LDA文档主题生成模型入门

海天一树

发布于 2018-07-25 14:22:10

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发布于 2018-07-25 14:22:10

文章被收录于专栏：海天一树

一、LDA简介

LDA（Latent Dirichlet Allocation）是一种文档主题生成模型，也称为一个三层贝叶斯概率模型，包含词、主题和文档三层结构。所谓生成模型，就是说，我们认为一篇文章的每个词都是通过“以一定概率选择了某个主题，并从这个主题中以一定概率选择某个词语”这样一个过程得到。文档到主题服从多项式分布，主题到词服从多项式分布。

LDA是一种非监督机器学习技术，可以用来识别大规模文档集（document collection）或语料库（corpus）中潜藏的主题信息。它采用了词袋（bag of words）的方法，这种方法将每一篇文档视为一个词频向量，从而将文本信息转化为了易于建模的数字信息。但是词袋方法没有考虑词与词之间的顺序，这简化了问题的复杂性，同时也为模型的改进提供了契机。每一篇文档代表了一些主题所构成的一个概率分布，而每一个主题又代表了很多单词所构成的一个概率分布。

二、安装LDA库

pip install lda

安装完成后，可以在python安装目录下的Lib/site-packages目录下看到lda相关的目录。

三、了解数据集

数据集位于lda安装目录的tests文件夹中，包含三个文件：reuters.ldac, reuters.titles, reuters.tokens。 reuters.titles包含了395个文档的标题 reuters.tokens包含了这395个文档中出现的所有单词，总共是4258个 reuters.ldac有395行，第i行代表第i个文档中各个词汇出现的频率。以第0行为例，第0行代表的是第0个文档，从reuters.titles中可查到该文档的标题为“UK: Prince Charles spearheads British royal revolution. LONDON 1996-08-20”。第0行的数据为： 159 0:1 2:1 6:1 9:1 12:5 13:2 20:1 21:4 24:2 29:1 …… 第一个数字159表示第0个文档里总共出现了159个单词（每个单词出现一或多次）， 0:1表示第0个单词出现了1次，从reuters.tokens查到第0个单词为church 2:1表示第2个单词出现了1次，从reuters.tokens查到第2个单词为years 6:1表示第6个单词出现了1次，从reuters.tokens查到第6个单词为told 9:1表示第9个单词出现了1次，从reuters.tokens查到第9个单词为year 12:5表示第12个单词出现了5次，从reuters.tokens查到第12个单词为charles …… 这里第1、3、4、5、7、8、10、11……个单词序号和次数没列出来，表示出现的次数为0

注意： 395个文档的原文是没有的。上述三个文档是根据这395个文档处理之后得到的。

四、程序实现

（一）载入数据

（1）查看文档中词出现的频率

import numpy as np
import lda
import lda.datasets
# document-term matrix
X = lda.datasets.load_reuters()
print("type(X): {}".format(type(X)))
print("shape: {}\n".format(X.shape))
print(X[:5, :5])        #前五行的前五列

运行结果：

type(X): <class 'numpy.ndarray'>
shape: (395, 4258)
[[ 1  0  1  0  0]
 [ 7  0  2  0  0]
 [ 0  0  0  1 10]
 [ 6  0  1  0  0]
 [ 0  0  0  2 14]]

观察reuters.ldac中的前5行的前5列，发现：第0行的前5列，单词编号为0，1，2，3，4的出现频次，正是1，0，1，0，0 第1行的前5列，单词编程为0，1，2，3，4的出现频次，正是7，0，2，0，0 ……

（2）查看词

# the vocab
vocab = lda.datasets.load_reuters_vocab()
print("type(vocab): {}".format(type(vocab)))
print("len(vocab): {}\n".format(len(vocab)))
print(vocab[:5])

运行结果：

type(vocab): <class 'tuple'>
len(vocab): 4258
('church', 'pope', 'years', 'people', 'mother')

可以看出，reuters.tokens中有4258个单词，前五个分别是church, pope, years, people, mother.

（3）查看文档标题

# titles for each story
titles = lda.datasets.load_reuters_titles()
print("type(titles): {}".format(type(titles)))
print("len(titles): {}\n".format(len(titles)))
print(titles[:5])       # 打印前五个文档的标题

运行结果：

type(titles): <class 'tuple'>
len(titles): 395
('0 UK: Prince Charles spearheads British royal revolution. LONDON 1996-08-20', 
'1 GERMANY: Historic Dresden church rising from WW2 ashes. DRESDEN, Germany 1996-08-21',
"2 INDIA: Mother Teresa's condition said still unstable. CALCUTTA 1996-08-23", 
'3 UK: Palace warns British weekly over Charles pictures. LONDON 1996-08-25', 
'4 INDIA: Mother Teresa, slightly stronger, blesses nuns. CALCUTTA 1996-08-25')

（4）查看前5个文档第0个词出现的次数

doc_id = 0
word_id = 0
while doc_id < 5:
    print("doc id: {} word id: {}".format(doc_id, word_id))
    print("-- count: {}".format(X[doc_id, word_id]))
    print("-- word : {}".format(vocab[word_id]))
    print("-- doc  : {}\n".format(titles[doc_id]))
    doc_id += 1

运行结果：

doc id: 0 word id: 0
-- count: 1
-- word : church
-- doc  : 0 UK: Prince Charles spearheads British royal revolution. LONDON 1996-08-20
doc id: 1 word id: 0
-- count: 7
-- word : church
-- doc  : 1 GERMANY: Historic Dresden church rising from WW2 ashes. DRESDEN, Germany 1996-08-21
doc id: 2 word id: 0
-- count: 0
-- word : church
-- doc  : 2 INDIA: Mother Teresa's condition said still unstable. CALCUTTA 1996-08-23
doc id: 3 word id: 0
-- count: 6
-- word : church
-- doc  : 3 UK: Palace warns British weekly over Charles pictures. LONDON 1996-08-25
doc id: 4 word id: 0
-- count: 0
-- word : church
-- doc  : 4 INDIA: Mother Teresa, slightly stronger, blesses nuns. CALCUTTA 1996-08-25

（二）训练模型

设置20个主题，500次迭代

model = lda.LDA(n_topics=20, n_iter=500, random_state=1)
model.fit(X)          # model.fit_transform(X) is also available

（三）主题-单词分布

计算前3个单词在所有主题（共20个）中所占的权重

topic_word = model.topic_word_
print("type(topic_word): {}".format(type(topic_word)))
print("shape: {}".format(topic_word.shape))
print(vocab[:3])
print(topic_word[:, :3])    #打印所有行(20)行的前3列

运行结果：

type(topic_word): <class 'numpy.ndarray'>
shape: (20, 4258)
('church', 'pope', 'years')
[[2.72436509e-06 2.72436509e-06 2.72708945e-03]
 [2.29518860e-02 1.08771556e-06 7.83263973e-03]
 [3.97404221e-03 4.96135108e-06 2.98177200e-03]
 [3.27374625e-03 2.72585033e-06 2.72585033e-06]
 [8.26262882e-03 8.56893407e-02 1.61980569e-06]
 [1.30107788e-02 2.95632328e-06 2.95632328e-06]
 [2.80145003e-06 2.80145003e-06 2.80145003e-06]
 [2.42858077e-02 4.66944966e-06 4.66944966e-06]
 [6.84655429e-03 1.90129250e-06 6.84655429e-03]
 [3.48361655e-06 3.48361655e-06 3.48361655e-06]
 [2.98781661e-03 3.31611166e-06 3.31611166e-06]
 [4.27062069e-06 4.27062069e-06 4.27062069e-06]
 [1.50994982e-02 1.64107142e-06 1.64107142e-06]
 [7.73480150e-07 7.73480150e-07 1.70946848e-02]
 [2.82280146e-06 2.82280146e-06 2.82280146e-06]
 [5.15309856e-06 5.15309856e-06 4.64294180e-03]
 [3.41695768e-06 3.41695768e-06 3.41695768e-06]
 [3.90980357e-02 1.70316633e-03 4.42279319e-03]
 [2.39373034e-06 2.39373034e-06 2.39373034e-06]
 [3.32493234e-06 3.32493234e-06 3.32493234e-06]]

计算所有行的比重之和（等于1）

for n in range(20):
    sum_pr = sum(topic_word[n,:])   # 第n行所有列的比重之和，等于1
    print("topic: {} sum: {}".format(n, sum_pr))

计算结果：

topic: 0 sum: 1.0000000000000875
topic: 1 sum: 1.0000000000001148
topic: 2 sum: 0.9999999999998656
topic: 3 sum: 1.0000000000000042
topic: 4 sum: 1.0000000000000928
topic: 5 sum: 0.9999999999999372
topic: 6 sum: 0.9999999999999049
topic: 7 sum: 1.0000000000001694
topic: 8 sum: 1.0000000000000906
topic: 9 sum: 0.9999999999999195
topic: 10 sum: 1.0000000000001261
topic: 11 sum: 0.9999999999998876
topic: 12 sum: 1.0000000000001268
topic: 13 sum: 0.9999999999999034
topic: 14 sum: 1.0000000000001892
topic: 15 sum: 1.0000000000000984
topic: 16 sum: 1.0000000000000768
topic: 17 sum: 0.9999999999999146
topic: 18 sum: 1.0000000000000364
topic: 19 sum: 1.0000000000001434

（四）计算各主题top-N个词

计算每个主题中，比重最大的5个词

n = 5
for i, topic_dist in enumerate(topic_word):
    topic_words = np.array(vocab)[np.argsort(topic_dist)][:-(n+1):-1]
    print('*Topic {}\n- {}'.format(i, ' '.join(topic_words)))

运行结果：

*Topic 0
- government british minister west group
*Topic 1
- church first during people political
*Topic 2
- elvis king wright fans presley
*Topic 3
- yeltsin russian russia president kremlin
*Topic 4
- pope vatican paul surgery pontiff
*Topic 5
- family police miami versace cunanan
*Topic 6
- south simpson born york white
*Topic 7
- order church mother successor since
*Topic 8
- charles prince diana royal queen
*Topic 9
- film france french against actor
*Topic 10
- germany german war nazi christian
*Topic 11
- east prize peace timor quebec
*Topic 12
- n't told life people church
*Topic 13
- years world time year last
*Topic 14
- mother teresa heart charity calcutta
*Topic 15
- city salonika exhibition buddhist byzantine
*Topic 16
- music first people tour including
*Topic 17
- church catholic bernardin cardinal bishop
*Topic 18
- harriman clinton u.s churchill paris
*Topic 19
- century art million museum city

（五）文档-主题分布

总共有395篇文档，计算前10篇文档最可能的主题

doc_topic = model.doc_topic_
print("type(doc_topic): {}".format(type(doc_topic)))
print("shape: {}".format(doc_topic.shape))
for n in range(10):
    topic_most_pr = doc_topic[n].argmax()
    print("doc: {} topic: {}".format(n, topic_most_pr))

运行结果：

type(doc_topic): <class 'numpy.ndarray'>
shape: (395, 20)
doc: 0 topic: 8
doc: 1 topic: 1
doc: 2 topic: 14
doc: 3 topic: 8
doc: 4 topic: 14
doc: 5 topic: 14
doc: 6 topic: 14
doc: 7 topic: 14
doc: 8 topic: 14
doc: 9 topic: 8

（六）可视化分析

（1）绘制主题0、主题5、主题9、主题14、主题19的词出现次数分布

import matplotlib.pyplot as plt
f, ax = plt.subplots(5, 1, figsize=(8, 6), sharex=True)
for i, k in enumerate([0, 5, 9, 14, 19]):
    print(i, k)
    ax[i].stem(topic_word[k, :], linefmt='b-',
               markerfmt='bo', basefmt='w-')
    ax[i].set_xlim(-50, 4350)
    ax[i].set_ylim(0, 0.08)
    ax[i].set_ylabel("Prob")
    ax[i].set_title("topic {}".format(k))
ax[4].set_xlabel("word")
plt.tight_layout()
plt.show()

运行结果：

（2）绘制文档1、文档3、文档4、文档8和文档9的主题分布

f, ax = plt.subplots(5, 1, figsize=(8, 6), sharex=True)
for i, k in enumerate([1, 3, 4, 8, 9]):
    ax[i].stem(doc_topic[k, :], linefmt='r-',
               markerfmt='ro', basefmt='w-')
    ax[i].set_xlim(-1, 21)
    ax[i].set_ylim(0, 1)
    ax[i].set_ylabel("Prob")
    ax[i].set_title("Document {}".format(k))
ax[4].set_xlabel("Topic")
plt.tight_layout()
plt.show()

运行结果：

五、完整代码

import numpy as np
import lda
import lda.datasets
# document-term matrix
X = lda.datasets.load_reuters()
print("type(X): {}".format(type(X)))
print("shape: {}\n".format(X.shape))
print(X[:5, :5])        #前五行的前五列
# the vocab
vocab = lda.datasets.load_reuters_vocab()
print("type(vocab): {}".format(type(vocab)))
print("len(vocab): {}\n".format(len(vocab)))
print(vocab[:5])
# titles for each story
titles = lda.datasets.load_reuters_titles()
print("type(titles): {}".format(type(titles)))
print("len(titles): {}\n".format(len(titles)))
print(titles[:5])       # 打印前五个文档的标题
print("\n************************************************************")
doc_id = 0
word_id = 0
while doc_id < 5:
    print("doc id: {} word id: {}".format(doc_id, word_id))
    print("-- count: {}".format(X[doc_id, word_id]))
    print("-- word : {}".format(vocab[word_id]))
    print("-- doc  : {}\n".format(titles[doc_id]))
    doc_id += 1
topicCnt = 20
model = lda.LDA(n_topics = topicCnt, n_iter = 500, random_state = 1)
model.fit(X)          # model.fit_transform(X) is also available
print("\n************************************************************")
topic_word = model.topic_word_
print("type(topic_word): {}".format(type(topic_word)))
print("shape: {}".format(topic_word.shape))
print(vocab[:3])
print(topic_word[:, :3])    #打印所有行(20)行的前3列
for n in range(20):
    sum_pr = sum(topic_word[n,:])   # 第n行所有列的比重之和，等于1
    print("topic: {} sum: {}".format(n, sum_pr))
print("\n************************************************************")
n = 5
for i, topic_dist in enumerate(topic_word):
    topic_words = np.array(vocab)[np.argsort(topic_dist)][:-(n+1):-1]
    print('*Topic {}\n- {}'.format(i, ' '.join(topic_words)))
print("\n************************************************************")
doc_topic = model.doc_topic_
print("type(doc_topic): {}".format(type(doc_topic)))
print("shape: {}".format(doc_topic.shape))
for n in range(10):
    topic_most_pr = doc_topic[n].argmax()
    print("doc: {} topic: {}".format(n, topic_most_pr))
print("\n************************************************************")
import matplotlib.pyplot as plt
f, ax = plt.subplots(5, 1, figsize=(8, 6), sharex=True)
for i, k in enumerate([0, 5, 9, 14, 19]):
    print(i, k)
    ax[i].stem(topic_word[k, :], linefmt='b-',
               markerfmt='bo', basefmt='w-')
    ax[i].set_xlim(-50, 4350)
    ax[i].set_ylim(0, 0.08)
    ax[i].set_ylabel("Prob")
    ax[i].set_title("topic {}".format(k))
ax[4].set_xlabel("word")
plt.tight_layout()
plt.show()
print("\n************************************************************")
f, ax = plt.subplots(5, 1, figsize=(8, 6), sharex=True)
for i, k in enumerate([1, 3, 4, 8, 9]):
    ax[i].stem(doc_topic[k, :], linefmt='r-',
               markerfmt='ro', basefmt='w-')
    ax[i].set_xlim(-1, 21)
    ax[i].set_ylim(0, 1)
    ax[i].set_ylabel("Prob")
    ax[i].set_title("Document {}".format(k))
ax[4].set_xlabel("Topic")
plt.tight_layout()
plt.show()

六、参考资料

（1） https://blog.csdn.net/eastmount/article/details/50824215

（2）http://chrisstrelioff.ws/sandbox/2014/11/13/getting_started_with_latent_dirichlet_allocation_in_python.html

七、推荐阅读

《LDA漫游指南》

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原始发表：2018-05-22，如有侵权请联系 cloudcommunity@tencent.com 删除

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