input: Write a function to analyze the sentiment of a given text and categorize it into positive, negative, and neutral sentiments. The function should use NLTK to tokenize the text and classify it using Naive Bayes Classifier. If the given text is empty, the sentiment should be categorized as neutral.
  
  assert analyze_sentiment("I love this product! It works perfectly.") == 'positive'
  assert analyze_sentiment("This is the worst experience I have ever had.") == 'negative'
  assert analyze_sentiment("Today is a good day, but I am feeling a bit tired.") == 'neutral'
  assert analyze_sentiment("") == 'neutral'
output: 
  def analyze_sentiment(text):
      if not text:
          return 'neutral'
      
      from nltk.tokenize import word_tokenize
      from nltk.classify import NaiveBayesClassifier
      from nltk.corpus import subjectivity
      from nltk.sentiment import SentimentAnalyzer
      from nltk.sentiment.util import extract_unigram_feats
      
      n_instances = 100
      subj_docs = [(sent, 'subj') for sent in subjectivity.sents(categories='subj')[:n_instances]]
      obj_docs = [(sent, 'obj') for sent in subjectivity.sents(categories='obj')[:n_instances]]
      
      train_data = subj_docs + obj_docs
      
      sentim_analyzer = SentimentAnalyzer()
      all_words_neg = sentim_analyzer.all_words([mark_negation(doc) for doc in train_data])
      
      unigram_feats = sentim_analyzer.unigram_word_feats(all_words_neg, min_freq=4)
      sentim_analyzer.add_feat_extractor(extract_unigram_feats, unigrams=unigram_feats)
      
      training_set = sentim_analyzer.apply_features(train_data)
      trainer = NaiveBayesClassifier.train
      classifier = sentim_analyzer.train(trainer, training_set)
      
      words = word_tokenize(text)
      feats = sentim_analyzer.extract_features(words)
      sentiment = classifier.classify(feats)
      
      if sentiment == 'subj':
          return 'positive'
      elif sentiment == 'obj':
          return 'negative'
      else:
          return 'neutral'
  