一、LDA簡介
LDA（Latent Dirichlet Allocation）是一種文檔主題生成模型，也稱為一個三層貝葉斯概率模型，包含詞、主題和文檔三層結(jié)構(gòu)。所謂生成模型，就是說，我們認(rèn)為一篇文章的每個詞都是通過“以一定概率選擇了某個主題，并從這個主題中以一定概率選擇某個詞語”這樣一個過程得到。文檔到主題服從多項式分布，主題到詞服從多項式分布。
LDA是一種非監(jiān)督機器學(xué)習(xí)技術(shù)，可以用來識別大規(guī)模文檔集（document collection）或語料庫（corpus）中潛藏的主題信息。它采用了詞袋（bag of words）的方法，這種方法將每一篇文檔視為一個詞頻向量，從而將文本信息轉(zhuǎn)化為了易于建模的數(shù)字信息。但是詞袋方法沒有考慮詞與詞之間的順序，這簡化了問題的復(fù)雜性，同時也為模型的改進(jìn)提供了契機。每一篇文檔代表了一些主題所構(gòu)成的一個概率分布，而每一個主題又代表了很多單詞所構(gòu)成的一個概率分布。
二、安裝LDA庫
pip install lda
安裝完成后，可以在python安裝目錄下的Lib/site-packages目錄下看到lda相關(guān)的目錄。
三、了解數(shù)據(jù)集
1.png
數(shù)據(jù)集位于lda安裝目錄的tests文件夾中，包含三個文件：reuters.ldac, reuters.titles, reuters.tokens。
reuters.titles包含了395個文檔的標(biāo)題
reuters.tokens包含了這395個文檔中出現(xiàn)的所有單詞，總共是4258個
reuters.ldac有395行，第i行代表第i個文檔中各個詞匯出現(xiàn)的頻率。以第0行為例，第0行代表的是第0個文檔，從reuters.titles中可查到該文檔的標(biāo)題為“UK: Prince Charles spearheads British royal revolution. LONDON 1996-08-20”。
第0行的數(shù)據(jù)為：
159 0:1 2:1 6:1 9:1 12:5 13:2 20:1 21:4 24:2 29:1 ……
第一個數(shù)字159表示第0個文檔里總共出現(xiàn)了159個單詞（每個單詞出現(xiàn)一或多次），
0:1表示第0個單詞出現(xiàn)了1次，從reuters.tokens查到第0個單詞為church
2:1表示第2個單詞出現(xiàn)了1次，從reuters.tokens查到第2個單詞為years
6:1表示第6個單詞出現(xiàn)了1次，從reuters.tokens查到第6個單詞為told
9:1表示第9個單詞出現(xiàn)了1次，從reuters.tokens查到第9個單詞為year
12:5表示第12個單詞出現(xiàn)了5次，從reuters.tokens查到第12個單詞為charles
……
這里第1、3、4、5、7、8、10、11……個單詞序號和次數(shù)沒列出來，表示出現(xiàn)的次數(shù)為0
注意：
395個文檔的原文是沒有的。上述三個文檔是根據(jù)這395個文檔處理之后得到的。
四、程序?qū)崿F(xiàn)
（一）載入數(shù)據(jù)
（1）查看文檔中詞出現(xiàn)的頻率
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
運行結(jié)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]]
觀察reuters.ldac中的前5行的前5列，發(fā)現(xiàn)：
第0行的前5列，單詞編號為0，1，2，3，4的出現(xiàn)頻次，正是1，0，1，0，0
第1行的前5列，單詞編程為0，1，2，3，4的出現(xiàn)頻次，正是7，0，2，0，0
……
（2）查看詞
# the vocab
vocab = lda.datasets.load_reuters_vocab()
print("type(vocab): {}".format(type(vocab)))
print("len(vocab): {}\n".format(len(vocab)))
print(vocab[:5])
運行結(jié)果：
type(vocab): <class 'tuple'>
len(vocab): 4258
('church', 'pope', 'years', 'people', 'mother')
可以看出，reuters.tokens中有4258個單詞，前五個分別是church, pope, years, people, mother.
（3）查看文檔標(biāo)題
# 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]) # 打印前五個文檔的標(biāo)題
運行結(jié)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個文檔第0個詞出現(xiàn)的次數(shù)
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
運行結(jié)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）訓(xùn)練模型
設(shè)置20個主題，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）主題-單詞分布
計算前3個單詞在所有主題（共20個）中所占的權(quán)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
運行結(jié)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]]
計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))
計算結(jié)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）計算各主題top-N個詞
計算每個主題中，比重最大的5個詞
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)))
運行結(jié)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）文檔-主題分布
總共有395篇文檔，計算前10篇文檔最可能的主題
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))
運行結(jié)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）可視化分析
（1）繪制主題0、主題5、主題9、主題14、主題19的詞出現(xiàn)次數(shù)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()
運行結(jié)果：
2.png
（2）繪制文檔1、文檔3、文檔4、文檔8和文檔9的主題分布
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()
運行結(jié)果：
3.png
五、完整代碼
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]) # 打印前五個文檔的標(biāo)題
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、參考資料
（1）
https://blog.csdn.net/eastmount/article/details/50824215
七、推薦閱讀
《LDA漫游指南》
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