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Created February 12, 2018 14:08
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Topic Modeling From Scratch in Python
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{"cells":[{"metadata":{"_uuid":"ae3e9a2d4fdf3c5781639d48f36e2b2c0e7c9f7a"},"cell_type":"markdown","source":"**Topic models** extract the key concepts in a set of documents. Each concept can be described by a list of keywords from most to least important. Then, each document can be connected to those concepts, or topics, to determine how representative that document is of that overall concept. **Latent Dirichlet Allocation (LDA)** is a common method of topic modeling. This technique uses a generative probabilistic model where each document consists of a combination of several topics and each term or word can be assigned to a specific topic.\n\n![](http://i65.tinypic.com/120t3rt.png)\n\nThe following pseudocode give a simple overview of the algorithm:\n\n![](http://i68.tinypic.com/1zbsd5f.png)\nFor the math behind in this algorithm I recommend you to read the following references: \n* Original LDA paper (journal version) Blei, Ng, and Jordan. \"Latent Dirichlet Allocation.\" JMLR, 2003.\n * http://www.jmlr.org/papers/volume3/blei03a/blei03a.pdf\n* Latent Dirichlet Allocation in Scala Part I - The Theory:\n * http://alexminnaar.com/latent-dirichlet-allocation-in-scala-part-i-the-theory.html\n* Latent Dirichlet Allocation: Towards a DeeperUnderstanding:\n * http://obphio.us/pdfs/lda_tutorial.pdf\n* Clustering and the EM algorithm:\n * https://www2.cs.duke.edu/courses/fall07/cps271/EM.pdf\n\n"},{"metadata":{"_cell_guid":"a860ad43-4e9a-43da-95df-f2c025643568","_uuid":"6483261e15a8dd27bc1405fa5641cc858ba0a9e2","trusted":true,"collapsed":true},"cell_type":"code","source":"# This Python 3 environment comes with many helpful analytics libraries installed\n# It is defined by the kaggle/python docker image: https://github.com/kaggle/docker-python\n# For example, here's several helpful packages to load in \n\nimport random\nfrom collections import Counter\nimport nltk\nimport matplotlib.pyplot as plt\nimport re\nfrom re import RegexFlag\nfrom wordcloud import WordCloud \n","execution_count":17,"outputs":[]},{"metadata":{"trusted":true,"collapsed":true,"_uuid":"52bee93eca41ff5c7f833f11e50bb5d64ff11051"},"cell_type":"code","source":"class LDA(object):\n '''\n Latent Dirichlet Allocation (LDA), a topic model designed for text documents.\n \n Topic models extract the key concepts in a set of documents. \n Each concept can be described by a list of keywords from most to least important. \n Then, each document can be connected to those concepts, or topics, to determine\n how representative that document is of that overall concept.\n '''\n def __init__(self, K, max_iteration):\n self.K = K\n self.max_iteration = max_iteration \n \n def sample_from_weights(self, weights):\n '''\n This function randomly choose an index based on an arbitrary set of weights.\n Return the first weight's index that is greater than or equal to a random number.\n '''\n total = sum(weights)\n rnd = total * random.random() # uniform between 0 and total\n for i, w in enumerate(weights):\n rnd -= w # return the smallest i such that\n if rnd <= 0: return i # sum(weights[:(i+1)]) >= rnd\n \n def p_topic_given_document(self, topic, d, alpha=0.1):\n '''\n P(topic|d,Alpha)\n The fraction of words in document d\n that are assigned to topic (plus some smoothing)\n ''' \n return ((self.document_topic_counts[d][topic] + alpha) / \n (self.document_lengths[d] + self.K * alpha))\n \n def p_word_given_topic(self, word, topic, beta=0.1):\n '''\n P(word|topic,Beta)\n The fraction of words assigned to topic\n that equal word (plus some smoothing)\n ''' \n return ((self.topic_word_counts[topic][word] + beta) / \n (self.topic_counts[topic] + self.W * beta))\n \n def topic_weight(self, d, word, topic):\n '''\n P(topic|word,Alpha,Beta) = P(topic|d,Alpha) * P(word|topic,Beta)\n Given a document and a word in that document,\n return the weight for the k-th topic\n ''' \n return self.p_word_given_topic(word, topic) * self.p_topic_given_document(topic, d)\n \n def choose_new_topic(self, d, word):\n return self.sample_from_weights([self.topic_weight(d, word, k)\n for k in range(self.K)])\n \n def gibbs_sample(self, document_topics):\n '''\n Gibbs sampling https://en.wikipedia.org/wiki/Gibbs_sampling.\n '''\n for _ in range(self.max_iteration):\n for d in range(self.D):\n for i, (word, topic) in enumerate(zip(documents[d],\n document_topics[d])): \n # remove this word / topic from the counts\n # so that it doesn't influence the weights\n self.document_topic_counts[d][topic] -= 1\n self.topic_word_counts[topic][word] -= 1\n self.topic_counts[topic] -= 1\n self.document_lengths[d] -= 1\n \n # choose a new topic based on the weights\n new_topic = self.choose_new_topic(d, word)\n document_topics[d][i] = new_topic\n \n # and now add it back to the counts\n self.document_topic_counts[d][new_topic] += 1\n self.topic_word_counts[new_topic][word] += 1\n self.topic_counts[new_topic] += 1\n self.document_lengths[d] += 1\n \n def run(self, documents): \n # How many times each topic is assigned to each document.\n self.document_topic_counts = [Counter()\n for _ in documents]\n # How many times each word is assigned to each topic.\n self.topic_word_counts = [Counter() for _ in range(self.K)]\n # The total number of words assigned to each topic.\n self.topic_counts = [0 for _ in range(self.K)]\n # The total number of words contained in each document.\n self.document_lengths = [len(d) for d in documents] \n self.distinct_words = set(word for document in documents for word in document)\n # The number of distinct words\n self.W = len(self.distinct_words)\n # The number of documents\n self.D = len(documents) \n # document_topics is a Collection that assign a topic (number between 0 and K-1) to each word in each document.\n # For example: document_topic[3][4] -> [4 document][id of topic assigned to 5 word]\n # This collection defines each document's distribution over topics, and\n # implicitly defines each topic's distribution over words.\n document_topics = [[random.randrange(self.K) for word in document]\n for document in documents]\n \n for d in range(self.D):\n for word, topic in zip(documents[d], document_topics[d]):\n self.document_topic_counts[d][topic] += 1\n self.topic_word_counts[topic][word] += 1\n self.topic_counts[topic] += 1\n \n self.gibbs_sample(document_topics)\n \n return(self.topic_word_counts, self.document_topic_counts) \n \n def plot_words_clouds_topic(self, topic_names, plt):\n for topic in range(self.K):\n data = [] \n text = \"\"\n for word, count in self.topic_word_counts[topic].most_common():\n if count > 1: \n data.append(word) \n text = ' '.join(data)\n # Generate a word cloud image\n wordcloud = WordCloud().generate(text) \n plt.figure()\n plt.imshow(wordcloud, interpolation='bilinear')\n plt.axis(\"off\")\n plt.title(\"Topic #\" + str(topic_names[topic]))\n plt.show() \n ","execution_count":18,"outputs":[]},{"metadata":{"trusted":true,"_uuid":"1d57bde157750f85dcb0a8573b4168ad8b7a5876"},"cell_type":"code","source":"random.seed(0) \n \n# Collection of documents. \ndocuments = [\n ['The sky is blue and beautiful.'],\n ['Love this blue and beautiful sky!'], \n ['The quick brown fox jumps over the lazy dog.'], \n [\"A king's breakfast has sausages, ham, bacon, eggs, toast and beans\"], \n ['I love green eggs, ham, sausages and bacon!'], \n ['The brown fox is quick and the blue dog is lazy!'], \n ['The sky is very blue and the sky is very beautiful today'], \n ['The dog is lazy but the brown fox is quick!'] \n]\n\ntopic_names = ['food', 'weather', 'animals']","execution_count":19,"outputs":[]},{"metadata":{"_uuid":"0e94b2b824c5b049fec62aa30af048a49b9d68cc"},"cell_type":"markdown","source":"We will need to pre-process the text removing special characters, extra whitespaces, digits and stopwords."},{"metadata":{"trusted":true,"collapsed":true,"_uuid":"ab0d714c26a664be308886dbaf1ef43156e60178"},"cell_type":"code","source":"def pre_process_documents(doc):\n wpt = nltk.WordPunctTokenizer()\n stop_words = nltk.corpus.stopwords.words('english')\n for i in range(len(doc)): \n # lower case and remove special characters\\whitespaces\n doc[i][0] = re.sub(r'[^a-zA-Z\\s]', '', doc[i][0], flags=RegexFlag.IGNORECASE | RegexFlag.A)\n doc[i][0] = doc[i][0].lower()\n doc[i][0] = doc[i][0].strip()\n # tokenize document\n tokens = wpt.tokenize(doc[i][0])\n # filter stopwords out of document\n filtered_tokens = [token for token in tokens if token not in stop_words] \n doc[i] = filtered_tokens\n return filtered_tokens\n\npre_processed_documents = pre_process_documents(documents)","execution_count":20,"outputs":[]},{"metadata":{"_uuid":"c3230b6ec1020203fe5aa11e805aac3ae24d2457"},"cell_type":"markdown","source":"Configure and run LDA:"},{"metadata":{"trusted":true,"_uuid":"31e5c3f156e3e37d78e5f5d76a1a37e8013c5924"},"cell_type":"code","source":"K = 3 \nmax_iteration = 1000\n\nlda = LDA(K, max_iteration)\nlda.run(documents) \nlda.plot_words_clouds_topic(topic_names, plt) ","execution_count":21,"outputs":[{"output_type":"display_data","data":{"text/plain":"<matplotlib.figure.Figure at 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SXK+gbfP7Vy9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\nrwujHqfPWisdt887h8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DAs5DuZt5XWszjlK2GzjgyGq87ou4VTtmmtJzHtZx6/QB/PIA/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\n858BaizkZuDBWMgAAAAASUVORK5CYII=\n"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"<matplotlib.figure.Figure 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A6wtO+O03ZXAtCtrssSq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5hxsNL2kd5dCLwyUtZJnZjSrJ3xLomQWAupfwlA5eaV67Ark/5XQ5zFPtH/TGBO4XrBo5vLMdd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\ng4G0sWNNukwAAAAASUVORK5CYII=\n"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":"<matplotlib.figure.Figure 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VZ3RZiLEyGf20n1sMLDj\nW/7qIpe+chyvskrPZ4VCsWUoEdgCon0Jel7chh5qtra5ZZvr3z5H6UZuc4NIyF1aYPL7l3CKzY5r\nM2Yx+MZuzJi1qWFKU3mufP0Upcnm+WqGxuBro/S/siOwj4PQNXqeG2L4U3sxos3NfirzJa587RSF\nq6rjm0LxoFAi0GaEJkju7AyMgAFYPjfHwsnpm9E/m8Grusy9e4P8leBFNHOkn9hgalNjSNdn/r0J\nJv70Qt3nchdWMszoXzlKfKSj6VqkJ86uv3qMaED+glt1uPHdi8z85Fpb3guFQrExlAi0GT1i0vPc\ncGAilO94zL9/Y/OngNvIjy2xdHoar9YcV29ELXo/MnJPm/29cEsO1759jqk3r+LZblP9pfhwin3/\nyXP1An4NNEtnz19/mvSeTNP4vusz+9Nxxr55Zt1hpgqFor0oEWgzRsSk6+hA4LXyTIHcpcW27nyl\n67N0epbaUnOWL0D3s0P3TFBbC7WlMpe+fJyl07NIeZcDV9THGf3iYfSQgTA0Rj6zl4GPj4LW7AjO\nnp/j0lc+oDyV3/S8FArF5nioQ0QfRUKdEWIDicBrldkipan2nQJWyF1dpJarEu1PNl2L9ScJZ2KU\nZzZfAK84nuXyHxwnNpAk2nfrGYUQmDGL4c/sIz+2jFOqseMLhzHjVlM0UG25zJWvnyJ7/v7nA5h6\nhLCVwjKi6HoIXTMQQkNKH893cb0qtlumamdxvdYJgg+6mIVAYJkxQmYSU4+g6xaaZqChIZFI6eH5\nDo5XxXFKVJ08nv9wOd4NPUTITGAaUQw9hKFZCKEjhAZS4ksP17dx3DI1p4jtFPGlyiLfCpQItJn4\nSEdwhrOE6nKZ6kLwjn0zVOdK2NkqUsqmRVezdBLbO9oiAgDz793g+p+cY+9vPNOUmR3tT7D7S0fx\nPZ/ESDowHHTizy4y/dZYW+ayFgQa0XAn6dgIqdgAsXCmsfhE0DQTTWj40sfzbRy3Qs3JU6oukCtN\nsVy4RsXOceeyL5HSD3yvt5qQEScZGyAR7SMWyhAJpbGMOKYRrouA0JGNBdTza9humZpdoFRdIF+e\nJle6QaWWRfJgQnGF0IiFMqQTIyQivUSs9M3PwtBDaJqBQAPkLVF2ilTsHFU7t2Ehq9SWmc9dxHY3\nV/jwcUWJQJtpdQrwPR97uYJbbn9DGN/xqC6UkJ5EGHeJgKFt2jl851g+4//+Aqk9GQY+tvPOsXSt\nUVdIBIaDLhyf5Nq3zuLb98cRHDLj9Hc+RSa1m3i4G9NoztkA0IWGrhlYRpRYuIuO+HZ60iUK5Rnm\ncheYXT6L494Sb1+6SOkhxP359TH0ML3pA/Sk99ZFzEqit+hxLARo6Bi6RchMkIj00pXcSc0pUa4t\nsFS4xszSacq1+xmRJYiHM/R1HaYjvo1YOIOpNycN3v56Q7cwdIuwlSQZCzavrpWl/Bi58qQSgRYo\nEWgz4UxwgpZvu9Sy1S2zJVTmS/Vs27vyAoSuEe6OtXesuSJXvnaKSHec9L7uO8tOa83+ByklxetZ\nLn35OKX74AcQCFKxIXYNvkYi0o+hh9a1axdCEDLjWMlRkrEBMslRrk6/SaE8g0TieTae77ZsNt8u\nhNBJx4bZ3vcSqehASxG79300wlaCkBknGR2gN32A63M/Y2b5LP4Wm4kMPURf52GGMs8QC3Wiaa17\nZygeDEoE2kyrxCnf8QPj+duFk68i/eZjvtC1TVUWDcSXLH04zZWvn+TAb71ApDfR8hdbSkltsczl\nr55g4cRUWzuTBaEJg67kKHuHP0nEStdtzBtECIFlROlO7SEa7uLCxJ+xVBjD9W0838Ek3MaZ30nI\njDPQdZSh7mcIm0lg8yXVhRAYeoh4pIe9Q58mGR3k+uxPA0xe7cE0omzvfYmRnufRhKEW/4cUJQJt\nRg8IDYW6OWgrzSBu1QksmyQEGOHmRK3NIj3J9FvXiA+mGP2VI5jx5haRAG7ZYeLPLjL1w6tbbgbS\nhE53ei+7B18nYnW0bdFZsWXvHfoUF278Gb7vbOkOOmKl2d73Mv2dT2Hom0v2C0IIgWmEGcocI2wl\nG6ecaWQbhcDUI2zreZGRnufRtdY/f770cNwytlvG912klGhCQ9ctLCOGoYc39DlKKfF8G9erUnXy\n+L5yKrdCiUCbCcqcBUDKdVXcXC++6wcXzxOi9Zw2iVdxWDo7x3Cu2lIEnEKN5fNzgYlm7UWQjo+w\nvfelewqAlBLHLVOxs9hOEU+6CDR0zcQyooRD6SabtRCCWLiLHX2vsFwY2zLnqmlE2d73MgNdR1va\n/VeewZceVTtHzSngejX8m89hYZkxwlZyVdu7phlkkrsQQnB56s8plGdpx4lACJ3ejgMMZo61FADP\nd8iXp8kWxylVFqg6OVyvhpQ+mmZi6mEioQ6S0QE6E9sIW82BBrfeC59ybRnbKWK75ZuiYrslbKdE\nubZEzWlvj/DHCSUC7Wa1tWELT8OrbZbW20NhrVjpCH0vbSPUGW35mlBHhJ7nh1k6PUN1fuscc5FQ\nmuHuZ0lE+1Y1TVXsZWaXz5ErTVKz8zheBV96CASaZjRCF5OkYoN0p/YQC98qeieERio2QDSUxtC3\nwhQkGMo8Q3/n4VUFwHErLOavsli4QqW2jO1W8HwbKf3Gc9QXUcuMk4j20ZPaSyLaG3gvTdPpSozi\n97mcm/hTbGfzvRySkT4Guo5gGc2+KCklrl9jfO4d5pbPUaourBr6aRkx0vERhjJP05nYHuiHkdJn\nZulD5rIXcL1q41/7gUVBPWooEWgzrRLBhBCINiRttUIYeqASSCm3pCyDZukMvj7K4OujGJHWx309\nZDDw6k6KE1nG/ujMlhSK04RJb3o/XcldaC18AFL6LOQuc3XmLUrV+VXzAGCSpcJVZpfPMtB1hL7O\nQzd31Lpmolvti7a6nZ7UXoYyx9C1ZhOQlPXQ1OXidSbm3yVXmsR2ivc04SzmrzC3fI6BriMMdD2F\nEXAy0DSdTGoPI9VFrkz/sDkZcB3omkkmtZtEtL+FGEvGpt/ixsL79/gM6thuifnsBUrVBXYPvkEm\ntQtN3BmaLIRGMjrA9bm3cT2Vgb5elAi0maC2jFDvL7AVtvkVzKgVGJaJL3HL7V14hSboeXaI0b9S\n7w9wz7klQox+8SnK04W19R9YJ9FQmqHuZ1vaz33fZTZ7jkuT36Nqry06yfVq5MtTlKoLlKoL7Oj7\nKCGztQN8s8TCGYZ7nw80e6zYt6cWT3Ft9qfU7Nya7feeb1OozHB5aol8eZodfR8lFu5qcpjrmsFg\n5hjZ0jgLucsbfo5oOEMmtSvwJCOlZHrpNJOLJ9YkADe/D59SdZ4r0z8iGuq843RWR5CKDdKT3sfU\n4okNz/1JRZWNaDPVgCbtAJqpYyaC7ebtwEqHA0VAerJlSYmNEt/Wwe5ff4b4UPOC5bteYP+BSE+c\nvb/xDMmdweW1N4pA0Nt5iGiouYAd1E8Ai4WrXJn64ZoF4HY832Zi/l0m5t/ZMmewppn0dz5FOtbc\ngQ7qzzC7fIbLU9+namc35MD1fJvppQ+5PPXnlGvLgaXBLSPGtp6XsMyN9qGo5wMkIsGmJ9spMrV4\n/I6ci/VQKE8zn72AlHeebOuO7gjdqd1bZKZ7vFEi0GaqLTqh6ZaOlQ431dJpF+FMLNDc5Ht+S2Ha\nCEbUZMfnD9J5qPkX3Xc9Fk5MM//eRGBBu9SuDDu/WC8n0S5MI0pPam/L6xU7x+TCCcq15U2NM7lw\nglx5clP3aMVKQleQGQigWJ3j2uzP1rV7DkYyn7vI1OKJwOxbIQSJSA+96X1sxIGlaxaJSF/L/Ils\n6camP4e57Hl82WzeFEIjEuogFg6u3qtojRKBNlOcyAb+vdA1QulIWxfAFfSwQTgTRegBu0jXD+wF\nsFEGPj7K4Bu7Ak0WxfEcl37/A87/i/fIX1kMbOXZ/7GdDP3CntU92esgFRsi3MJG7zds6MvF62w2\n6sVxy0wuHMffhL08CE0YpGNDxCM9gdel9Jlc+IBytT0ZvlJ6TC2coFSdDzwNmEaUruQoYTM48301\ndM0gFm590itW5jZ8ClihHukTvNGyjFjLE6GiNUoE2kxxMocfsAsGCHVGiXRvvOVjK6K9CaxkcDy1\n73gUrm9u97VCx8FednzhEFbiziO3lBK3ZHPt22dZPDlN9sIcV75+KtA/YsYstv/SATLHNlcKYIX6\nDjp452k7RZbyY5teeAAkklxpilK1vYXvLDNGR2J7y1DKQmWWxXx7Q1JrbpGZpTOB1+qngb4NlWrQ\nNIOQ1VzEEOohobU2FLLzpUelRckLU48QMoPHV7RGiUCbcQo1ls/NBV6LDSSJb0u3fcz0vu6WYZrF\niWxbitbFhlLs+bVjpHZlmnwP0pdMvznG9W+dxXc8pCeZ+uFVxr9zvtk/oAkSOzrZ9VePktixuV2b\nqUdIRvsRd0WLQCMctLbMcvHapsa4Hdstspi/2takqoiVpiM+EnhNSslc9jw1p/2lNuZy57Hd4B11\n2EqSjg23NE+1QggNywj+OfR8B9fbfN0sicRuIeorIb6K9aFEoM24ZYe5dycCTSHhTIyOfT2BrRY3\nih426DjUR6hFlM78ezcCy0msBysdZvSLh+l5cQQtoGdx7tIC5//lu3f4AXzH4/IfHGfx1HST2UFr\ntJ3c+cWnCHW1zjG4F/FID1aLejpS+hQr8xtyBrfC9Wzy5Wl8vz0ht5rQScUGMI3gz852iuRKk1tS\nBtpxyyzlg6u5CqGRiPa3NLO1QiDQRPDPtu+77SkFLWXL90OIeq7HZkqFPImod6vN+LbH0ulZqgER\nOUITZI4NEB9u32kgOdpFx76ewMXZrTjMvz+5KXO4ZukMvDrKwOu70K1ms0tlvsilrxynEuAQry1X\nuPyV44Gd1DRDZ/Djowy+viuwF/NaiIY70Vvs/HzpUKjMbOi+rZHYTgG7TdmnmmaQjA62vF6qLW5Z\npqvnu2RLN1pej0XqJbfXSyuzlRBao0z0JhECbbXqrVI++IYPjxhKBLaA4kSWheNTgdeSO7voeX64\nZY2h9WBETXpfGCGxPdissvThDMUbwY7qNSEgtTvDzl8+TDjA3ORWHCb+/UXm370RGPsvfcnih9Nc\n/8457HxzEo+VCrPzC4dI7+/ZUDZ12ExhtDBZeL5Lqbqw/pveA8ettm1hFkJfNZqlUstiO1uTZS2l\nR7m21HJXHTJihK046/lgpPRx/WCTj66Zbam6KqjXPWo1vuc7KlN4nSgR2AJqS2Xmfj4eGJqphwy2\nfW4/iR2dmxtEQMf+Xgbf2BWYsetWXW587xJOceN2WDMeYveXjgaKjPQlCx9MMv6n51etC+SWHG58\n9xJzb483+QcA4kNpdn/pWJOz+d7Uyz23Wlik9KnYmxDAFriNZi3tQNdMIqHWp8J6TaCty4B13ErL\nMhFCaESsjlXLV9yNLz1sO1ggdc3EMmObNtUIIYhYwZse13dwvMqm7v8kokRgC5CeZO7dCWZ/fj2w\nZEN0IMnB3/kIsaHUxkIlNUFyV4b9v/VCoGlJ+j5zP7/Owompeo+BDaAZGrt+5Qg9z480O4KlJHdl\ngStfP0UxwNRzN5W5Ipe/epLs+blmX4mAzNMD7P61Y2hWs4O3FYZmNfoEBPcv8KXXljo4d+N59Q5k\n7cBaRcQ836lX1gyIiW8Xnm9TXeVUE7JSq5temu7nUKwGB0UIoREP92C2cByvlYiVJtwiAslxSlRq\n7Rf+xx0lAltEbanM9W+fJXtxvmnhE0LQdaSfY//Na2SODWDE1h6FYcQsMscGOPpfv0rHgZ7ABbpw\nPcu1b5+jPL0xp6gwNAY+PsrIZ/c1ma2klNSWK4x94zTz799YW38ACdnz81z6gxP1Dmh3OYr1kMHw\np/Yw/Mk9a654quvWqtErrlvdkgXU9128FiaP9RIyWocLe56z5XVwfN9dVdDqJ621C7Pn1cgWb+C1\nKNvcmdi+yWQuQW/HwcBw2npxwBzFSrAIKVqjRGALWTozy9i/O01tqRwYIdN1pJ+jf/fj7P7SUbqf\nGyLSG0cEOHg1QyPal6D72SF2f+kYT/+3r9Gxv6c5KkaCna1y/U/OsXhyamMOMlEPOd35lw/Xs5Dv\nTgrzJNNvXmXiuxfXff+Zt8a48d1LTf4DIQShrig7Pn+IzoN9azodaZqx6gLl+ltTutpvNHFvB6Ye\nppXN3Zfulnf9qj9La0Ez9XBg+G0rJJJidY5iZTbweiSUpr/zMKa+sSZHiWgfPel9gXPypUu+PLUl\nJsDHHVVAbiuRMPnnV4gNptjrOq4/AAAgAElEQVT1paNNBeSEJogPpdj9a08z+NooucuLlKbz2Nnq\nzXBLPWwQ7ogSHUiQ3NFFtD/R1OB9BbfmMP6n55n4s4t41Y2F40V7E+z4pUOkdncHhl7mLi1w9d9+\niF9b/y5b+pKxPz5D+kAP3cfujIoRQpAc7WTHFw5RnitSvkcbyroZqPUeZqsWUIm/qSqbt1NvrN5i\nHOm3PTu5eQy5arjrek4BK1RqyyzmrxKP9ATu2Ps6DlKqzDEx//66QkZj4Qw7el8mGmruFSGlpGbn\nmV0+iwoNWj9KBLYY3/YY++ZpjKjFjs8fDAyH1AyN+EgH8ZEOpC/xau5NJ6pmaOjhe7fmk77kxncv\nceVrp7CzG7NZG1GTwV/YRd/L29ED7PO1XIUrXz3ZsjTGWqjMFrjy1ZPEBpJEe+8MQdQMnZ4XRsiP\nLXHlqydXrX4q0FZ9T7ZqAZVSti1ZbDUnaX2UrY5yWX0MIXTEOsO2XK/GfO4iXclRUgFZx7pmsa33\nJUwjytTiyXs2vNeEQWdiO0Pdz9CZ2NGyn8Bs9twWhAQ/GSgRuA/Ulipc+vIH1LJldn7hMOGuKGjB\nPWOFJlatz3830pc4JZvr3z7Lla+forqwsZDClRyG0S8+hRVQ7dSruVz747PM/vz6pkpBS08y//4k\nY390mj2//gxm1LrDImLGLHZ+4TD5K4vM/OTahsda7+K1LtrUpWc1MRGNf7aa1caoC976yZenmVw4\nTthMYJnxpg5tITPBSM8LdKf3kitNki3eoFSdx2k4wg3NwjSiJKJ9dCZ2kIz2YxmxwJNJvcfCNSbm\n3m3bCe1JQ4nAfaK2XOHK106Rv7zEzi8epuNAD2YitOH69Cv1enKXF7n2zTPM/Ow6boteBmshNpxm\n/994ITCD13c8pt8aY/w75zcVcrqCV6n3HY4PpRn65J6mU4eVDrP/N5+neCNH4WrwTlHK1c0yW5o1\n2qbid77vIgn2Cggh1mWP3whCaKuOUe/Lu34ZkNJjaukkYSvOcPfzTRnRNxveh3uIhTP0dx5ufJay\n8X7c6uSmCb3lZ+n7LtnSZL1PxBaU1nhSUCJwH/Ftj9mfXyd7YY6hT+ym76M7SGzvIJQOI7S1LVrS\nl9SyFQpjS8z+fJypH16hPL255CUzGWLPX3+axGhns73Vl+QuLzL2R6fbWo20Ol9i7I9OExtK0nW4\n/44y2EII4iMd7P2NZ/jwH/2Y2nKzeUtKb1URWG/dm7WiNRamdlAvDR28yGrCWFeM/kYQQlu1CfxK\ny8qN4PsOV2d+DGgMZo4GZh8LIRDosM73U0qJ61VZzF9hbPYnFMrKDLQZHisRWD43x6U/OBFod1/6\ncCawdO6DoLZc4crXP2T2Z+N0Hu4jtTtDfChFpDdOqCOKETXRDA1JfRfuFm1q2QqVuRKlqRy5S4ss\nfThNcbw9kRB6yCB3aSFYTHxJ7tICS6fb/4uWvTjPxd8/Tsf+ycBeCE6x1jKz2vNtfNnaZ7BVzUWE\n0NcVO78attvadKdpxpYJ2c0xhL7q++S45U2ZWHzfZWz2J1SdHP0dh0lG+9FbdH9bK/WaUHPMLJ9h\nZum0igZqA4+XCJyZZflMcHjaQ4eUFCeyFCeyGFGTcCZGqCOCmQihhw20xqLouz5uxcEp1LCzVaqL\npU21izQjSTJ7XkAIjaWx41Rzc1TnS1z5w5PterJVCaf76D34MZCwPHaCuZ9fZO7n4+u+j+vZeF7r\n90HXTXTNbHvxNU0zNr2QrWA7xfoiG7AT1hvN4uvGoq3ZvGia2bLqJ0DNLW0618LzakwtnKBcXWJn\n/8foiI9syFTn+y7F6gILuUss5C9TKE9vSWG9J5HHSgQeVdyyQ3E827ad/Wqkhg/Qs+9lNN1ASp/p\nk9/d8jFvx4wmyYw+W0/uWZ4mP31xQ/fxpYvjVfClF9B4XKAJnZCZpFxbbMe0b3Jrcd48rlejZheI\nhptLiAihYZlxDN1qQ0exYAzNImQFF4mTUlKt5Rp+gc0RCXXQ33mYeLibFQ9I/VQuqTkFPN/F1MNo\nDdOUlB6eZ1Nzi5RryxQrcxTK01TsbKOUxta8H08qSgSeMIS24mi7P9EnW0nVzuN5DprRvJPWGl2u\n2i0Cph7eRA/eO/GlR6EyGygCUE+usozYlix6AkE4lG6ZuOX5DuXa8qbLP6djQ+wd/nSj7WT9c5JS\n4rhlZpfPMrHwHjW70PBF3fp5lMibzv96zoSHygHYGpQIPGFkx08TinUgkSyOffCgp7MpyrVlPL+G\nSfPOXBcGiUgf87mNnTRaYRrRddfZb4Xvu+RKk/R27A+8HgtlGqeZ9rSWvB1NM0m1aGwP9aQv291c\nwEEsnGHv8KdJxW4lBq4IwNWZt7ixzoQxxdagROAJwynnuPH+nzzoabSFUnUex6sSpnlR1jSDRLQX\nTRhtW2gEgrCVImTE2nK/eqmDaVyvFtgRK2yliIW7yJbG2x4Dr2sWHfFtLa8Xq3NUW1QEXev9R3pe\nIBHpbbo2s3xWCcBDhKodpHhkqdSy1OxCYNSXEBqRUMcmC5bdia6HSEb72lIXf4WqnSPfIsRR03Q6\nE9s3XGtnNeKR7pZN4T3foVCZXTV66V6kYoN0JnYg7krwcr0aU4vHlQA8RCgRUDyy+LLeHavVghKx\n0nQmtrdtPNOI0pnY2bb7AdScPMuFsZbhy13JUaItFuvN0N/5VGCo60pv5nxpGrmJyKB0fISQmWjy\nO5VrS21t+anYPMoc1GaMUIzkwG5SwweJpHsRuoFTypGbOEt24gy1UpaBY5+ic9tT5CYvMPHON299\nsxCkBvcz8uIXALjx3rdYvnYqcBzNDNN/+HU6dz6NU85x/WffoLLc3M0s3ruTHR/9VbgrLM+zK8yd\nfYuFy++s6/mEZmDF06QG9hLr2U4o0YVh1cMMXbtErbBEeXGS3OR5qrnZDZVY0HSTzO7n6TnwCkhJ\nbvI8s2d+hF1qjp5ayF1iuPvZwKQnQw+TSe1mMX+1ZZ37tSKERndyV8vd80bxfIelwjV60vuJR5or\nwxp6mJGe5ylW5tpWWrozuZOu5GjgNSl9sqUb5MuTG76/EDoRK7VKItqjHZDwuKFEoI2Y0RSDT3+G\nrtFnAIH0HDzXxgwniPfupGPHEaZP/YBo52B98Qw325Y1wyIU77j5dSuEEOhWlFC8AwFoenDWpfRc\nnEoBTTcRuo5uRTHDcTwzhGYG9+dthW5F6dx+hL7DrxNK1CNapO/hex4ICCW7iHdvp3PHMYxwjOmT\n38V311dmQreiZPY8T//h1xGawdLYCebO/ThQAAAKlRmyxYlA56oQgnR8hP6uw4zN/GRTi2g01MVQ\nz3NbUo4iV55kPneBaKijKQdBCEF3ag+DXUeZmH9v02aUWDjDzr5XCN1V0wdWavJnmVk6vamIJIGo\nv08Ba3080kMqPsRC7qKq9fOQoESgTWhGiN4Dr9C5/SjS9ygvTlKYuYJdzqJpBuF0L4m+UQaP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jSp2JnqTqqsf1qKBFQKBQbpmLnWtbmSUb76Uhs36KRBSEzyejAq3TER2gqmyElrlthPndJ9TK+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\nYaQISCQSSQ8jRUAikUh6mP8PfxauvXqu668AAAAASUVORK5CYII=\n"},"metadata":{}}]},{"metadata":{"trusted":true,"_uuid":"9a16bc1952b9f73e7bb820fcb1bf0a0a8e3c78a7"},"cell_type":"code","source":"topic_word_counts = lda.topic_word_counts\nfor k, word_counts in enumerate(topic_word_counts):\n for word, count in word_counts.most_common():\n if count > 0: print(k, word, count)\n\ndocument_topic_counts = lda.document_topic_counts\nfor document, topic_counts in zip(documents, document_topic_counts):\n print(document)\n for topic, count in topic_counts.most_common():\n if count > 0:\n print(topic_names[topic], count)\n print()","execution_count":22,"outputs":[{"output_type":"stream","text":"0 sausages 2\n0 ham 2\n0 bacon 2\n0 eggs 2\n0 love 2\n0 kings 1\n0 green 1\n0 toast 1\n0 beans 1\n0 breakfast 1\n1 sky 4\n1 blue 4\n1 beautiful 3\n1 today 1\n2 dog 3\n2 brown 3\n2 fox 3\n2 lazy 3\n2 quick 3\n2 jumps 1\n['sky', 'blue', 'beautiful']\nweather 3\n\n['love', 'blue', 'beautiful', 'sky']\nweather 3\nfood 1\n\n['quick', 'brown', 'fox', 'jumps', 'lazy', 'dog']\nanimals 6\n\n['kings', 'breakfast', 'sausages', 'ham', 'bacon', 'eggs', 'toast', 'beans']\nfood 8\n\n['love', 'green', 'eggs', 'ham', 'sausages', 'bacon']\nfood 6\n\n['brown', 'fox', 'quick', 'blue', 'dog', 'lazy']\nanimals 5\nweather 1\n\n['sky', 'blue', 'sky', 'beautiful', 'today']\nweather 5\n\n['dog', 'lazy', 'brown', 'fox', 'quick']\nanimals 5\n\n","name":"stdout"}]}],"metadata":{"language_info":{"name":"python","version":"3.6.4","mimetype":"text/x-python","codemirror_mode":{"name":"ipython","version":3},"pygments_lexer":"ipython3","nbconvert_exporter":"python","file_extension":".py"},"kernelspec":{"display_name":"Python 3","language":"python","name":"python3"}},"nbformat":4,"nbformat_minor":1}
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