word2vec原理与实现

定义

word2vec是一种把词转到某种向量空间的方法，在新的向量空间，词之间的相互关系，上下文关系都以某种程度被表征出来。

方法

词向量的转换方法有两种： CBOW(Continouns bags of words)和Skip-gram。
以下图示为CBOW的网络结构图

上图中的x1，x2,….Xc代表的是源码中的context向量中的每个单词，这个上下文的窗口大小对每个词都是随机取值的。

源码解读

这里选取一个开源实现代码：Word2vec GitHub code
训练流程：

1. 加载文件，初始化词汇表
2. 初始化神经网络和霍夫曼树
3. 多进程训练
   
   1. 遍历文档每一行，为每行生成词索引向量
      
      1. 根据window大小配置该词的上下文context
      2. 输入NN训练

训练核心算法：

def train(fi, fo, cbow, neg, dim, alpha, win, min_count, num_processes, binary):
    # Read train file to init vocab
    vocab = Vocab(fi, min_count)

    # Init net
    syn0, syn1 = init_net(dim, len(vocab))

    global_word_count = Value('i', 0)
    table = None
    if neg > 0:#默认参数是5
        print 'Initializing unigram table'
        table = UnigramTable(vocab)
    else: #没有负样本，使用hierarchical softmax
        print 'Initializing Huffman tree'
        vocab.encode_huffman()

    # Begin training using num_processes workers
    t0 = time.time()
    pool = Pool(processes=num_processes, initializer=__init_process,
                initargs=(vocab, syn0, syn1, table, cbow, neg, dim, alpha,
                          win, num_processes, global_word_count, fi))
    pool.map(train_process, range(num_processes))
    t1 = time.time()
    print
    print 'Completed training. Training took', (t1 - t0) / 60, 'minutes'

    # Save model to file
    save(vocab, syn0, fo, binary)

def train_process(pid):
    # Set fi to point to the right chunk of training file
    #因为是多进程处理数据，所以根据进程号做好数据块划分
    start = vocab.bytes / num_processes * pid
    end = vocab.bytes if pid == num_processes - 1 else vocab.bytes / num_processes * (pid + 1)
    fi.seek(start)
    #print 'Worker %d beginning training at %d, ending at %d' % (pid, start, end)

    alpha = starting_alpha

    word_count = 0
    last_word_count = 0
    #遍历数据块
    while fi.tell() < end:
        line = fi.readline().strip()
        # Skip blank lines
        if not line:
            continue

        # 为一行句子初始化索引向量
        sent = vocab.indices(['<bol>'] + line.split() + ['<eol>'])
        #遍历一句话中的每个词
        for sent_pos, token in enumerate(sent):
            if word_count % 10000 == 0:
                global_word_count.value += (word_count - last_word_count)
                last_word_count = word_count

                # 更新alpha值
                alpha = starting_alpha * (1 - float(global_word_count.value) / vocab.word_count)
                if alpha < starting_alpha * 0.0001: alpha = starting_alpha * 0.0001

                # Print progress info
                sys.stdout.write("\rAlpha: %f Progress: %d of %d (%.2f%%)" %
                                 (alpha, global_word_count.value, vocab.word_count,
                                  float(global_word_count.value) / vocab.word_count * 100))
                sys.stdout.flush()

            # Randomize window size, where win is the max window size
            #随机初始化一个窗口大小
            current_win = np.random.randint(low=1, high=win+1)
            context_start = max(sent_pos - current_win, 0)
            context_end = min(sent_pos + current_win + 1, len(sent))
            #构造输入的上下文向量[x1,x2,...x_c]
            context = sent[context_start:sent_pos] + sent[sent_pos+1:context_end] # Turn into an iterator?

            # CBOW
            if cbow:
                # Compute neu1
                #对上下文单词的词向量求均值做为输入层
                neu1 = np.mean(np.array([syn0[c] for c in context]), axis=0)
                assert len(neu1) == dim, 'neu1 and dim do not agree'

                # Init neu1e with zeros
                neu1e = np.zeros(dim)

                # Compute neu1e and update syn1
                #先处理target向量，也就是标签向量
                if neg > 0:
                    classifiers = [(token, 1)] + [(target, 0) for target in table.sample(neg)]
                else:
                    #把词汇表中的该单词对应的索引和标签向量压成标签对
                    classifiers = zip(vocab[token].path, vocab[token].code)
                for target, label in classifiers:
                    z = np.dot(neu1, syn1[target])
                    p = sigmoid(z)
                    g = alpha * (label - p)
                    #计算反向回传的值
                    neu1e += g * syn1[target] # Error to backpropagate to syn0
                    #更新输出层值
                    syn1[target] += g * neu1  # Update syn1

                # Update syn0
                for context_word in context:
                    syn0[context_word] += neu1e

            # Skip-gram
            else:
                for context_word in context:
                    # Init neu1e with zeros
                    neu1e = np.zeros(dim)

                    # Compute neu1e and update syn1
                    if neg > 0:
                        classifiers = [(token, 1)] + [(target, 0) for target in table.sample(neg)]
                    else:
                        classifiers = zip(vocab[token].path, vocab[token].code)
                    for target, label in classifiers:
                        z = np.dot(syn0[context_word], syn1[target])
                        p = sigmoid(z)
                        g = alpha * (label - p)
                        neu1e += g * syn1[target]              # Error to backpropagate to syn0
                        syn1[target] += g * syn0[context_word] # Update syn1

                    # Update syn0
                    syn0[context_word] += neu1e

            word_count += 1

    # Print progress info
    global_word_count.value += (word_count - last_word_count)
    sys.stdout.write("\rAlpha: %f Progress: %d of %d (%.2f%%)" %
                     (alpha, global_word_count.value, vocab.word_count,
                      float(global_word_count.value)/vocab.word_count * 100))
    sys.stdout.flush()
    fi.close()

这里边用到了一个很重要的类Vocab，该类里边将会负责对词汇进行霍夫曼树编码：

#这个类用来存储霍夫曼树
class VocabItem:
    def __init__(self, word):
        self.word = word
        self.count = 0
        self.path = None # Path (list of indices) from the root to the word (leaf)
        self.code = None # Huffman encoding

class Vocab:
    def __init__(self, fi, min_count):
        vocab_items = []
        vocab_hash = {}
        word_count = 0
        fi = open(fi, 'r')

        # Add special tokens <bol> (beginning of line) and <eol> (end of line)
        for token in ['<bol>', '<eol>']:
            vocab_hash[token] = len(vocab_items)
            vocab_items.append(VocabItem(token))

        for line in fi:
            tokens = line.split()
            for token in tokens:
                if token not in vocab_hash:
                    vocab_hash[token] = len(vocab_items)
                    vocab_items.append(VocabItem(token))

                #assert vocab_items[vocab_hash[token]].word == token, 'Wrong vocab_hash index'
                vocab_items[vocab_hash[token]].count += 1
                word_count += 1

                if word_count % 10000 == 0:
                    sys.stdout.write("\rReading word %d" % word_count)
                    sys.stdout.flush()

            # Add special tokens <bol> (beginning of line) and <eol> (end of line)
            vocab_items[vocab_hash['<bol>']].count += 1
            vocab_items[vocab_hash['<eol>']].count += 1
            word_count += 2

        self.bytes = fi.tell()
        self.vocab_items = vocab_items         # List of VocabItem objects
        self.vocab_hash = vocab_hash           # Mapping from each token to its index in vocab
        self.word_count = word_count           # Total number of words in train file

        # Add special token <unk> (unknown),
        # merge words occurring less than min_count into <unk>, and
        # sort vocab in descending order by frequency in train file
        self.__sort(min_count)

        #assert self.word_count == sum([t.count for t in self.vocab_items]), 'word_count and sum of t.count do not agree'
        print 'Total words in training file: %d' % self.word_count
        print 'Total bytes in training file: %d' % self.bytes
        print 'Vocab size: %d' % len(self)

    def __getitem__(self, i):
        return self.vocab_items[i]

    def __len__(self):
        return len(self.vocab_items)

    def __iter__(self):
        return iter(self.vocab_items)

    def __contains__(self, key):
        return key in self.vocab_hash

    def __sort(self, min_count):
        tmp = []
        tmp.append(VocabItem('<unk>'))
        unk_hash = 0

        count_unk = 0
        for token in self.vocab_items:
            if token.count < min_count:
                count_unk += 1
                tmp[unk_hash].count += token.count
            else:
                tmp.append(token)

        tmp.sort(key=lambda token : token.count, reverse=True)

        # Update vocab_hash
        vocab_hash = {}
        for i, token in enumerate(tmp):
            vocab_hash[token.word] = i

        self.vocab_items = tmp
        self.vocab_hash = vocab_hash

        print
        print 'Unknown vocab size:', count_unk

    def indices(self, tokens):
        return [self.vocab_hash[token] if token in self else self.vocab_hash['<unk>'] for token in tokens]

    def encode_huffman(self):
        # Build a Huffman tree
        vocab_size = len(self)
        count = [t.count for t in self] + [1e15] * (vocab_size - 1)
        parent = [0] * (2 * vocab_size - 2)
        binary = [0] * (2 * vocab_size - 2)

        pos1 = vocab_size - 1
        pos2 = vocab_size

        for i in xrange(vocab_size - 1):
            # Find min1
            if pos1 >= 0:
                if count[pos1] < count[pos2]:
                    min1 = pos1
                    pos1 -= 1
                else:
                    min1 = pos2
                    pos2 += 1
            else:
                min1 = pos2
                pos2 += 1

            # Find min2
            if pos1 >= 0:
                if count[pos1] < count[pos2]:
                    min2 = pos1
                    pos1 -= 1
                else:
                    min2 = pos2
                    pos2 += 1
            else:
                min2 = pos2
                pos2 += 1

            count[vocab_size + i] = count[min1] + count[min2]
            parent[min1] = vocab_size + i
            parent[min2] = vocab_size + i
            binary[min2] = 1

        # Assign binary code and path pointers to each vocab word
        root_idx = 2 * vocab_size - 2
        for i, token in enumerate(self):
            path = [] # List of indices from the leaf to the root
            code = [] # Binary Huffman encoding from the leaf to the root

            node_idx = i
            while node_idx < root_idx:
                if node_idx >= vocab_size: path.append(node_idx)
                code.append(binary[node_idx])
                node_idx = parent[node_idx]
            path.append(root_idx)

            # These are path and code from the root to the leaf
            token.path = [j - vocab_size for j in path[::-1]]
            token.code = code[::-1]