Task 5: Homework（附代码）（Stanford CS224N NLP with Deep Learning Winter 2019）

Task 5: Homework——英文词向量的探索

词向量

  自然语言理解的问题要转化为机器学习的问题，第一步肯定是要找一种方法把这些符号数学化。
  NLP 中最直观，也是到目前为止最常用的词表示方法是 One-hot Representation，这种方法把每个词表示为一个很长的向量。这个向量的维度是词表大小，其中绝大多数元素为 0，只有一个维度的值为 1，这个维度就代表了当前的词。

举个例子， 　　
   “话筒”表示为 [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 …] 　　
   “麦克”表示为 [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 …] 　　
每个词都是茫茫 0 海中的一个 1。

  这种 One-hot Representation 如果采用稀疏方式存储，会是非常的简洁：也就是给每个词分配一个数字 ID。比如刚才的例子中，话筒记为 3，麦克记为 8（假设从 0 开始记）。如果要编程实现的话，用 Hash 表给每个词分配一个编号就可以了。这么简洁的表示方法配合上最大熵、SVM、CRF 等等算法已经很好地完成了 NLP 领域的各种主流任务。
  当然这种表示方法也存在一个重要的问题就是“词汇鸿沟”现象：任意两个词之间都是孤立的。光从这两个向量中看不出两个词是否有关系，哪怕是话筒和麦克这样的同义词也不能幸免于难。
  Deep Learning 中一般用到的词向量并不是刚才提到的用 One-hot Representation 表示的那种很长的词向量，而是用 Distributed Representation表示的一种低维实数向量。这种向量一般长成这个样子：[0.792, −0.177, −0.107, 0.109, −0.542, …]。维度以 50 维和 100 维比较常见。这种向量的表示不是唯一的。
  Distributed representation 最大的贡献就是让相关或者相似的词，在距离上更接近了。向量的距离可以用最传统的欧氏距离来衡量，也可以用 cos 夹角来衡量。用这种方式表示的向量，“麦克”和“话筒”的距离会远远小于“麦克”和“天气”。可能理想情况下“麦克”和“话筒”的表示应该是完全一样的，但是由于有些人会把英文名“迈克”也写成“麦克”，导致“麦克”一词带上了一些人名的语义，因此不会和“话筒”完全一致。

  词向量是下游NLP任务(如问答、文本生成、机器翻译等) 的基本组件，词向量的好坏能在很大程度上影响下游任务的性能。这里我们将探索两类词向量：共现矩阵 和 word2vec 。

  各种词向量的特点：

• One-hot：维度灾难 and 语义鸿沟
• 矩阵分解（LSA）：利用全局语料特征，但SVD求解计算复杂度大
• 基于NNLM/RNNLM的词向量：词向量为副产物，存在效率不高等问题
• Word2vec、fastText：优化效率高，但是基于局部语料
• glove：基于全局预料，结合了LSA和word2vec的优点
• ELMo、GPT、BERT：动态特征

  从one-hot到word2vec到ELMo，可以看到技术的演进总是在现有基础上解决之前的问题，同时引出新的问题。总结一下比较经典的语言模型：word2vec、glove、ELMo、BERT。可参考前面的几个博客：

• Task 1: Introduction and Word Vectors
• Task 2: Word Vectors and Word Senses
• Task 3: Subword Models
• Task 4: Contextual Word Embeddings

本项目需要下载的包

  1. reuters.zip
    nltk.download(‘reuters’)，我这里没有下载成功。我是将这条命令注释掉后，手动下载的 reuters 数据，网上有很多教如何手动下载安装的教程。
    除 nltk 外，其他包都可以通过 conda install 或 pip install 安装 。
  2. word2vec-google-news-300.gz
    百度，找到对应的数据 word2vec-google-news-300.gz 和 init.py，下载好后，放入项目源码。

  可参考我的项目：

Part 1：基于计数的词向量

  大多数词向量模型都是基于一个观点：

扫描二维码关注公众号，回复： 11573994 查看本文章

You shall know a word by the company it keeps (Firth, J. R. 1957:11)

  Co-Occurrence

• 这里我们使用词共现矩阵A，aij表示在词wi周围，词wj出现了多少次。根据定义易知A是一个对称阵，因为假设词wj在词wi出现了m词，那么词wi也在词wj出现了m次，因此 aij= m，那么共现次数怎么计算呢？下面以一个例子解释。

• 首先要选定两个词相隔多远算是共现了，即选定 window 的大小。window 表示词wiwi周围 |window| 之内的单词都算是与词wi共现。
  假设选定window = n，则词wi前n个单词和后n个单词与wi共现。

  • 下面举一个具体的例子。选择 window = 1

  • Document 1: “all that glitters is not gold”
  • Document 2: “all is well that ends well”

    • 得到的共现矩阵为

  注：
  我们一般会给句子（段落/文档）前后增加 “START” 和 “END” 表示起始和结尾。并且也统计到共现矩阵中。举一个例子，“all”行，“is” 列，为1，表示词 all 周围 is只出现了一次。看我们的语料可发现，is 只在 Dicument 2中出现在all周围。其他计算类似。

  由上面的介绍可知，我们得到的词共现矩阵 A∈Rn×n，n为词表大小。因此我们可以将每行当作每个词的词向量。但向量维度随着语料中的词表大小而增大，且很稀疏，因此我们可以对其进行降维（dimensionality reduction）。
  这里我们使用奇异值分解 SVD (Singular Value Decomposition) 来对矩阵进行分解

• SVD的介绍：https://davetang.org/file/Singular_Value_Decomposition_Tutorial.pdf
• 我们选择上图中矩阵 U的前 k 列作为我们的词向量。

  大多数词向量的实现的核心是 相似词 ，也就是同义词，因为它们有相似的上下文。这里我们介绍一种策略叫做 共现矩阵 (更多信息可以查看 这里 )
  这部分要实现的是，给定语料库，根据共现矩阵计算词向量，得到语料库中每个词的词向量，流程如下：

• 计算语料库的单词集
• 计算共现矩阵
• 使用SVD降维
• 分析词向量

问题1.1：实现不同单词

  计算语料库的单词数量、单词集

def distinct_words(corpus):
    """ Determine a list of distinct words for the corpus.
        Params:
            corpus (list of list of strings): corpus of documents
        Return:
            corpus_words (list of strings): list of distinct words across the corpus, sorted (using python 'sorted' function)
            num_corpus_words (integer): number of distinct words across the corpus
    """
    corpus_words = []
    num_corpus_words = -1

    # Write your implementation here.
    corpus = [w for sent in corpus for w in sent]
    corpus_words = list(set(corpus))
    corpus_words = sorted(corpus_words)
    num_corpus_words = len(corpus_words)
    # 返回的结果是语料库中的所有单词按照字母顺序排列的。
    return corpus_words, num_corpus_words

问题1.2：实现共现矩阵

  计算给定语料库的共现矩阵。具体来说，对于每一个词 w，统计前、后方 window_size 个词的出现次数

def compute_co_occurrence_matrix(corpus, window_size=4):
    """ Compute co-occurrence matrix for the given corpus and window_size (default of 4).

        Note: Each word in a document should be at the center of a window. Words near edges will have a smaller
              number of co-occurring words.

              For example, if we take the document "START All that glitters is not gold END" with window size of 4,
              "All" will co-occur with "START", "that", "glitters", "is", and "not".

        Params:
            corpus (list of list of strings): corpus of documents
            window_size (int): size of context window
        Return:
            M (numpy matrix of shape (number of corpus words, number of corpus words)):
                Co-occurence matrix of word counts.
                The ordering of the words in the rows/columns should be the same as the ordering of the words given by the distinct_words function.
            word2Ind (dict): dictionary that maps word to index (i.e. row/column number) for matrix M.
    """
    words, num_words = distinct_words(corpus)
    M = None
    word2Ind = {}

    # Write your implementation here.
    M = np.zeros(shape=(num_words, num_words), dtype=np.int32)
    for i in range(num_words):
        word2Ind[words[i]] = i

    for sent in corpus:
        for p in range(len(sent)):
            ci = word2Ind[sent[p]]

            # preceding
            for w in sent[max(0, p - window_size):p]:
                wi = word2Ind[w]
                M[ci][wi] += 1

            # subsequent
            for w in sent[p + 1:p + 1 + window_size]:
                wi = word2Ind[w]
                M[ci][wi] += 1

    return M, word2Ind

问题1.3：实现降到k维

  这一步是降维。在问题1.2得到的是一个N x N的矩阵（N是单词集的大小），使用scikit-learn实现的SVD（奇异值分解），从这个大矩阵里分解出一个含k个特制的N x k 小矩阵。

  注意：
    在numpy、scipy和scikit-learn都提供了一些SVD的实现，但是只有scipy、sklearn有Truncated SVD，并且只有sklearn提供了计算大规模SVD的高效的randomized算法，详情参考sklearn.decomposition.TruncatedSVD
。

def reduce_to_k_dim(M, k=2):
    """ Reduce a co-occurence count matrix of dimensionality (num_corpus_words, num_corpus_words)
        to a matrix of dimensionality (num_corpus_words, k) using the following SVD function from Scikit-Learn:
            - http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.TruncatedSVD.html

        Params:
            M (numpy matrix of shape (number of corpus words, number of corpus words)): co-occurence matrix of word counts
            k (int): embedding size of each word after dimension reduction
        Return:
            M_reduced (numpy matrix of shape (number of corpus words, k)): matrix of k-dimensioal word embeddings.
                    In terms of the SVD from math class, this actually returns U * S
    """
    n_iters = 10  # Use this parameter in your call to `TruncatedSVD`
    M_reduced = None
    print("Running Truncated SVD over %i words..." % (M.shape[0]))

    # Write your implementation here.
    svd = TruncatedSVD(n_components=k)
    svd.fit(M.T)
    M_reduced = svd.components_.T

    print("Done.")
    return M_reduced

问题1.4：实现 plot_embeddings

  基于matplotlib，用scatter 画 “×”，用 text 写字

def plot_embeddings(M_reduced, word2Ind, words):
    """ Plot in a scatterplot the embeddings of the words specified in the list "words".
        NOTE: do not plot all the words listed in M_reduced / word2Ind.
        Include a label next to each point.

        Params:
            M_reduced (numpy matrix of shape (number of unique words in the corpus , 2)): matrix of 2-dimensioal word embeddings
            word2Ind (dict): dictionary that maps word to indices for matrix M
            words (list of strings): words whose embeddings we want to visualize
    """
    # Write your implementation here.
    fig = plt.figure()
    plt.style.use("seaborn-whitegrid")
    for word in words:
        point = M_reduced[word2Ind[word]]
        plt.scatter(point[0], point[1], marker="^")
        plt.annotate(word, xy=(point[0], point[1]), xytext=(point[0], point[1] + 0.1))

# 测试解决方案图
print("-" * 80)
print("Outputted Plot:")

M_reduced_plot_test = np.array([[1, 1], [-1, -1], [1, -1], [-1, 1], [0, 0]])
word2Ind_plot_test = {'test1': 0, 'test2': 1, 'test3': 2, 'test4': 3, 'test5': 4}
words = ['test1', 'test2', 'test3', 'test4', 'test5']
plot_embeddings(M_reduced_plot_test, word2Ind_plot_test, words)

print("-" * 80)
print()

效果：

问题1.5：共现打印分析

  将词嵌入到2个维度上，归一化，最终词向量会落到一个单位圆内，在坐标系上寻找相近的词。

reuters_corpus = read_corpus()
M_co_occurrence, word2Ind_co_occurrence = compute_co_occurrence_matrix(reuters_corpus)
M_reduced_co_occurrence = reduce_to_k_dim(M_co_occurrence, k=2)

# Rescale (normalize) the rows to make them each of unit-length
M_lengths = np.linalg.norm(M_reduced_co_occurrence, axis=1)
M_normalized = M_reduced_co_occurrence / M_lengths[:, np.newaxis] # broadcasting

words = ['barrels', 'bpd', 'ecuador', 'energy', 'industry', 'kuwait', 'oil', 'output', 'petroleum', 'venezuela']

plot_embeddings(M_normalized, word2Ind_co_occurrence, words)
plt.show()

效果：

Part 2：基于预测的词向量

  目前，基于预测的词向量是最流行的，比如word2vec。现在我们来探索word2vec生成的词向量。
  这一部分主要是使用gensim探索词向量，不是自己实现word2vec，所使用的词向量维度是300，由google发布。
  首先使用SVD降维，将300维降2维，方便打印查看。

def load_word2vec(embeddings_fp="./GoogleNews-vectors-negative300.bin"):
    """ Load Word2Vec Vectors
        Param:
            embeddings_fp (string) - path to .bin file of pretrained word vectors
        Return:
            wv_from_bin: All 3 million embeddings, each lengh 300
                This is the KeyedVectors format: https://radimrehurek.com/gensim/models/deprecated/keyedvectors.html
    """
    embed_size = 300
    print("Loading 3 million word vectors from file...")
    ## 自己下载的文件
    wv_from_bin = KeyedVectors.load_word2vec_format(embeddings_fp, binary=True)
    vocab = list(wv_from_bin.vocab.keys())
    print("Loaded vocab size %i" % len(vocab))
    return wv_from_bin
wv_from_bin = load_word2vec()
print()

问题2.1：word2vec打印分析

  和问题1.5一样

def get_matrix_of_vectors(wv_from_bin, required_words=['barrels', 'bpd', 'ecuador', 'energy', 'industry', 'kuwait', 'oil', 'output', 'petroleum', 'venezuela']):
    """ Put the word2vec vectors into a matrix M.
        Param:
            wv_from_bin: KeyedVectors object; the 3 million word2vec vectors loaded from file
        Return:
            M: numpy matrix shape (num words, 300) containing the vectors
            word2Ind: dictionary mapping each word to its row number in M
    """
    import random
    words = list(wv_from_bin.vocab.keys())
    print("Shuffling words ...")
    random.shuffle(words)
    words = words[:10000]       # 选10000个加入
    print("Putting %i words into word2Ind and matrix M..." % len(words))
    word2Ind = {}
    M = []
    curInd = 0
    for w in words:
        try:
            M.append(wv_from_bin.word_vec(w))
            word2Ind[w] = curInd
            curInd += 1
        except KeyError:
            continue
    for w in required_words:
        try:
            M.append(wv_from_bin.word_vec(w))
            word2Ind[w] = curInd
            curInd += 1
        except KeyError:
            continue
    M = np.stack(M)
    print("Done.")
    return M, word2Ind

# 测试解决方案图
print("-" * 80)
print("Outputted Plot:")
print("-" * 80)

M, word2Ind = get_matrix_of_vectors(wv_from_bin)
M_reduced = reduce_to_k_dim(M, k=2)         # 减到了2维
plt.tight_layout()
words = ['barrels', 'bpd', 'ecuador', 'energy', 'industry', 'kuwait', 'oil', 'output', 'petroleum', 'venezuela']
plot_embeddings(M_reduced, word2Ind, words)
plt.show()

问题2.2：一词多义

  找到一个有多个含义的词（比如 “leaves”，“scoop”），这种词的top-10相似词（根据余弦相似度）里有两个词的意思不一样。比如"leaves"（叶子，花瓣）的top-10词里有"vanishes"（消失）和"stalks"（茎秆）。
  这里我找到的词是"column"（列），它的top-10里有"columnist"（专栏作家）和"article"（文章）

w0 = "column"
w0_mean = wv_from_bin.most_similar(w0)
print("column：", w0_mean)
print()

结果：

问题2.3：近义词和反义词

  找到三个词(w1, w2, w3)，其中w1和w2是近义词，w1和w3是反义词，但是w1和w3的距离<w1和w2的距离。例如：w1=“happy”，w2=“cheerful”，w3=“sad”
  为什么反义词的相似度反而更大呢（距离越小说明越相似）？因为他们的上下文通常非常一致。

w1 = "love"
w2 = "like"
w3 = "hate"
w1_w2_dist = wv_from_bin.distance(w1, w2)
w1_w3_dist = wv_from_bin.distance(w1, w3)
print("Synonyms {}, {} have cosine distance: {}".format(w1, w2, w1_w2_dist))
print("Antonyms {}, {} have cosine distance: {}".format(w1, w3, w1_w3_dist))
print()

结果：

问题2.4：类比

  vman 对于 king，相当于woman对于___，这样的问题也可以用word2vec来解决。
  这里我们找另外一组类比。

print("类比 man : him :: woman : her：")
pprint.pprint(wv_from_bin.most_similar(positive=['woman', 'him'], negative=['man']))
print()

结果：

  可以看到正确的计算出了"queen"

问题2.5：错误的类比

  找到一个错误的类比，树：树叶 ：：花：花瓣

print("错误的类比 tree : leaf :: flower : petal：")
pprint.pprint(wv_from_bin.most_similar(positive=['leaf', 'flower'], negative=['tree']))
print()

结果：

  结果输出的里面没有“花瓣”

问题2.6：偏见分析

  注意偏见是很重要的比如性别歧视、种族歧视等，执行下面代码，分析两个问题：

(a) 哪个词与“woman”和“boss”最相似，和“man”最不相似?
(b) 哪个词与“man”和“boss”最相似，和“woman”最不相似?

print("偏见 woman : boss :: man：")
pprint.pprint(wv_from_bin.most_similar(positive=['woman', 'boss'], negative=['man']))
print()
print("偏见 man : boss :: woman：")
pprint.pprint(wv_from_bin.most_similar(positive=['man', 'boss'], negative=['woman']))
print()

结果：

  第一个类比 男人:女人 :: 老板:___，最合适的词应该是"landlady"（老板娘）之类的，但是top-10里只有"manageress"（女经理），“receptionist”（接待员）之类的词。

  第二个类比 女人:男人 :: 老板:___，输出的如图所示。

问题2.7：自行分析偏见

  这里我找的例子是：

     男人:女人 :: 医生:___
     女人:男人 :: 医生:___

print("自行分析偏见 woman : doctor :: man：")
pprint.pprint(wv_from_bin.most_similar(positive=['woman', 'doctor'], negative=['man']))
print()
print("自行分析偏见 man : doctor :: woman：")
pprint.pprint(wv_from_bin.most_similar(positive=['man', 'doctor'], negative=['woman']))
print()

结果：

  第一个类比中，我们看到了"nurse"（护士），这是一个有偏见的类比

问题2.8：思考偏见问题

  什么会导致词向量里的偏见？
  1.训练集的偏见。 机器学习产生的结果取决于你的训练集。机器学习产生的偏见实际上就是人类写的文章中带有的偏见。如果文章中经常将 racing 和 man 一起出现，那它们之间的距离会非常近，而到 woman 这个单词就会很远。
  2.数据量的不足。 因为我们只引入了10000个词汇量，如果数据量更大一点，说不定能够消除偏见。
  3.由于算法设计的原因而导致的偏见。可能有些词的出现拉远了某两个词之间的距离。

【参考资料】

  斯坦福cs224n-2019链接：https://web.stanford.edu/class/archive/cs/cs224n/cs224n.1194/

【附：完整代码】

# 导入包
import sys
assert sys.version_info[0]==3
assert sys.version_info[1] >= 5

from gensim.models import KeyedVectors  # KeyedVectors:实现实体（单词、文档、图片都可以）和向量之间的映射。每个实体由其字符串id标识。
from gensim.test.utils import datapath
import pprint     #  输出的更加规范易读
import matplotlib.pyplot as plt
plt.rcParams['figure.figsize'] = [10, 5]  #  plt.rcParams主要作用是设置画的图的分辨率，大小等信息
# import nltk
# nltk.download('reuters')    # 这个可以从GitHub下载， 网址：https://github.com/nltk/nltk_data/tree/gh-pages/packages/corpora
from nltk.corpus import reuters
import numpy as np
import random
import rando
import scipy as sp
from sklearn.decomposition import TruncatedSVD
from sklearn.decomposition import PCA

START_TOKEN = '<START>'
END_TOKEN = '<END>'

np.random.seed(0)
random.seed(0)

# 导入 "reuters" 语料库
def read_corpus(category="crude"):
    """ Read files from the specified Reuter's category.
        Params:
            category (string): category name
        Return:
            list of lists, with words from each of the processed files
    """
    files = reuters.fileids(category)    # 类别为crude文档
    # 每个文档都转化为小写， 并在开头结尾加标识符
    return [[START_TOKEN] + [w.lower() for w in list(reuters.words(f))] + [END_TOKEN] for f in files]
print()

# 导入语料库的函数，简单的进行了一下预处理，
# 在每句话的前面和后面各加了一个标识符，表示句子的开始和结束，然后把每个单词分开。
# pprint模块格式化打印
# pprint.pprint(object, stream=None, indent=1, width=80, depth=None, *, compact=False)
# width：控制打印显示的宽度。默认为80个字符。注意：当单个对象的长度超过width时，并不会分多行显示，而是会突破规定的宽度。
# compact：默认为False。如果值为False，超过width规定长度的序列会被分散打印到多行。如果为True，会尽量使序列填满width规定的宽度。
reuters_corpus = read_corpus()
pprint.pprint(reuters_corpus[:1], compact=True, width=100)  # compact 设置为False是一行一个单词

# 问题1.1：实现不同单词
# 计算语料库的单词数量、单词集
def distinct_words(corpus):
    """ Determine a list of distinct words for the corpus.
        Params:
            corpus (list of list of strings): corpus of documents
        Return:
            corpus_words (list of strings): list of distinct words across the corpus, sorted (using python 'sorted' function)
            num_corpus_words (integer): number of distinct words across the corpus
    """
    corpus_words = []
    num_corpus_words = -1

    # Write your implementation here.
    corpus = [w for sent in corpus for w in sent]
    corpus_words = list(set(corpus))
    corpus_words = sorted(corpus_words)
    num_corpus_words = len(corpus_words)
    # 返回的结果是语料库中的所有单词按照字母顺序排列的。
    return corpus_words, num_corpus_words

# 问题1.2：实现共现矩阵
# 计算给定语料库的共现矩阵。具体来说，对于每一个词 w，统计前、后方 window_size 个词的出现次数\
def compute_co_occurrence_matrix(corpus, window_size=4):
    """ Compute co-occurrence matrix for the given corpus and window_size (default of 4).

        Note: Each word in a document should be at the center of a window. Words near edges will have a smaller
              number of co-occurring words.

              For example, if we take the document "START All that glitters is not gold END" with window size of 4,
              "All" will co-occur with "START", "that", "glitters", "is", and "not".

        Params:
            corpus (list of list of strings): corpus of documents
            window_size (int): size of context window
        Return:
            M (numpy matrix of shape (number of corpus words, number of corpus words)):
                Co-occurence matrix of word counts.
                The ordering of the words in the rows/columns should be the same as the ordering of the words given by the distinct_words function.
            word2Ind (dict): dictionary that maps word to index (i.e. row/column number) for matrix M.
    """
    words, num_words = distinct_words(corpus)
    M = None
    word2Ind = {}

    # Write your implementation here.
    M = np.zeros(shape=(num_words, num_words), dtype=np.int32)
    for i in range(num_words):
        word2Ind[words[i]] = i

    for sent in corpus:
        for p in range(len(sent)):
            ci = word2Ind[sent[p]]

            # preceding
            for w in sent[max(0, p - window_size):p]:
                wi = word2Ind[w]
                M[ci][wi] += 1

            # subsequent
            for w in sent[p + 1:p + 1 + window_size]:
                wi = word2Ind[w]
                M[ci][wi] += 1

    return M, word2Ind

# 问题1.3：实现降到k维
# 这一步是降维。
# 在问题1.2得到的是一个N x N的矩阵（N是单词集的大小），使用scikit-learn实现的SVD（奇异值分解），从这个大矩阵里分解出一个含k个特制的N x k 小矩阵。
def reduce_to_k_dim(M, k=2):
    """ Reduce a co-occurence count matrix of dimensionality (num_corpus_words, num_corpus_words)
        to a matrix of dimensionality (num_corpus_words, k) using the following SVD function from Scikit-Learn:
            - http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.TruncatedSVD.html

        Params:
            M (numpy matrix of shape (number of corpus words, number of corpus words)): co-occurence matrix of word counts
            k (int): embedding size of each word after dimension reduction
        Return:
            M_reduced (numpy matrix of shape (number of corpus words, k)): matrix of k-dimensioal word embeddings.
                    In terms of the SVD from math class, this actually returns U * S
    """
    n_iters = 10  # Use this parameter in your call to `TruncatedSVD`
    M_reduced = None
    print("Running Truncated SVD over %i words..." % (M.shape[0]))

    # Write your implementation here.
    svd = TruncatedSVD(n_components=k)
    svd.fit(M.T)
    M_reduced = svd.components_.T

    print("Done.")
    return M_reduced

# 问题1.4 实现 plot_embeddings
# 编写一个函数来绘制2D空间中的一组2D矢量。
# 基于matplotlib，用scatter 画 “×”，用 text 写字
def plot_embeddings(M_reduced, word2Ind, words):
    """ Plot in a scatterplot the embeddings of the words specified in the list "words".
        NOTE: do not plot all the words listed in M_reduced / word2Ind.
        Include a label next to each point.

        Params:
            M_reduced (numpy matrix of shape (number of unique words in the corpus , 2)): matrix of 2-dimensioal word embeddings
            word2Ind (dict): dictionary that maps word to indices for matrix M
            words (list of strings): words whose embeddings we want to visualize
    """
    # Write your implementation here.
    fig = plt.figure()
    plt.style.use("seaborn-whitegrid")
    for word in words:
        point = M_reduced[word2Ind[word]]
        plt.scatter(point[0], point[1], marker="^")
        plt.annotate(word, xy=(point[0], point[1]), xytext=(point[0], point[1] + 0.1))

# 测试解决方案图
print("-" * 80)
print("Outputted Plot:")

M_reduced_plot_test = np.array([[1, 1], [-1, -1], [1, -1], [-1, 1], [0, 0]])
word2Ind_plot_test = {'test1': 0, 'test2': 1, 'test3': 2, 'test4': 3, 'test5': 4}
words = ['test1', 'test2', 'test3', 'test4', 'test5']
plot_embeddings(M_reduced_plot_test, word2Ind_plot_test, words)

print("-" * 80)
print()

# 问题1.5：共现打印分析
# 将词嵌入到2个维度上，归一化，最终词向量会落到一个单位圆内，在坐标系上寻找相近的词。
reuters_corpus = read_corpus()
M_co_occurrence, word2Ind_co_occurrence = compute_co_occurrence_matrix(reuters_corpus)
M_reduced_co_occurrence = reduce_to_k_dim(M_co_occurrence, k=2)

# Rescale (normalize) the rows to make them each of unit-length
M_lengths = np.linalg.norm(M_reduced_co_occurrence, axis=1)
M_normalized = M_reduced_co_occurrence / M_lengths[:, np.newaxis] # broadcasting

words = ['barrels', 'bpd', 'ecuador', 'energy', 'industry', 'kuwait', 'oil', 'output', 'petroleum', 'venezuela']

plot_embeddings(M_normalized, word2Ind_co_occurrence, words)
plt.show()

# Part 2：基于预测的词向量
# 使用gensim探索词向量，不是自己实现word2vec，所使用的词向量维度是300，由google发布。
def load_word2vec(embeddings_fp="./GoogleNews-vectors-negative300.bin"):
    """ Load Word2Vec Vectors
        Param:
            embeddings_fp (string) - path to .bin file of pretrained word vectors
        Return:
            wv_from_bin: All 3 million embeddings, each lengh 300
                This is the KeyedVectors format: https://radimrehurek.com/gensim/models/deprecated/keyedvectors.html
    """
    embed_size = 300
    print("Loading 3 million word vectors from file...")
    ## 自己下载的文件
    wv_from_bin = KeyedVectors.load_word2vec_format(embeddings_fp, binary=True)
    vocab = list(wv_from_bin.vocab.keys())
    print("Loaded vocab size %i" % len(vocab))
    return wv_from_bin
wv_from_bin = load_word2vec()
print()

# 首先使用SVD降维，将300维降2维，方便打印查看。
# 问题2.1：word2vec打印分析
# 和问题1.5一样
def get_matrix_of_vectors(wv_from_bin, required_words=['barrels', 'bpd', 'ecuador', 'energy', 'industry', 'kuwait', 'oil', 'output', 'petroleum', 'venezuela']):
    """ Put the word2vec vectors into a matrix M.
        Param:
            wv_from_bin: KeyedVectors object; the 3 million word2vec vectors loaded from file
        Return:
            M: numpy matrix shape (num words, 300) containing the vectors
            word2Ind: dictionary mapping each word to its row number in M
    """
    import random
    words = list(wv_from_bin.vocab.keys())
    print("Shuffling words ...")
    random.shuffle(words)
    words = words[:10000]       # 选10000个加入
    print("Putting %i words into word2Ind and matrix M..." % len(words))
    word2Ind = {}
    M = []
    curInd = 0
    for w in words:
        try:
            M.append(wv_from_bin.word_vec(w))
            word2Ind[w] = curInd
            curInd += 1
        except KeyError:
            continue
    for w in required_words:
        try:
            M.append(wv_from_bin.word_vec(w))
            word2Ind[w] = curInd
            curInd += 1
        except KeyError:
            continue
    M = np.stack(M)
    print("Done.")
    return M, word2Ind

# 测试解决方案图
print("-" * 80)
print("Outputted Plot:")
print("-" * 80)

M, word2Ind = get_matrix_of_vectors(wv_from_bin)
M_reduced = reduce_to_k_dim(M, k=2)         # 减到了2维
plt.tight_layout()
words = ['barrels', 'bpd', 'ecuador', 'energy', 'industry', 'kuwait', 'oil', 'output', 'petroleum', 'venezuela']
plot_embeddings(M_reduced, word2Ind, words)
plt.show()

# 问题2.2：一词多义
# 找到一个有多个含义的词（比如 “leaves”，“scoop”），这种词的top-10相似词（根据余弦相似度）里有两个词的意思不一样。比如"leaves"（叶子，花瓣）的top-10词里有"vanishes"（消失）和"stalks"（茎秆）。
# 这里我找到的词是"column"（列），它的top-10里有"columnist"（专栏作家）和"article"（文章）
w0 = "column"
w0_mean = wv_from_bin.most_similar(w0)
print("column：", w0_mean)
print()

# 问题2.3：近义词和反义词
# 找到三个词(w1, w2, w3)，其中w1和w2是近义词，w1和w3是反义词，但是w1和w3的距离<w1和w2的距离。
# 例如：w1=“happy”，w2=“cheerful”，w3=“sad”
w1 = "love"
w2 = "like"
w3 = "hate"
w1_w2_dist = wv_from_bin.distance(w1, w2)
w1_w3_dist = wv_from_bin.distance(w1, w3)
print("Synonyms {}, {} have cosine distance: {}".format(w1, w2, w1_w2_dist))
print("Antonyms {}, {} have cosine distance: {}".format(w1, w3, w1_w3_dist))
print()

# 问题2.4：类比
# man 对于 king，相当于woman对于___，这样的问题也可以用word2vec来解决
# man : him :: woman : her
print("类比 man : him :: woman : her：")
pprint.pprint(wv_from_bin.most_similar(positive=['woman', 'him'], negative=['man']))
print()


# 问题2.5：错误的类比
# 找到一个错误的类比，树：树叶 ：：花：花瓣
print("错误的类比 tree : leaf :: flower : petal：")
pprint.pprint(wv_from_bin.most_similar(positive=['leaf', 'flower'], negative=['tree']))
print()

# 问题2.6：偏见分析
# 注意偏见是很重要的比如性别歧视、种族歧视等，执行下面代码，分析两个问题：
# (a) 哪个词与“woman”和“boss”最相似，和“man”最不相似?
# (b) 哪个词与“man”和“boss”最相似，和“woman”最不相似?
print("偏见 woman : boss :: man：")
pprint.pprint(wv_from_bin.most_similar(positive=['woman', 'boss'], negative=['man']))
print()
print("偏见 man : boss :: woman：")
pprint.pprint(wv_from_bin.most_similar(positive=['man', 'boss'], negative=['woman']))
print()

# 问题2.7：自行分析偏见
#     男人:女人 :: 医生:___
#     女人:男人 :: 医生:___
print("自行分析偏见 woman : doctor :: man：")
pprint.pprint(wv_from_bin.most_similar(positive=['woman', 'doctor'], negative=['man']))
print()
print("自行分析偏见 man : doctor :: woman：")
pprint.pprint(wv_from_bin.most_similar(positive=['man', 'doctor'], negative=['woman']))
print()