# TextRank: Bringing Order into Texts

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2 3 Starting from arbitrary values assigned to each node in the graph, the computation iterates until convergence below a given threshold is achieved 1. After running the algorithm, a score is associated with each vertex, which represents the importance of the vertex within the graph. Notice that the final values obtained after TextRank runs to completion are not affected by the choice of the initial value, only the number of iterations to convergence may be different. It is important to notice that although the TextRank applications described in this paper rely on an algorithm derived from Google s PageRank (Brin and Page, 1998), other graph-based ranking algorithms such as e.g. HITS (Kleinberg, 1999) or Positional Function (Herings et al., 2001) can be easily integrated into the TextRank model (Mihalcea, 2004). 2.1 Undirected Graphs Although traditionally applied on directed graphs, a recursive graph-based ranking algorithm can be also applied to undirected graphs, in which case the outdegree of a vertex is equal to the in-degree of the vertex. For loosely connected graphs, with the number of edges proportional with the number of vertices, undirected graphs tend to have more gradual convergence curves. Figure 1 plots the convergence curves for a randomly generated graph with 250 vertices and 250 edges, for a convergence threshold of As the connectivity of the graph increases (i.e. larger number of edges), convergence is usually achieved after fewer iterations, and the convergence curves for directed and undirected graphs practically overlap. 2.2 Weighted Graphs In the context of Web surfing, it is unusual for a page to include multiple or partial links to another page, and hence the original PageRank definition for graph-based ranking is assuming unweighted graphs. However, in our model the graphs are build from natural language texts, and may include multiple or partial links between the units (vertices) that are extracted from text. It may be therefore useful to indicate and incorporate into the model the strength of the connection between two vertices and as a weight added to the corresponding edge that connects the two vertices. 1 Convergence is achieved when the error rate for any vertex in the graph falls below a given threshold. The error rate of a vertex " \$ is defined as the difference between the real score of the vertex K #"%\$?& and the score computed at iteration, #"%\$#&. Since the real score is not known apriori, this error rate is approximated with the difference between #"%\$#& +0. the #"%\$#& scores computed at. two successive Error rate Convergence curves (250 vertices, 250 edges) undirected/unweighted undirected/weighted directed/unweighted directed/weighted Number of iterations Figure 1: Convergence curves for graph-based ranking: directed/undirected, weighted/unweighted graph, 250 vertices, 250 edges. Consequently, we introduce a new formula for graph-based ranking that takes into account edge weights when computing the score associated with a vertex in the graph. Notice that a similar formula can be defined to integrate vertex weights. K #"%\$ &'(*)!+-.&/ H =! #" ; H :<;=?> H 4 & H Figure 1 plots the convergence curves for the same sample graph from section 2.1, with random weights in the interval 0 10 added to the edges. While the final vertex scores (and therefore rankings) differ significantly as compared to their unweighted alternatives, the number of iterations to convergence and the shape of the convergence curves is almost identical for weighted and unweighted graphs. 2.3 Text as a Graph To enable the application of graph-based ranking algorithms to natural language texts, we have to build a graph that represents the text, and interconnects words or other text entities with meaningful relations. Depending on the application at hand, text units of various sizes and characteristics can be added as vertices in the graph, e.g. words, collocations, entire sentences, or others. Similarly, it is the application that dictates the type of relations that are used to draw connections between any two such vertices, e.g. lexical or semantic relations, contextual overlap, etc. Regardless of the type and characteristics of the elements added to the graph, the application of graphbased ranking algorithms to natural language texts consists of the following main steps:

4 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 systems and systems of mixed types. types solutions systems linear diophantine strict sets equations system constraints algorithms inequations compatibility minimal nonstrict construction criteria natural upper components numbers bounds Keywords assigned by TextRank: linear constraints; linear diophantine equations; natural numbers; nonstrict inequations; strict inequations; upper bounds Keywords assigned by human annotators: linear constraints; linear diophantine equations; minimal generating sets; non strict inequations; set of natural numbers; strict inequations; upper bounds Figure 2: Sample graph build for keyphrase extraction from an Inspec abstract the text is tokenized, and annotated with part of speech tags a preprocessing step required to enable the application of syntactic filters. To avoid excessive growth of the graph size by adding all possible combinations of sequences consisting of more than one lexical unit (ngrams), we consider only single words as candidates for addition to the graph, with multi-word keywords being eventually reconstructed in the post-processing phase. Next, all lexical units that pass the syntactic filter are added to the graph, and an edge is added between those lexical units that co-occur within a window of words. After the graph is constructed (undirected unweighted graph), the score associated with each vertex is set to an initial value of 1, and the ranking algorithm described in section 2 is run on the graph for several iterations until it converges usually for iterations, at a threshold of Once a final score is obtained for each vertex in the graph, vertices are sorted in reversed order of their score, and the top vertices in the ranking are retained for post-processing. While may be set to any fixed value, usually ranging from 5 to 20 keywords (e.g. (Turney, 1999) limits the number of keywords extracted with his GenEx system to five), we are using a more flexible approach, which decides the number of keywords based on the size of the text. For the data used in our experiments, which consists of relatively short abstracts, is set to a third of the number of vertices in the graph. During post-processing, all lexical units selected as potential keywords by the TextRank algorithm are marked in the text, and sequences of adjacent keywords are collapsed into a multi-word keyword. For instance, in the text Matlab code for plotting ambiguity functions, if both Matlab and code are selected as potential keywords by TextRank, since they are adjacent, they are collapsed into one single keyword Matlab code. Figure 2 shows a sample graph built for an abstract from our test collection. While the size of the abstracts ranges from 50 to 350 words, with an average size of 120 words, we have deliberately selected a very small abstract for the purpose of illustration. For this example, the lexical units found to have higher importance by the TextRank algorithm are (with the TextRank score indicated in parenthesis): numbers (1.46), inequations (1.45), linear (1.29), diophantine (1.28), upper (0.99), bounds (0.99), strict (0.77). Notice that this ranking is different than the one rendered by simple word frequencies. For the same text, a frequency approach provides the following top-ranked lexical units: systems (4), types (3), solutions (3), minimal (3), linear (2), inequations (2), algorithms (2). All other lexical units have a frequency of 1, and therefore cannot be ranked, but only listed. 3.2 Evaluation The data set used in the experiments is a collection of 500 abstracts from the Inspec database, and the corresponding manually assigned keywords. This is the same test data set as used in the keyword extraction experiments reported in (Hulth, 2003). The Inspec abstracts are from journal papers from Computer Science and Information Technology. Each abstract comes with two sets of keywords assigned by professional indexers: controlled keywords, restricted to a given thesaurus, and uncontrolled keywords, freely assigned by the indexers. We follow the evaluation approach from (Hulth, 2003), and use the uncontrolled set of keywords. In her experiments, Hulth is using a total of 2000 abstracts, divided into 1000 for training, 500 for development, and 500 for test 2. Since our approach is completely unsupervised, no training/development data is required, and we are only using the test docu- 2 Many thanks to Anette Hulth for allowing us to run our algorithm on the data set used in her keyword extraction experiments, and for making available the training/test/development data split.

5 Assigned Correct Method Total Mean Total Mean Precision Recall F-measure TextRank Undirected, Co-occ.window=2 6, , Undirected, Co-occ.window=3 6, , Undirected, Co-occ.window=5 6, , Undirected, Co-occ.window=10 6, , Directed, forward, Co-occ.window=2 6, , Directed, backward, Co-occ.window=2 6, , Hulth (2003) Ngram with tag 7, , NP-chunks with tag 4, , Pattern with tag 7, , Table 1: Results for automatic keyword extraction using TextRank or supervised learning (Hulth, 2003) ments for evaluation purposes. The results are evaluated using precision, recall, and F-measure. Notice that the maximum recall that can be achieved on this collection is less than 100%, since indexers were not limited to keyword extraction as our system is but they were also allowed to perform keyword generation, which eventually results in keywords that do not explicitly appear in the text. For comparison purposes, we are using the results of the state-of-the-art keyword extraction system reported in (Hulth, 2003). Shortly, her system consists of a supervised learning scheme that attempts to learn how to best extract keywords from a document, by looking at a set of four features that are determined for each candidate keyword: (1) within-document frequency, (2) collection frequency, (3) relative position of the first occurrence, (4) sequence of part of speech tags. These features are extracted from both training and test data for all candidate keywords, where a candidate keyword can be: Ngrams (unigrams, bigrams, or trigrams extracted from the abstracts), NP-chunks (noun phrases), patterns (a set of part of speech patterns detected from the keywords attached to the training abstracts). The learning system is a rule induction system with bagging. Our system consists of the TextRank approach described in Section 3.1, with a co-occurrence windowsize set to two, three, five, or ten words. Table 1 lists the results obtained with TextRank, and the best results reported in (Hulth, 2003). For each method, the table lists the total number of keywords assigned, the mean number of keywords per abstract, the total number of correct keywords, as evaluated against the set of keywords assigned by professional indexers, and the mean number of correct keywords. The table also lists precision, recall, and F-measure. Discussion. TextRank achieves the highest precision and F-measure across all systems, although the recall is not as high as in supervised methods possibly due the limitation imposed by our approach on the number of keywords selected, which is not made in the supervised system 3. A larger window does not seem to help on the contrary, the larger the window, the lower the precision, probably explained by the fact that a relation between words that are further apart is not strong enough to define a connection in the text graph. Experiments were performed with various syntactic filters, including: all open class words, nouns and adjectives, and nouns only, and the best performance was achieved with the filter that selects nouns and adjectives only. We have also experimented with a setting where no part of speech information was added to the text, and all words - except a predefined list of stopwords - were added to the graph. The results with this setting were significantly lower than the systems that consider part of speech information, which corroborates with previous observations that linguistic information helps the process of keyword extraction (Hulth, 2003). Experiments were also performed with directed graphs, where a direction was set following the natural flow of the text, e.g. one candidate keyword recommends (and therefore has a directed arc to) the candidate keyword that follows in the text, keeping the restraint imposed by the co-occurrence relation. We have also tried the reversed direction, where a lexical unit points to a previous token in the text. Table 1 includes the results obtained with directed graphs for a co-occurrence window of 2. Regardless of the direction chosen for the arcs, results obtained with directed graphs are worse than results obtained with undirected graphs, which suggests that despite a natural flow in running text, there is no natural direction that can be established between co- 3 The fact that the supervised system does not have the capability to set a cutoff threshold on the number of keywords, but it only makes a binary decision on each candidate word, has the downside of not allowing for a precision-recall curve, which prohibits a comparison of such curves for the two methods.

7 of two sentences with the length of each sentence. Formally, given two sentences and, with a sentence being represented by the set of words that appear in the sentence: \$, the similarity of and is defined as: \$ 4 K 2!#"\$ % \$ &'!#"\$ % 4 & Other sentence similarity measures, such as string kernels, cosine similarity, longest common subsequence, etc. are also possible, and we are currently evaluating their impact on the summarization performance. The resulting graph is highly connected, with a weight associated with each edge, indicating the strength of the connections established between various sentence pairs in the text. The text is therefore represented as a weighted graph, and consequently we are using the weighted graph-based ranking formula introduced in Section 2.2. After the ranking algorithm is run on the graph, sentences are sorted in reversed order of their score, and the top ranked sentences are selected for inclusion in the summary. Figure 3 shows a text sample, and the associated weighted graph constructed for this text. The figure also shows sample weights attached to the edges connected to vertex 9 4, and the final TextRank score computed for each sentence. The sentences with the highest rank are selected for inclusion in the abstract. For this sample article, the sentences with id-s 9, 15, 16, 18 are extracted, resulting in a summary of about 100 words, which according to automatic evaluation measures, is ranked the second among summaries produced by 15 other systems (see Section 4.2 for evaluation methodology). 4.2 Evaluation We evaluate the TextRank sentence extraction algorithm on a single-document summarization task, using 567 news articles provided during the Document Understanding Evaluations 2002 (DUC, 2002). For each article, TextRank generates an 100-words summary the task undertaken by other systems participating in this single document summarization task. For evaluation, we are using the ROUGE evaluation toolkit, which is a method based on Ngram statistics, found to be highly correlated with human evaluations (Lin and Hovy, 2003). Two manually produced reference summaries are provided, and used in the evaluation process 5. 4 Weights are listed to the right or above the edge they correspond to. Similar weights are computed for each edge in the graph, but are not displayed due to space restrictions. 5 ROUGE is available at cyl/rouge/. Fifteen different systems participated in this task, and we compare the performance of TextRank with the top five performing systems, as well as with the baseline proposed by the DUC evaluators consisting of a 100-word summary constructed by taking the first sentences in each article. Table 2 shows the results obtained on this data set of 567 news articles, including the results for TextRank (shown in bold), the baseline, and the results of the top five performing systems in the DUC 2002 single document summarization task (DUC, 2002). ROUGE score Ngram(1,1) stemmed System basic stemmed no-stopwords (a) (b) (c) S S TextRank S S Baseline S Table 2: Results for single document summarization: TextRank, top 5 (out of 15) DUC 2002 systems, and baseline. Evaluation takes into account (a) all words; (b) stemmed words; (c) stemmed words, and no stopwords. Discussion. TextRank succeeds in identifying the most important sentences in a text based on information exclusively drawn from the text itself. Unlike other supervised systems, which attempt to learn what makes a good summary by training on collections of summaries built for other articles, TextRank is fully unsupervised, and relies only on the given text to derive an extractive summary, which represents a summarization model closer to what humans are doing when producing an abstract for a given document. Notice that TextRank goes beyond the sentence connectivity in a text. For instance, sentence 15 in the example provided in Figure 3 would not be identified as important based on the number of connections it has with other vertices in the graph, but it is identified as important by TextRank (and by humans see the reference summaries displayed in the same figure). Another important aspect of TextRank is that it gives a ranking over all sentences in a text which means that it can be easily adapted to extracting very short summaries (headlines consisting of one The evaluation is done using the Ngram(1,1) setting of ROUGE, which was found to have the highest correlation with human judgments, at a confidence level of 95%. Only the first 100 words in each summary are considered.

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