笔者很早就对LDA模型着迷，最近在学习gensim库发现了LDA比较有意义且项目较为完整的Tutorials,于是乎就有本系列,本系列包含三款：Latent Dirichlet Allocation、Author-Topic Model、Dynamic Topic Models

案例与数据主要来源，jupyter notebook可见gensim的官方github
详细解释可见：Dynamic Topic Modeling in Python
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1、理论介绍

论文出处：

David Blei does a good job explaining the theory behind this in this Google talk. If you prefer to directly read the paper on DTM by Blei and Lafferty

参考博客：This

相关作用：

Dynamic Topic Models (DTM) leverages the knowledge of different documents belonging to a different time-slice in an attempt to map how the words in a topic change over time.
同时，DTM每个时期都有同样K个主题数，性能是C++版本的DTM模型的5-7倍

• （1）You want to find semantically similar documents; one from the very
  beginning of your time-line, and one in the very end.
  从一个时间点到另外时间点中，相似文章有哪些。基于时间的主题，里面的关键词却会发生相应变化。
  传统的相似技术不可能做到这样的效果，相同的主题基本内容不变，但是关键词会随着时间而发生变化，也就是所谓的：Time corrected
  Document Similarity 具有时间校对功能的文档相似性
• （2）第二个性能：观察主题中，关键词随时间如何变化，随着时间变化，一开始主题中的词语比较发散式，之后会变得越来越成熟。相关理论可见：
  
• （3）常规性能 the points of interest would be in what the topics are and
  how the documents are made up of these topics.

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2 Dynamic Topic Models模型需要材料

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3、Dynamic Topic Models函数解析

3.1 主函数解析

LdaSeqModel(corpus=None, time_slice=None, id2word=None, alphas=0.01, num_topics=10, initialize='gensim', sstats=None, lda_model=None, obs_variance=0.5, chain_variance=0.005, passes=10, random_state=None, lda_inference_max_iter=25, em_min_iter=6, em_max_iter=20, chunksize=100)

常规参数可参考：pyLDA系列︱gensim中的主题模型（Latent Dirichlet Allocation）
不太一样的参数：

• time_slice（最重要）,time_slice = [438, 430,
  456]代表着，三个月的时间里，第一个有438篇文章，第二个月有430篇文章，第三个月有456篇文章。当然可以以年月日以及任意计量时间都可以。
• chain_variance:话题演变的快慢是由参数variance影响着,其实LDA中Beta参数的高斯参数，chain_variance的默认是0.05，提高该值可以让演变加速
• initialize:两种训练DTM模型的方式，第一种直接用语料，第二种用已经训练好的LDA中的个别统计参数矩阵给入作训练。

最简训练模式：

%time ldaseq = ldaseqmodel.LdaSeqModel(corpus=corpus, id2word=dictionary, time_slice=time_slice, num_topics=5)

3.2 两种训练模式

• 第一种就是上面提到的最简模式，也就是initialize='gensim'：

ldaseqmodel.LdaSeqModel(corpus=corpus, id2word=dictionary, time_slice=time_slice, num_topics=5)

• 第二种模式initialize='own'： 已经有了训练好的LDA模型，可以把一些参数解析出来，然后给入模型，此时就需要调整.
  You can use your own sstats of an LDA model previously trained as
  well by specifying ‘own’ and passing a np matrix through sstats. If
  you wish to just pass a previously used LDA model, pass it through
  lda_model Shape of sstats is (vocab_len, num_topics)
  .

4、辅助参数及功能点

4.1 辅助函数一：print_topics

print_topics(time=0, top_terms=20)

不同时期的5个主题的概况，其中time是指时期阶段，官方案例中训练有三个时期，就是三个月，那么time可选:[0,1,2]，返回的内容格式为：(word, word_probability)

from gensim.models import ldaseqmodel
from gensim.corpora import Dictionary, bleicorpus
import numpy
from gensim.matutils import hellinger

%time ldaseq = ldaseqmodel.LdaSeqModel(corpus=corpus, id2word=dictionary, time_slice=time_slice, num_topics=5)

ldaseq.print_topics(time=1)
>>> [[(u'blair', 0.0062483544617615841),
  (u'labour', 0.0059223974769828398)],
  [(u'film', 0.0050860317914258307),
  (u'minister', 0.0044210871797581213)],
  [(u'government', 0.0039312390246381002),
  (u'election', 0.0038787664682510613)],
  [(u'prime', 0.0038773564950156151),
  (u'party', 0.0036428824115890975)],
  [(u'brown', 0.0034964052703373195),
  (u'howard', 0.0032628247571913969)]

返回的内容是，每个时期的5个主题，案例中为时期记号为’0’的时期中，5个主题内关键词分别是什么。

4.2 辅助函数二：print_topic_times

print_topic_times(topic, top_terms=20)

不同主题三个时期的情况

ldaseq.print_topic_times(topic=0)
>>> [[(u'blair', 0.0061528696567048772),
  (u'labour', 0.0054905202853533239)],
  [(u'film', 0.0051444037762632807),
  (u'minister', 0.0043556939573101399)],
  [(u'government', 0.0038839073759585367),
  (u'election', 0.0037979240057325865)]

返回的内容是：每个主题的3个时期，主题重要词分别是啥。

4.3 辅助函数三：doc_topics

doc_topics(doc_number)

不同文档主题偏好（常规）

doc = ldaseq.doc_topics(558) # check the 558th document in the corpuses topic distribution
print (doc)
>>> [  5.46298825e-05   2.18468637e-01   5.46298825e-05   5.46298825e-05    7.81367474e-01]

五个主题中，第558篇文章对1，4号主题更为偏好。
当然可以通过解析corpus来进行核实：

words = [dictionary[word_id] for word_id, count in corpus[558]]
print (words)
>>> [u'set', u'time,"', u'chairman', u'decision', u'news', u'director', u'former', u'vowed', u'"it', u'results', u'club', u'third', u'home', u'paul', u'saturday.', u'south', u'conference']

4.4 新文档预测

如果有一个新文档过来，怎么进行预测呢？

doc_football_1 = ['economy', 'bank', 'mobile', 'phone', 'markets', 'buy', 'football', 'united', 'giggs']
doc_football_1 = dictionary.doc2bow(doc_football_1)
doc_football_1 = ldaseq[doc_football_1]
print (doc_football_1)
>>> [ 0.00110497  0.00110497  0.00110497  0.00110497  0.99558011]

步骤就是先把doc_football_1 文档分词，然后进行dictionary.doc2bow矢量化，然后就可以用ldaseq模型进行预测，可见结果,与doc_topics 类似，返回的是该新文档，与四号主题比较贴合。

4.5 跨时间+主题属性的文档相似性（核心功能）

dtms主题建模更方便的用途之一是我们可以比较不同时间范围内的文档，并查看它们在主题方面的相似程度。当这些时间段中的单词不一定重叠时，这是非常有用的。

doc_football_2 = ['arsenal', 'fourth', 'wenger', 'oil', 'middle', 'east', 'sanction', 'fluctuation']
doc_football_2 = dictionary.doc2bow(doc_football_2)
doc_football_2 = ldaseq[doc_football_2]
>>> array([ 0.00141844,  0.00141844,  0.00141844,  0.00141844,  0.99432624])

hellinger(doc_football_1, doc_football_2)
>>> 0.0062680905375190245

步骤跟之前的预测差不多，先把文档dictionary.doc2bow矢量化，然后变成文档主题偏好向量(1*5)，然后根据两个文档的主题偏好向量用hellinger距离进行求相似。

4.6 可视化模型DTMvis

from gensim.models.wrappers.dtmmodel import DtmModel
from gensim.corpora import Dictionary, bleicorpus
import pyLDAvis

# dtm_path = "/Users/bhargavvader/Downloads/dtm_release/dtm/main"
# dtm_model = DtmModel(dtm_path, corpus, time_slice, num_topics=5, id2word=dictionary, initialize_lda=True)
# dtm_model.save('dtm_news')

# if we've saved before simply load the model
# ldaseq_chain.save('dtm_news')
dtm_model = DtmModel.load('dtm_news')

doc_topic, topic_term, doc_lengths, term_frequency, vocab = dtm_model.dtm_vis(time=0, corpus=corpus)
vis_wrapper = pyLDAvis.prepare(topic_term_dists=topic_term, doc_topic_dists=doc_topic, doc_lengths=doc_lengths, vocab=vocab, term_frequency=term_frequency)
pyLDAvis.display(vis_wrapper)

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5、话题一致性评价指标

from gensim.models.coherencemodel import CoherenceModel
import pickle

# we just have to specify the time-slice we want to find coherence for.
topics_wrapper = dtm_model.dtm_coherence(time=0)  # 标准模型
topics_dtm = ldaseq.dtm_coherence(time=2)   # 本次模型

# running u_mass coherence on our models
cm_wrapper = CoherenceModel(topics=topics_wrapper, corpus=corpus, dictionary=dictionary, coherence='u_mass')
cm_DTM = CoherenceModel(topics=topics_dtm, corpus=corpus, dictionary=dictionary, coherence='u_mass')

print ("U_mass topic coherence")
print ("Wrapper coherence is ", cm_wrapper.get_coherence())
print ("DTM Python coherence is", cm_DTM.get_coherence())

# to use 'c_v' we need texts, which we have saved to disk.
texts = pickle.load(open('Corpus/texts', 'rb'))
cm_wrapper = CoherenceModel(topics=topics_wrapper, texts=texts, dictionary=dictionary, coherence='c_v')
cm_DTM = CoherenceModel(topics=topics_dtm, texts=texts, dictionary=dictionary, coherence='c_v')

print ("C_v topic coherence")
print ("Wrapper coherence is ", cm_wrapper.get_coherence())
print ("DTM Python coherence is", cm_DTM.get_coherence())

该部分解释较少，详情可见：
We also, however, have the option of passing our own model or suff stats values. Our final DTM results are heavily influenced by what we pass over here. We already know what a “Good” or “Bad” LDA model is (if not, read about it here).