形式对$\text{One-hot}$向量重新进行认知。

文本表征：$\text{One-hot}$向量

自然语言$(\text{Natural Language})$是人类交流和思维的主要工具。例如汉语、英语都是自然语言的例子。其本质上是一种离散化的符号系统。以某一种语言为例，我们能够使用到的词语集合$\mathcal{V}$表示如下：
其中$|\mathcal{V}|$表示词语集合$\mathcal{V}$中的词语数量;${\omega }_i(i=1,2,\cdots |\mathcal{V}|)$表示某个具体词语。
$$\mathcal{V}=\{{\omega }_1,{\omega }_2,\cdots ,{\omega }_{|\mathcal{V}|}\}$$
面对的第一个问题：如何表示这些词语。我们需要将这些词语转化为机器学习模型能够识别的数字特征。因此，最初始的动机就此形成：词语以数字向量的形式表示出来——词语表征$(\text{Word Representation})$。

而$\text{One-hot}$表征$(\text{One-hot Representation})$就是其中最简单、最直接的表征方式。以上述词语集合$\mathcal{V}$为例，其内部的每个词${\omega }^{(i)}(i=1,2,\cdots ,|\mathcal{V}|)$都可以使用长度为$|\mathcal{V}|$的向量进行表示：

• 其中$i=1,2,\cdots ,|\mathcal{V}|$可表示每个词语在$\mathcal{V}$中的编号/位置信息。
• 以${\omega }^{(1)},{\omega }^{(2)}$为例，对应的$\text{One-hot}$向量分别表示为‘第$1,2$个位置’为$1$，其余位置信息均为$0$的向量。
  $$\{\begin{array}{l}{\omega }^{(1)}=\underset{\text{length}=|\mathcal{V}|}{(1,0,0,\cdots ,0{)}^T}\\ {\omega }^{(2)}=\underset{\text{length}=|\mathcal{V}|}{(0,1,0,\cdots ,0{)}^T}\end{array}$$

关于$\text{One-hot}$向量的优点：该向量与词语集合$\mathcal{V}$中的任意一个词语均存在映射关系，并且在向量转换过程中，没有存在特征信息丢失的情况。

关于$\text{One-hot}$向量的缺点：

• 每个词语的维度数量等于词语集合的长度$|\mathcal{V}|$。当词语集合$\mathcal{V}$过于庞大是，使得词语的维度数量过高，从而引发维数灾难$(\text{Curse of Dimensionality})$。
• 各维度特征之间属于离散关系，或者说：各维度特征之间不存在关联关系。
• 并且任意一个基于$\text{One-hot}$向量表示的词语${\omega }^{(i)}(i=1,2,\cdots ,|\mathcal{V}|)$均有如下性质：
  $$\sum _{j=1}^{|\mathcal{V}|}{\omega }_j^{(i)}=1;{\omega }_j^{(i)}\in \{0,1\}$$
  也就是说：各特征向量中仅有$1$位存在特征信息，而其他的$|\mathcal{V}|-1$位均是无效信息。这种表示也被称作局部表征$(\text{Local Representation})$。

而离散性质与局部表征两种缺陷导致：很难表达词语之间的相似度$(\text{Similarity})$。任意从$\mathcal{V}$中取出两个词语${\omega }^{(i)},{\omega }^{(j)}(i,j\in \{1,2,\cdots ,|\mathcal{V}|\},i\ne j)$，它们对应的内积结果$[{\omega }^{(i)}{]}^T\cdot {\omega }^{(j)}=0$恒成立。
对应的‘余弦相似度结果’$=0$,从而导致'各词语向量'之间正交，向量之间没有关联关系。

上述就是对$\text{One-hot}$的一个简单认知。但我们需要纠正一个错误认知：词语之间相似度与序列信息需要区分开。

• 相似度是词语向量用来描述词语之间关系的一个性质。它可以使用模型进行学习，但这里$\text{One-hot}$向量并没有这种性质；
• 而序列信息是模型从文本序列中学习出的信息，不否认序列信息在学习过程中与文本表征有关，但这里想说的是：即便是$\text{One-hot}$向量，它同样存在序列信息。

这里使用$\text{One-hot}$向量为例，使用循环神经网络模型对序列进行预测。

简单示例:文本序列的预测任务

文章末尾附完整代码。

数据预处理过程

生成文本数据

对应代码表示如下：

def GetTxtFile(WritePath,SeqInput,RepeatNum=500):
    """
    :param WritePath:D:\code_work\MachineLearning/FlareData.txt
    :param SeqInput:"Deep learning is to learn the internal laws and presentation levels of sample data."
    :param RepeatNum:500
    :return:FlareData.txt
    """
    with open(WritePath,"w",encoding="UTF-8") as f:
        for _ in range(RepeatNum):
            f.write(SeqInput)
            f.write("\n")
        f.close()
    return 0

对应结果返回如下：

这个句子是网上随意找的句子，并将其重复若干次作为数据集。而这里重复若干次的目的仅在于：示例中最小化特征分布的多样性。当然也可以尝试直接截取一段较长文本。
这个多样性是指：无论如何去选取其中一段文本，各字母的后续结果总是‘有限的’。这里我们更关注模型是否能够学习出序列信息，因而特征分布构建的简单一点。

遍历数据集，构建字典

这里以一个字符作为一个向量单元。首先对数据集格式进行整理，并去重$(\text{Set})$得到所有出现过的字符，并将字符与对应编号构建字典。具体代码如下：

def GetStringDict(SeqPath):

    def ReadData(SeqPath):
        Data = open(SeqPath).read().replace("\n", " ").replace("\r", " ")
        return Data

    def DelRepeat(Data):
        letters = list(set(Data))
        return letters

    def GetLetterDict(LetterList):
        IndexLetterDict = {i: j for i, j in enumerate(LetterList)}
        LetterIndexDict = {j: i for i, j in enumerate(LetterList)}
        return IndexLetterDict, LetterIndexDict

    Data = ReadData(SeqPath)
    LetterList = DelRepeat(Data)
    IndextoLetter, LettertoIndex = GetLetterDict(LetterList)

    return Data, IndextoLetter, LettertoIndex

关于映射字典的返回结果如下：

# IndextoLetter -> length:20
{0: 't', 1: 'g', 2: '.', 3: 'm', 4: 'D', 5: 'a', 6: 'w', 7: 'v', 8: 'r', 9: 'p', 10: ' ', 11: 'e', 12: 'n', 13: 'h', 14: 'o', 15: 'f', 16: 'l', 17: 's', 18: 'd', 19: 'i'}
# LettertoIndex
{'t': 0, 'g': 1, '.': 2, 'm': 3, 'D': 4, 'a': 5, 'w': 6, 'v': 7, 'r': 8, 'p': 9, ' ': 10, 'e': 11, 'n': 12, 'h': 13, 'o': 14, 'f': 15, 'l': 16, 's': 17, 'd': 18, 'i': 19}

抓取数据，创建训练样本、标签

以大小为$20$个字符串长度的窗口抓取字符数据，根据循环神经网络的描述，这里根据$20$个序列长度(时刻)的序列信息预测下一时刻的输出信息。

对应代码表示如下：
窗口大小$\text{Slide}$大小为$20$,移动步长默认为$1$

def ExtractData(Data,Slide):
    x = list()
    y = list()
    for i in range(len(Data) - Slide):
        x.append([a for a in Data[i:i+Slide]])
        y.append(Data[i+Slide])
    return x,y

对应数据中前$5$个结果表示如下：
第$1$行是原始数据信息，用于比对。

Deep learning is to learn the internal laws and presentation levels of sample data.
Token:['D', 'e', 'e', 'p', ' ', 'l', 'e', 'a', 'r', 'n', 'i', 'n', 'g', ' ', 'i', 's', ' ', 't', 'o', ' ']
Label:l
----------------------------------------------------------------------------------------------------------
Token:['e', 'e', 'p', ' ', 'l', 'e', 'a', 'r', 'n', 'i', 'n', 'g', ' ', 'i', 's', ' ', 't', 'o', ' ', 'l']
Label:e
----------------------------------------------------------------------------------------------------------
Token:['e', 'p', ' ', 'l', 'e', 'a', 'r', 'n', 'i', 'n', 'g', ' ', 'i', 's', ' ', 't', 'o', ' ', 'l', 'e']
Label:a
----------------------------------------------------------------------------------------------------------
Token:['p', ' ', 'l', 'e', 'a', 'r', 'n', 'i', 'n', 'g', ' ', 'i', 's', ' ', 't', 'o', ' ', 'l', 'e', 'a']
Label:r
----------------------------------------------------------------------------------------------------------
Token:[' ', 'l', 'e', 'a', 'r', 'n', 'i', 'n', 'g', ' ', 'i', 's', ' ', 't', 'o', ' ', 'l', 'e', 'a', 'r']
Label:n

字符特征与数字特征转换

上述抓取的信息就是样本、标签的原始形式。需要将原始的字符特征与各字符对应的$\text{Index}$进行转换，而转换后的$\text{Index}$特征作为$\text{One-hot}$向量的特征信息：

def LettertoIndexData(x,y,LettertoIndex):
    xtoIndex = list()
    ytoIndex = list()
    for i in range(len(x)):
        xtoIndex.append([LettertoIndex[Letter] for Letter in x[i]])
        ytoIndex.append([LettertoIndex[Letter] for Letter in y[i]])
    return xtoIndex,ytoIndex

与上述抓取的$5$个结果相对应，得到该结果的$\text{Index}$特征信息表示如下：

[15, 14, 14, 3, 4, 11, 14, 5, 18, 2, 9, 2, 13, 4, 9, 1, 4, 7, 0, 4]
[11]
-------------------------------------------------------------------
[14, 14, 3, 4, 11, 14, 5, 18, 2, 9, 2, 13, 4, 9, 1, 4, 7, 0, 4, 11]
[14]
-------------------------------------------------------------------
[14, 3, 4, 11, 14, 5, 18, 2, 9, 2, 13, 4, 9, 1, 4, 7, 0, 4, 11, 14]
[5]
-------------------------------------------------------------------
[3, 4, 11, 14, 5, 18, 2, 9, 2, 13, 4, 9, 1, 4, 7, 0, 4, 11, 14, 5]
[18]
-------------------------------------------------------------------
[4, 11, 14, 5, 18, 2, 9, 2, 13, 4, 9, 1, 4, 7, 0, 4, 11, 14, 5, 18]
[2]
-------------------------------------------------------------------

将数字特征转化为$\text{One-hot}$向量

仅将xtoIndex转化至$\text{One-hot}$向量格式，ytoIndex作为分类标签使用。

def DataProcessing(Data,LettertoIndex,Slide=20):

    def GetOneHot(IndexToken,Slide):
        assert IndexToken < Slide
        OneHotInit = np.zeros(Slide,dtype=np.int16)
        OneHotInit[IndexToken] = 1
        return OneHotInit

    LetterX,Lettery = ExtractData(Data,Slide)
    IndexTokenX,IndexTokeny = LettertoIndexData(LetterX,Lettery,LettertoIndex)
    Label = list(np.array(IndexTokeny).flatten())

    OnehotToken = list()
    for SubSilde in IndexTokenX:
        OnehotSlideToken = list()
        for i in SubSilde:
            OnehotResult = GetOneHot(i,Slide)
            OnehotSlideToken.append(OnehotResult)
        OnehotToken.append(OnehotSlideToken)

    return np.array(OnehotToken),Label

这里仅示例某窗口内的特征信息与对应的$\text{One-hot}$向量结果如下：

# xtoIndex;20
[10, 4, 4, 14, 15, 7, 4, 0, 8, 2, 18, 2, 12, 15, 18, 17, 15, 3, 19, 15]
# One-hot Result;(20,20)
[[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
 [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
 [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
 [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
 [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
 [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0]
 [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
 [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
 [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]
 [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
 [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
 [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]
 [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]]

模型构建

这里使用$\text{keras}$构建一个$\text{LSTM}$神经网络模型：
第一层是$\text{LSTM}$加$\text{ReLU}$激活函数;
第二层是'全连接神经网络'加$\text{Softmax}$激活函数。

from keras.models import Sequential
from keras.layers import Dense,LSTM

def GetModel(X_train,NumLetters):
    model = Sequential()
    model.add(LSTM(units=20,input_shape=(X_train.shape[1],X_train.shape[2]),activation="relu"))
    model.add(Dense(units=NumLetters,activation="softmax"))
    model.compile(optimizer="adam",loss="categorical_crossentropy",metrics=["accuracy"])
    return model

训练及预测过程

这里$\text{NewLetters}$作为测试，选择了原始数据的一部分，观察它的输出结果：

def Console(SeqPath):

    def GetyTrainOneHot(y_train,NumLetters):

        yTrainList = list()
        for i in y_train:
            OneHotResult = GetOneHot(i,NumLetters)
            yTrainList.append(OneHotResult)
        return np.array(yTrainList)

    Data, IndextoLetter, LettertoIndex = GetStringDict(SeqPath=SeqPath)
    NumLetters = len(LettertoIndex)
    X,y = DataProcessing(Data, LettertoIndex)
    X_Train,X_test,y_train,y_test = train_test_split(X,y,test_size=0.1,random_state=10)
    y_train_category = GetyTrainOneHot(y_train,NumLetters)

    Model = GetModel(X_Train,NumLetters)
    Model.fit(X_Train,y_train_category,batch_size=500,epochs=10)

    NewLetters = "is to learn the internal laws and presentation levels of sample data."
    xNew,yNew = DataProcessing(NewLetters,LettertoIndex)
    yNewPred = [np.argmax(i) for i in Model.predict(xNew)]
    print("".join([IndextoLetter[i] for i in yNewPred]))

输出结果返回如下：

Epoch 1/10
76/76 [==============================] - 2s 10ms/step - loss: 2.7461 - accuracy: 0.1332
Epoch 2/10
76/76 [==============================] - 1s 9ms/step - loss: 2.4212 - accuracy: 0.2519
Epoch 3/10
76/76 [==============================] - 1s 9ms/step - loss: 1.5785 - accuracy: 0.5274
Epoch 4/10
76/76 [==============================] - 1s 9ms/step - loss: 0.8844 - accuracy: 0.7459
Epoch 5/10
76/76 [==============================] - 1s 9ms/step - loss: 0.4660 - accuracy: 0.8764
Epoch 6/10
76/76 [==============================] - 1s 10ms/step - loss: 0.4800 - accuracy: 0.9009
Epoch 7/10
76/76 [==============================] - 1s 10ms/step - loss: 0.7330 - accuracy: 0.7894
Epoch 8/10
76/76 [==============================] - 1s 10ms/step - loss: 0.0548 - accuracy: 1.0000
Epoch 9/10
76/76 [==============================] - 1s 10ms/step - loss: 0.0254 - accuracy: 1.0000
Epoch 10/10
76/76 [==============================] - 1s 10ms/step - loss: 0.0154 - accuracy: 1.0000

可以看出，该模型能够学习到序列信息并收敛。比较输入测试结果与模型的预测结果：

# input
is to learn the internal laws and presentation levels of sample data.
# Predict
2/2 [==============================] - 0s 2ms/step
rnal laws and presentation levels of sample data.

它们之间相差的字符数正好是一个窗口大小：

# length:20
is to learn the inte

实际上：基于当前窗口(窗口内的序列信息)，预测下一个字符(下一时刻信息)。验证了循环神经网络中的思想。

# Slide = 20
    for i in range(0,xNew.shape[0] - 20):
        print(NewLetters[i:i+20], "  predict new latter is:  ",IndextoLetter[yNewPred[i]])

返回结果如下：

is to learn the inte   predict new latter is:   r
s to learn the inter   predict new latter is:   n
 to learn the intern   predict new latter is:   a
to learn the interna   predict new latter is:   l
o learn the internal   predict new latter is:    
 learn the internal    predict new latter is:   l
learn the internal l   predict new latter is:   a
earn the internal la   predict new latter is:   w
arn the internal law   predict new latter is:   s
rn the internal laws   predict new latter is:    
n the internal laws    predict new latter is:   a
 the internal laws a   predict new latter is:   n
the internal laws an   predict new latter is:   d
he internal laws and   predict new latter is:    
e internal laws and    predict new latter is:   p
 internal laws and p   predict new latter is:   r
internal laws and pr   predict new latter is:   e
nternal laws and pre   predict new latter is:   s
ternal laws and pres   predict new latter is:   e
ernal laws and prese   predict new latter is:   n
rnal laws and presen   predict new latter is:   t
nal laws and present   predict new latter is:   a
al laws and presenta   predict new latter is:   t
l laws and presentat   predict new latter is:   i
 laws and presentati   predict new latter is:   o
laws and presentatio   predict new latter is:   n
aws and presentation   predict new latter is:    
ws and presentation    predict new latter is:   l
s and presentation l   predict new latter is:   e

附：完整代码

import numpy as np
from keras.models import Sequential
from keras.layers import Dense,LSTM
from sklearn.model_selection import train_test_split


def GetTxtFile(WritePath,SeqInput,RepeatNum=500):
    """
    :param WritePath:D:\code_work\MachineLearning/FlareData.txt
    :param SeqInput:"Deep learning is to learn the internal laws and presentation levels of sample data."
    :param RepeatNum:500
    :return:
    """
    with open(WritePath,"w",encoding="UTF-8") as f:
        for _ in range(RepeatNum):
            f.write(SeqInput)
            f.write("\n")
        f.close()

    return 0


def GetStringDict(SeqPath):

    def ReadData(SeqPath):
        Data = open(SeqPath).read().replace("\n", " ").replace("\r", " ")
        return Data

    def DelRepeat(Data):
        letters = list(set(Data))
        return letters

    def GetLetterDict(LetterList):
        IndexLetterDict = {i: j for i, j in enumerate(LetterList)}
        LetterIndexDict = {j: i for i, j in enumerate(LetterList)}
        return IndexLetterDict, LetterIndexDict

    Data = ReadData(SeqPath)
    LetterList = DelRepeat(Data)
    IndextoLetter, LettertoIndex = GetLetterDict(LetterList)

    return Data, IndextoLetter, LettertoIndex


def ExtractData(Data,Slide):
    x = list()
    y = list()
    for i in range(len(Data) - Slide):
        x.append([a for a in Data[i:i+Slide]])
        y.append(Data[i+Slide])
    return x,y

def LettertoIndexData(x,y,LettertoIndex):
    xtoIndex = list()
    ytoIndex = list()
    for i in range(len(x)):
        xtoIndex.append([LettertoIndex[Letter] for Letter in x[i]])
        ytoIndex.append([LettertoIndex[Letter] for Letter in y[i]])
    return xtoIndex,ytoIndex


def GetOneHot(IndexToken,NumLetters):

    assert IndexToken < NumLetters
    OneHotInit = np.zeros(NumLetters,dtype=np.int16)
    OneHotInit[IndexToken] = 1
    return OneHotInit

def DataProcessing(Data,LettertoIndex,Slide=20):

    LetterX,Lettery = ExtractData(Data,Slide)
    IndexTokenX,IndexTokeny = LettertoIndexData(LetterX,Lettery,LettertoIndex)
    Label = list(np.array(IndexTokeny).flatten())

    OnehotToken = list()
    for SubSilde in IndexTokenX:
        OnehotSlideToken = list()
        for i in SubSilde:
            OnehotResult = GetOneHot(i,len(LettertoIndex))
            OnehotSlideToken.append(OnehotResult)
        OnehotToken.append(OnehotSlideToken)
    return np.array(OnehotToken),Label


def GetModel(X_train,NumLetters):
    model = Sequential()
    model.add(LSTM(units=20,input_shape=(X_train.shape[1],X_train.shape[2]),activation="relu"))
    model.add(Dense(units=NumLetters,activation="softmax"))
    model.compile(optimizer="adam",loss="categorical_crossentropy",metrics=["accuracy"])
    return model

def Console(SeqPath):

    def GetyTrainOneHot(y_train,NumLetters):

        yTrainList = list()
        for i in y_train:
            OneHotResult = GetOneHot(i,NumLetters)
            yTrainList.append(OneHotResult)
        return np.array(yTrainList)

    Data, IndextoLetter, LettertoIndex = GetStringDict(SeqPath=SeqPath)
    NumLetters = len(LettertoIndex)
    X,y = DataProcessing(Data, LettertoIndex)
    X_Train,X_test,y_train,y_test = train_test_split(X,y,test_size=0.1,random_state=10)
    y_train_category = GetyTrainOneHot(y_train,NumLetters)

    Model = GetModel(X_Train,NumLetters)
    Model.fit(X_Train,y_train_category,batch_size=500,epochs=10)

    NewLetters = "is to learn the internal laws and presentation levels of sample data."
    xNew,yNew = DataProcessing(NewLetters,LettertoIndex)
    yNewPred = [np.argmax(i) for i in Model.predict(xNew)]
    print("".join([IndextoLetter[i] for i in yNewPred]))

    # Slide = 20
    for i in range(0,xNew.shape[0] - 20):
        print(NewLetters[i:i+20], "  predict new latter is:  ",IndextoLetter[yNewPred[i]])
        

if __name__ == '__main__':
    SeqPath = "D:\code_work\MachineLearning/FlareData.txt"
    Console(SeqPath)

相关参考：
Word Representation(1) - Background