Based on:
TextRank: Bringing Order into Texts - by Rada Mihalcea and Paul Tarau
The input text is given below
#Source of text:
#https://www.researchgate.net/publication/227988510_Automatic_Keyword_Extraction_from_Individual_Documents
Text = "Compatibility of systems of linear constraints over the set of natural numbers. \
Criteria of compatibility of a system of linear Diophantine equations, strict inequations, and \
nonstrict inequations are considered. \
Upper bounds for components of a minimal set of solutions and \
algorithms of construction of minimal generating sets of solutions for all \
types of systems are given. \
These criteria and the corresponding algorithms for constructing \
a minimal supporting set of solutions can be used in solving all the \
considered types of systems and systems of mixed types."The raw input text is cleaned off non-printable characters (if any) and turned into lower case. The processed input text is then tokenized using NLTK library functions.
import nltk
from nltk import word_tokenize
import string
#nltk.download('punkt')
def clean(text):
text = text.lower()
printable = set(string.printable)
text = filter(lambda x: x in printable, text) #filter funny characters, if any.
return text
Cleaned_text = clean(Text)
text = word_tokenize(Cleaned_text)
print "Tokenized Text: \n"
print textTokenized Text:
['compatibility', 'of', 'systems', 'of', 'linear', 'constraints', 'over', 'the', 'set', 'of', 'natural', 'numbers', '.', 'criteria', 'of', 'compatibility', 'of', 'a', 'system', 'of', 'linear', 'diophantine', 'equations', ',', 'strict', 'inequations', ',', 'and', 'nonstrict', 'inequations', 'are', 'considered', '.', 'upper', 'bounds', 'for', 'components', 'of', 'a', 'minimal', 'set', 'of', 'solutions', 'and', 'algorithms', 'of', 'construction', 'of', 'minimal', 'generating', 'sets', 'of', 'solutions', 'for', 'all', 'types', 'of', 'systems', 'are', 'given', '.', 'these', 'criteria', 'and', 'the', 'corresponding', 'algorithms', 'for', 'constructing', 'a', 'minimal', 'supporting', 'set', 'of', 'solutions', 'can', 'be', 'used', 'in', 'solving', 'all', 'the', 'considered', 'types', 'of', 'systems', 'and', 'systems', 'of', 'mixed', 'types', '.']
NLTK is again used for POS tagging the input text so that the words can be lemmatized based on their POS tags.
Description of POS tags:
http://www.ling.upenn.edu/courses/Fall_2003/ling001/penn_treebank_pos.html
#nltk.download('averaged_perceptron_tagger')
POS_tag = nltk.pos_tag(text)
print "Tokenized Text with POS tags: \n"
print POS_tagTokenized Text with POS tags:
[('compatibility', 'NN'), ('of', 'IN'), ('systems', 'NNS'), ('of', 'IN'), ('linear', 'JJ'), ('constraints', 'NNS'), ('over', 'IN'), ('the', 'DT'), ('set', 'NN'), ('of', 'IN'), ('natural', 'JJ'), ('numbers', 'NNS'), ('.', '.'), ('criteria', 'NNS'), ('of', 'IN'), ('compatibility', 'NN'), ('of', 'IN'), ('a', 'DT'), ('system', 'NN'), ('of', 'IN'), ('linear', 'JJ'), ('diophantine', 'NN'), ('equations', 'NNS'), (',', ','), ('strict', 'JJ'), ('inequations', 'NNS'), (',', ','), ('and', 'CC'), ('nonstrict', 'JJ'), ('inequations', 'NNS'), ('are', 'VBP'), ('considered', 'VBN'), ('.', '.'), ('upper', 'JJ'), ('bounds', 'NNS'), ('for', 'IN'), ('components', 'NNS'), ('of', 'IN'), ('a', 'DT'), ('minimal', 'JJ'), ('set', 'NN'), ('of', 'IN'), ('solutions', 'NNS'), ('and', 'CC'), ('algorithms', 'NN'), ('of', 'IN'), ('construction', 'NN'), ('of', 'IN'), ('minimal', 'JJ'), ('generating', 'VBG'), ('sets', 'NNS'), ('of', 'IN'), ('solutions', 'NNS'), ('for', 'IN'), ('all', 'DT'), ('types', 'NNS'), ('of', 'IN'), ('systems', 'NNS'), ('are', 'VBP'), ('given', 'VBN'), ('.', '.'), ('these', 'DT'), ('criteria', 'NNS'), ('and', 'CC'), ('the', 'DT'), ('corresponding', 'JJ'), ('algorithms', 'NN'), ('for', 'IN'), ('constructing', 'VBG'), ('a', 'DT'), ('minimal', 'JJ'), ('supporting', 'NN'), ('set', 'NN'), ('of', 'IN'), ('solutions', 'NNS'), ('can', 'MD'), ('be', 'VB'), ('used', 'VBN'), ('in', 'IN'), ('solving', 'VBG'), ('all', 'PDT'), ('the', 'DT'), ('considered', 'VBN'), ('types', 'NNS'), ('of', 'IN'), ('systems', 'NNS'), ('and', 'CC'), ('systems', 'NNS'), ('of', 'IN'), ('mixed', 'JJ'), ('types', 'NNS'), ('.', '.')]
The tokenized text (mainly the nouns and adjectives) is normalized by lemmatization. In lemmatization different grammatical counterparts of a word will be replaced by single basic lemma. For example, 'glasses' may be replaced by 'glass'.
Details about lemmatization:
https://nlp.stanford.edu/IR-book/html/htmledition/stemming-and-lemmatization-1.html
#nltk.download('wordnet')
from nltk.stem import WordNetLemmatizer
wordnet_lemmatizer = WordNetLemmatizer()
adjective_tags = ['JJ','JJR','JJS']
lemmatized_text = []
for word in POS_tag:
if word[1] in adjective_tags:
lemmatized_text.append(str(wordnet_lemmatizer.lemmatize(word[0],pos="a")))
else:
lemmatized_text.append(str(wordnet_lemmatizer.lemmatize(word[0]))) #default POS = noun
print "Text tokens after lemmatization of adjectives and nouns: \n"
print lemmatized_textText tokens after lemmatization of adjectives and nouns:
['compatibility', 'of', 'system', 'of', 'linear', 'constraint', 'over', 'the', 'set', 'of', 'natural', 'number', '.', 'criterion', 'of', 'compatibility', 'of', 'a', 'system', 'of', 'linear', 'diophantine', 'equation', ',', 'strict', 'inequations', ',', 'and', 'nonstrict', 'inequations', 'are', 'considered', '.', 'upper', 'bound', 'for', 'component', 'of', 'a', 'minimal', 'set', 'of', 'solution', 'and', 'algorithm', 'of', 'construction', 'of', 'minimal', 'generating', 'set', 'of', 'solution', 'for', 'all', 'type', 'of', 'system', 'are', 'given', '.', 'these', 'criterion', 'and', 'the', 'corresponding', 'algorithm', 'for', 'constructing', 'a', 'minimal', 'supporting', 'set', 'of', 'solution', 'can', 'be', 'used', 'in', 'solving', 'all', 'the', 'considered', 'type', 'of', 'system', 'and', 'system', 'of', 'mixed', 'type', '.']
The lemmatized text is POS tagged here. The tags will be used for filtering later on.
POS_tag = nltk.pos_tag(lemmatized_text)
print "Lemmatized text with POS tags: \n"
print POS_tagLemmatized text with POS tags:
[('compatibility', 'NN'), ('of', 'IN'), ('system', 'NN'), ('of', 'IN'), ('linear', 'JJ'), ('constraint', 'NN'), ('over', 'IN'), ('the', 'DT'), ('set', 'NN'), ('of', 'IN'), ('natural', 'JJ'), ('number', 'NN'), ('.', '.'), ('criterion', 'NN'), ('of', 'IN'), ('compatibility', 'NN'), ('of', 'IN'), ('a', 'DT'), ('system', 'NN'), ('of', 'IN'), ('linear', 'JJ'), ('diophantine', 'JJ'), ('equation', 'NN'), (',', ','), ('strict', 'JJ'), ('inequations', 'NNS'), (',', ','), ('and', 'CC'), ('nonstrict', 'JJ'), ('inequations', 'NNS'), ('are', 'VBP'), ('considered', 'VBN'), ('.', '.'), ('upper', 'JJ'), ('bound', 'NN'), ('for', 'IN'), ('component', 'NN'), ('of', 'IN'), ('a', 'DT'), ('minimal', 'JJ'), ('set', 'NN'), ('of', 'IN'), ('solution', 'NN'), ('and', 'CC'), ('algorithm', 'NN'), ('of', 'IN'), ('construction', 'NN'), ('of', 'IN'), ('minimal', 'JJ'), ('generating', 'VBG'), ('set', 'NN'), ('of', 'IN'), ('solution', 'NN'), ('for', 'IN'), ('all', 'DT'), ('type', 'NN'), ('of', 'IN'), ('system', 'NN'), ('are', 'VBP'), ('given', 'VBN'), ('.', '.'), ('these', 'DT'), ('criterion', 'NN'), ('and', 'CC'), ('the', 'DT'), ('corresponding', 'JJ'), ('algorithm', 'NN'), ('for', 'IN'), ('constructing', 'VBG'), ('a', 'DT'), ('minimal', 'JJ'), ('supporting', 'NN'), ('set', 'NN'), ('of', 'IN'), ('solution', 'NN'), ('can', 'MD'), ('be', 'VB'), ('used', 'VBN'), ('in', 'IN'), ('solving', 'VBG'), ('all', 'PDT'), ('the', 'DT'), ('considered', 'VBN'), ('type', 'NN'), ('of', 'IN'), ('system', 'NN'), ('and', 'CC'), ('system', 'NN'), ('of', 'IN'), ('mixed', 'JJ'), ('type', 'NN'), ('.', '.')]
Any word from the lemmatized text, which isn't a noun, adjective, or gerund (or a 'foreign word'), is here considered as a stopword (non-content). This is based on the assumption that usually keywords are noun, adjectives or gerunds.
Punctuations are added to the stopword list too.
stopwords = []
wanted_POS = ['NN','NNS','NNP','NNPS','JJ','JJR','JJS','VBG','FW']
for word in POS_tag:
if word[1] not in wanted_POS:
stopwords.append(word[0])
punctuations = list(str(string.punctuation))
stopwords = stopwords + punctuationsEven if we remove the aforementioned stopwords, still some extremely common nouns, adjectives or gerunds may remain which are very bad candidates for being keywords (or part of it).
An external file constituting a long list of stopwords is loaded and all the words are added with the previous stopwords to create the final list 'stopwords-plus' which is then converted into a set.
(Source of stopwords data: https://www.ranks.nl/stopwords)
Stopwords-plus constitute the sum total of all stopwords and potential phrase-delimiters.
(The contents of this set will be later used to partition the lemmatized text into n-gram phrases. But, for now, I will simply remove the stopwords, and work with a 'bag-of-words' approach. I will be developing the graph using unigram texts as vertices)
stopword_file = open("long_stopwords.txt", "r")
#Source = https://www.ranks.nl/stopwords
lots_of_stopwords = []
for line in stopword_file.readlines():
lots_of_stopwords.append(str(line.strip()))
stopwords_plus = []
stopwords_plus = stopwords + lots_of_stopwords
stopwords_plus = set(stopwords_plus)
#Stopwords_plus contain total set of all stopwordsRemoving stopwords from lemmatized_text. Processeced_text condtains the result.
processed_text = []
for word in lemmatized_text:
if word not in stopwords_plus:
processed_text.append(word)
print processed_text['compatibility', 'system', 'linear', 'constraint', 'set', 'natural', 'number', 'criterion', 'compatibility', 'system', 'linear', 'diophantine', 'equation', 'strict', 'inequations', 'nonstrict', 'inequations', 'upper', 'bound', 'component', 'minimal', 'set', 'solution', 'algorithm', 'construction', 'minimal', 'generating', 'set', 'solution', 'type', 'system', 'criterion', 'algorithm', 'constructing', 'minimal', 'supporting', 'set', 'solution', 'solving', 'type', 'system', 'system', 'mixed', 'type']
Vocabulary will only contain unique words from processed_text.
vocabulary = list(set(processed_text))
print vocabulary['upper', 'set', 'constructing', 'number', 'solving', 'system', 'compatibility', 'strict', 'criterion', 'type', 'minimal', 'supporting', 'generating', 'linear', 'diophantine', 'component', 'bound', 'nonstrict', 'inequations', 'natural', 'algorithm', 'constraint', 'equation', 'solution', 'construction', 'mixed']
TextRank is a graph based model, and thus it requires us to build a graph. Each words in the vocabulary will serve as a vertex for graph. The words will be represented in the vertices by their index in vocabulary list.
The weighetd_edge matrix contains the information of edge connections among all vertices. I am building a graph with wieghted undirected edges.
weighted_edge[i][j] contains the weight of the connecting edge between the word vertex represented by vocabulary index i and the word vertex represented by vocabulary j.
If weighted_edge[i][j] is zero, it means no edge or connection is present between the words represented by index i and j.
There is a connection between the words (and thus between i and j which represents them) if the words co-occur within a window of a specified 'window_size' in the processed_text.
I am increasing value of the weighted_edge[i][j] is increased by (1/(distance between positions of words currently represented by i and j)) for every connection discovered between the same words in different locations of the text.
The covered_coocurrences list (which is contain the list of pairs of absolute positions in processed_text of the words whose coocurrence at that location is already checked) is managed so that the same two words located in the same positions in processed_text are not repetitively counted while sliding the window one text unit at a time.
The score of all vertices are intialized to one.
Self-connections are not considered, so weighted_edge[i][i] will be zero.
import numpy as np
import math
vocab_len = len(vocabulary)
weighted_edge = np.zeros((vocab_len,vocab_len),dtype=np.float32)
score = np.zeros((vocab_len),dtype=np.float32)
window_size = 3
covered_coocurrences = []
for i in xrange(0,vocab_len):
score[i]=1
for j in xrange(0,vocab_len):
if j==i:
weighted_edge[i][j]=0
else:
for window_start in xrange(0,(len(processed_text)-window_size+1)):
window_end = window_start+window_size
window = processed_text[window_start:window_end]
if (vocabulary[i] in window) and (vocabulary[j] in window):
index_of_i = window_start + window.index(vocabulary[i])
index_of_j = window_start + window.index(vocabulary[j])
# index_of_x is the absolute position of the xth term in the window
# (counting from 0)
# in the processed_text
if [index_of_i,index_of_j] not in covered_coocurrences:
weighted_edge[i][j]+=1/math.fabs(index_of_i-index_of_j)
covered_coocurrences.append([index_of_i,index_of_j])inout[i] will contain the total no. of undirected connections\edges associated withe the vertex represented by i.
inout = np.zeros((vocab_len),dtype=np.float32)
for i in xrange(0,vocab_len):
for j in xrange(0,vocab_len):
inout[i]+=weighted_edge[i][j]The formula used for scoring a vertex represented by i is:
score[i] = (1-d) + d x [ Summation(j) ( (weighted_edge[i][j]/inout[j]) x score[j] ) ] where j belongs to the list of vertices that has a connection with i.
d is the damping factor.
The score is iteratively updated until convergence.
MAX_ITERATIONS = 50
d=0.85
threshold = 0.0001 #convergence threshold
for iter in xrange(0,MAX_ITERATIONS):
prev_score = np.copy(score)
for i in xrange(0,vocab_len):
summation = 0
for j in xrange(0,vocab_len):
if weighted_edge[i][j] != 0:
summation += (weighted_edge[i][j]/inout[j])*score[j]
score[i] = (1-d) + d*(summation)
if np.sum(np.fabs(prev_score-score)) <= threshold: #convergence condition
print "Converging at iteration "+str(iter)+"...."
breakConverging at iteration 29....
for i in xrange(0,vocab_len):
print "Score of "+vocabulary[i]+": "+str(score[i])Score of upper: 0.816792
Score of set: 2.27184
Score of constructing: 0.667288
Score of number: 0.688316
Score of solving: 0.642318
Score of system: 2.12032
Score of compatibility: 0.944584
Score of strict: 0.823772
Score of criterion: 1.22559
Score of type: 1.08101
Score of minimal: 1.78693
Score of supporting: 0.653705
Score of generating: 0.652645
Score of linear: 1.2717
Score of diophantine: 0.759295
Score of component: 0.737641
Score of bound: 0.786006
Score of nonstrict: 0.827216
Score of inequations: 1.30824
Score of natural: 0.688299
Score of algorithm: 1.19365
Score of constraint: 0.674411
Score of equation: 0.799815
Score of solution: 1.6832
Score of construction: 0.659809
Score of mixed: 0.235822
Paritioning lemmatized_text into phrases using the stopwords in it as delimeters. The phrases are also candidates for keyphrases to be extracted.
phrases = []
phrase = " "
for word in lemmatized_text:
if word in stopwords_plus:
if phrase!= " ":
phrases.append(str(phrase).strip().split())
phrase = " "
elif word not in stopwords_plus:
phrase+=str(word)
phrase+=" "
print "Partitioned Phrases (Candidate Keyphrases): \n"
print phrasesPartitioned Phrases (Candidate Keyphrases):
[['compatibility'], ['system'], ['linear', 'constraint'], ['set'], ['natural', 'number'], ['criterion'], ['compatibility'], ['system'], ['linear', 'diophantine', 'equation'], ['strict', 'inequations'], ['nonstrict', 'inequations'], ['upper', 'bound'], ['component'], ['minimal', 'set'], ['solution'], ['algorithm'], ['construction'], ['minimal', 'generating', 'set'], ['solution'], ['type'], ['system'], ['criterion'], ['algorithm'], ['constructing'], ['minimal', 'supporting', 'set'], ['solution'], ['solving'], ['type'], ['system'], ['system'], ['mixed', 'type']]
Repeating phrases\keyphrase candidates has no purpose here, anymore.
unique_phrases = []
for phrase in phrases:
if phrase not in unique_phrases:
unique_phrases.append(phrase)
print "Unique Phrases (Candidate Keyphrases): \n"
print unique_phrasesUnique Phrases (Candidate Keyphrases):
[['compatibility'], ['system'], ['linear', 'constraint'], ['set'], ['natural', 'number'], ['criterion'], ['linear', 'diophantine', 'equation'], ['strict', 'inequations'], ['nonstrict', 'inequations'], ['upper', 'bound'], ['component'], ['minimal', 'set'], ['solution'], ['algorithm'], ['construction'], ['minimal', 'generating', 'set'], ['type'], ['constructing'], ['minimal', 'supporting', 'set'], ['solving'], ['mixed', 'type']]
Removing single word keyphrase-candidates that are present multi-word alternatives.
for word in vocabulary:
#print word
for phrase in unique_phrases:
if (word in phrase) and ([word] in unique_phrases) and (len(phrase)>1):
#if len(phrase)>1 then the current phrase is multi-worded.
#if the word in vocabulary is present in unique_phrases as a single-word-phrase
# and at the same time present as a word within a multi-worded phrase,
# then I will remove the single-word-phrase from the list.
unique_phrases.remove([word])
print "Thinned Unique Phrases (Candidate Keyphrases): \n"
print unique_phrases Thinned Unique Phrases (Candidate Keyphrases):
[['compatibility'], ['system'], ['linear', 'constraint'], ['natural', 'number'], ['criterion'], ['linear', 'diophantine', 'equation'], ['strict', 'inequations'], ['nonstrict', 'inequations'], ['upper', 'bound'], ['component'], ['minimal', 'set'], ['solution'], ['algorithm'], ['construction'], ['minimal', 'generating', 'set'], ['constructing'], ['minimal', 'supporting', 'set'], ['solving'], ['mixed', 'type']]
Scoring the phrases (candidate keyphrases) and building up a list of keyphrases by listing untokenized versions of tokenized phrases\candidate-keyphrases. Phrases are scored by adding the score of their members (words\text-units that were ranked by the graph algorithm)
phrase_scores = []
keywords = []
for phrase in unique_phrases:
phrase_score=0
keyword = ''
for word in phrase:
keyword += str(word)
keyword += " "
phrase_score+=score[vocabulary.index(word)]
phrase_scores.append(phrase_score)
keywords.append(keyword.strip())
i=0
for keyword in keywords:
print "Keyword: '"+str(keyword)+"', Score: "+str(phrase_scores[i])
i+=1Keyword: 'compatibility', Score: 0.944583714008
Keyword: 'system', Score: 2.12031626701
Keyword: 'linear constraint', Score: 1.94610738754
Keyword: 'natural number', Score: 1.37661552429
Keyword: 'criterion', Score: 1.2255872488
Keyword: 'linear diophantine equation', Score: 2.83080631495
Keyword: 'strict inequations', Score: 2.13201224804
Keyword: 'nonstrict inequations', Score: 2.135455966
Keyword: 'upper bound', Score: 1.60279768705
Keyword: 'component', Score: 0.737640619278
Keyword: 'minimal set', Score: 4.05876886845
Keyword: 'solution', Score: 1.68319940567
Keyword: 'algorithm', Score: 1.19365406036
Keyword: 'construction', Score: 0.659808635712
Keyword: 'minimal generating set', Score: 4.71141409874
Keyword: 'constructing', Score: 0.66728836298
Keyword: 'minimal supporting set', Score: 4.71247345209
Keyword: 'solving', Score: 0.642318367958
Keyword: 'mixed type', Score: 1.31682945788
Ranking keyphrases based on their calculated scores. Displaying top 'keywords_num' no. of keyphrases.
sorted_index = np.flip(np.argsort(phrase_scores),0)
keywords_num = 10
print "Keywords:\n"
for i in xrange(0,keywords_num):
print str(keywords[sorted_index[i]])+", ",Keywords:
minimal supporting set, minimal generating set, minimal set, linear diophantine equation, nonstrict inequations, strict inequations, system, linear constraint, solution, upper bound,
Compatibility of systems of linear constraints over the set of natural numbers. Criteria of compatibility of a system of linear Diophantine equations, strict inequations, and nonstrict inequations are considered. Upper bounds for components of a minimal set of solutions and algorithms of construction of minimal generating sets of solutions for all types of systems are given. These criteria and the corresponding algorithms for constructing a minimal supporting set of solutions can be used in solving all the considered types of systems and systems of mixed types.
- minimal supporting set,
- minimal generating set,
- minimal set,
- linear diophantine equation,
- nonstrict inequations,
- strict inequations,
- system,
- linear constraint,
- solution,
- upper bound,