pLSA(probabilistic Latent Semantic Analysis)，概率潛在語義分析模型，是1999年Hoffman提出的一個被稱為第一個能解決一詞多義問題的模型，通過在文檔與單詞之間建立一層主題（Topic），將文檔與單詞的直接關聯轉化為文檔與主題的關聯以及主題與單詞的關聯。這里采用EM算法進行估計，可能存在差錯，望積極批評指正。

# -*- coding: utf-8 -*-import mathimport randomimport jiebaimport codecsimport datetimeclass pLSA_lph():  def __init__(self, ntopic = 5):    self.n_doc = 0    self.n_word = 0    self.n_topic = ntopic    self.corpus = None    self.p_z_dw = None    self.p_w_z = None    self.p_z_d = None    self.likelihood = 0    self.vocab = None    self.stop_words = [u'，', u'。', u'、', u'（', u'）', u'·', u'！', u' ', u'：', u'“', u'”', u'/n']  # 每行和為1的正實數，概率分布;  def _rand_mat(self, sizex, sizey):    ret = []    for i in xrange(sizex):      ret.append([])      for _ in xrange(sizey):        ret[-1].append(random.random())      norm = sum(ret[-1])      for j in xrange(sizey):        ret[-1][j] /= norm    return ret  #從文本中計算詞頻稀疏矩陣，這里存儲模型仿照LDA  def loadCorpus(self, fn):    # 中文分詞    f = open(fn, 'r')    text = f.readlines()    text = r' '.join(text)    seg_generator = jieba.cut(text)    seg_list = [i for i in seg_generator if i not in self.stop_words]    seg_list = r' '.join(seg_list)    # 切割統計所有出現的詞納入詞典    seglist = seg_list.split(" ")    self.vocab = []    for word in seglist:      if (word != u' ' and word not in self.vocab):        self.vocab.append(word)    self.n_word =len(self.vocab)    CountMatrix = []    f.seek(0, 0)    # 統計每個文檔中出現的詞頻    for line in f:      # 置零      count = [0 for i in range(len(self.vocab))]      text = line.strip()      # 但還是要先分詞      seg_generator = jieba.cut(text)      seg_list = [i for i in seg_generator if i not in self.stop_words]      seg_list = r' '.join(seg_list)      seglist = seg_list.split(" ")      # 查詢詞典中的詞出現的詞頻      for word in seglist:        if word in self.vocab:          count[self.vocab.index(word)] += 1      CountMatrix.append(count)    f.close()    self.corpus = CountMatrix    self.n_doc = len(CountMatrix)    #初始化    self.p_z_d = self._rand_mat(self.n_topic, self.n_doc)    self.p_w_z = self._rand_mat(self.n_word, self.n_topic)    self.p_z_dw =[]    for k in range(self.n_topic):      self.p_z_dw.append(self._rand_mat(self.n_doc, self.n_word))  def _e_step(self):    for k in range(self.n_topic):      for d in range(self.n_doc):        for j in range(self.n_word):          _d_wz_zd = 0          for kk in range(self.n_topic):            _d_wz_zd += self.p_w_z[j][kk]*self.p_z_d[kk][d]          if _d_wz_zd <= 0:            _d_wz_zd = 1e-6          self.p_z_dw[k][d][j] = self.p_w_z[j][k]*self.p_z_d[k][d]/_d_wz_zd  def _m_step(self):    print "updating Pn(Wj|Zk).../r"    for j in range(self.n_word):      for k in range(self.n_topic):        _d_dw_zdw = 0        for d in range(self.n_doc):          _d_dw_zdw += self.corpus[d][j]*self.p_z_dw[k][d][j]        _d_dw_zdw_sum = 0        for jj in range(self.n_word):          _d_dw_zdw_i = 0          for d in range(self.n_doc):            _d_dw_zdw_i += self.corpus[d][jj]*self.p_z_dw[k][d][jj]          _d_dw_zdw_sum += _d_dw_zdw_i        if _d_dw_zdw_sum <= 0:          _d_dw_zdw_sum = 1e-6        self.p_w_z[j][k] = _d_dw_zdw/_d_dw_zdw_sum    print "updating Pn(Zk|Di).../r"    for k in range(self.n_topic):      for d in range(self.n_doc):        _d_dw_zdw = 0        for j in range(self.n_word):          _d_dw_zdw += self.corpus[d][j]*self.p_z_dw[k][d][j]        _d_dw_zdw_sum = 0        for kk in range(self.n_topic):          _d_dw_zdw_i = 0          for j in range(self.n_word):            _d_dw_zdw_i += self.corpus[d][j]*self.p_z_dw[kk][d][j]          _d_dw_zdw_sum += _d_dw_zdw_i        if _d_dw_zdw_sum <= 0:          _d_dw_zdw_sum = 1e-6        self.p_z_d[k][d] = _d_dw_zdw/_d_dw_zdw_sum  #計算最大似然值  def _cal_max_likelihood(self):    self.likelihood = 0    for d in range(self.n_doc):      for j in range(self.n_word):        _dP_wjdi = 0        for k in range(self.n_topic):          _dP_wjdi += self.p_w_z[j][k]*self.p_z_d[k][d]        _dP_wjdi = 1.0/self.n_doc*_dP_wjdi        self.likelihood += self.corpus[d][j]*math.log(_dP_wjdi)  #迭代訓練  def train(self, n_iter = 100, d_delta = 1e-6,log_fn = "log.log"):    itr = 0    delta =10e9    _likelihood = 0    f = open(log_fn, 'w')    while itr < n_iter and delta > d_delta:      _likelihood = self.likelihood      self._e_step()      self._m_step()      self._cal_max_likelihood()      itr += 1      delta = abs(self.likelihood - _likelihood)      t1 = datetime.datetime.now().strftime('%Y-%m-%d-%y %H:%M:%S');      f.write("%s iteration %d, max-likelihood = %.6f/n"%(t1, itr, self.likelihood))      print "%s iteration %d, max-likelihood = %.6f"%(t1, itr, self.likelihood)    f.close()  def printVocabulary(self):    print "vocabulary:"    for word in self.vocab:      print word,    print  def saveVocabulary(self, fn):    f = codecs.open(fn, 'w', 'utf-8')    for word in self.vocab:      f.write("%s/n"%word)    f.close()  def printWordOfTopic(self):    for k in range(self.n_topic):      print "Topic %d"%k,      for j in range(self.n_word):        print self.p_w_z[j][k],      print  def saveWordOfTopic(self,fn):    f = open(fn, 'w')    for j in range(self.n_word):      f.write(", w%d"%j)    f.write("/n")    for k in range(self.n_topic):      f.write("topic %d"%k)      for j in range(self.n_word):        f.write(", %.6f"%self.p_w_z[j][k])      f.write("/n")    f.close()  def printTopicOfDoc(self):    for d in range(self.n_doc):      print "Doc %d"%d,      for k in range(self.n_topic):        print self.p_z_d[k][d],      print  def saveTopicOfDoc(self, fn):    f = open(fn, 'w')    for k in range(self.n_topic):      f.write(", z%d" % k)    f.write("/n")    for d in range(self.n_doc):      f.write("doc %d" % d)      for k in range(self.n_topic):        f.write(", %.6f" % self.p_z_d[k][d])      f.write("/n")    f.close()