We adopt three cohesion measures: clue words, semantic similarity and cosine similarity as the weight of the edges.

We adopt three cohesion metrics, clue words, semantic similarity and cosine similarity , to measure the weight of the edges.

In Section 3.3, we developed three ways to compute the weight of an edge in the sentence quotation graph, i.e., clue words, semantic similarity based on WordNet and cosine similarity .

The widely used cosine similarity does not perform well.

The above experiments show that the widely used cosine similarity and the more sophisticated semantic similarity in WordNet are less accurate than the basic CWS in the summarization framework.

and (3) cosine similarity that is based on the word TFIDF vector.

3.3.3 Cosine Similarity

Cosine similarity is a popular metric to compute the similarity of two text units.

(Carenini et al., 2007), semantic similarity and cosine similarity .

In the rest of this paper, let CWS denote the Generalized ClueWordSummarizer when the edge weight is based on clue words, and let CWS-Cosine and CWS-Semantic denote the summarizer when the edge weight is cosine similarity and semantic similarity respectively.

This is a commonly used setup in the CQA community (Wang et al., 2009).4 Thus, for a given question, all its answers are fetched from the answer collection, and an initial ranking is constructed based on the cosine similarity between theirs and the question’s lemma vector representations, with lemmas weighted using tfidf (Ch.

The candidate answers are scored using a linear interpolation of two cosine similarity scores: one between the entire parent document and question (to model global context), and a second between the answer candidate and question (for local context).6 Because the number of answer candidates is typically large (e.g., equal to the number of paragraphs in the textbook), we return the N top candidates with the highest scores.

The following hyper parameters were tuned using grid search to maximize P@1 on each development partition: (a) the segment matching thresholds that determine the minimum cosine similarity between an answer segment and a question for the segment to be labeled QSEG; and (b)

6We empirically observed that this combination of scores performs better than using solely the cosine similarity between the answer and question.

If text before or after a marker out to a given sentence range matches the entire text of the question (with a cosine similarity score larger than a threshold), that argument takes on the label QSEG, or OTHER otherwise.

The values of the discourse features are the mean of the similarity scores (e. g., cosine similarity using tfidf weighting) of the two marker arguments and the corresponding question.

(2011) extracted 47 cue phrases such as because from a small collection of web documents, and used the cosine similarity between an answer candidate and a bag of words containing these cue phrases as a single feature in their reranking model for non-factoid why QA.

Cosine Similarity .

Given a question q and its :andidate answer 3, their cosine similarity can be :omputed as follows:

Method P@1(%) MRR (%) Nearest Answer 21.25 38.72 Cosine Similarity 23.15 43.50 HowNet 22.55 41.63 KL divergence 25 .30 51.40 DBN (without FT) 41.45 59.64 DBN (with FT) 45.00 62.03

Because of this situation, the traditional relevance computing methods based on word co-occurrence, such as Cosine similarity and KL—divergence, are not effective for question-

This is similar to cosine similarity except that the l-norm is used instead of the 2-norm.

We are not including this method in our experiments, but we will give the equation here, as traditional document similarity measures (e.g., cosine similarity ) perform poorly on this task although there also are known alternatives with good results (Sahami and Heilman, 2006).

To calculate PPR+cos, we computed 20 iterations with a decay factor of 0.8 and used the cosine similarity with the 2-norm in the denominator to compare two vectors.

We compute 20 iterations of PPR+cos to reach convergence and then calculate a single cosine similarity .

Another important similarity measure is cosine similarity of Personalized PageRank (PPR) vectors.

These approaches use at least one of cosine similarity , PageRank and SimRank.

Given a query document vector q, we use the Cosine similarity measure to evaluate the similarity between q and a document a: in a dataset:

However, such a brute-force search does not scale to massive datasets since the search time complexity for each query is 0(n); additionally, the computational cost spent on Cosine similarity calculation is also nontrivial.

(1) It tries to preserve the Cosine similarity of the original data with a probabilistic guarantee (Charikar, 2002).

We first evaluate the quality of term vectors and ITQ binary codes by conducting the whole list Cosine similarity ranking and hamming distance ranking, respectively.

For each query document, the top-K candidate documents with highest Cosine similarity scores and shortest hamming distances are returned, then we calculate the average precision for each K. Fig.

for example, one can store 250 million documents with 1.9G memory using only 64 bits for each document while a large news corpus such as the English Gigaword fifth edition1 stores 10 million documents in a 26G hard drive; 2) the time efficiency of manipulating binary codes, for example, computing the hamming distance between a pair of binary codes is several orders of magnitude faster than computing the real-valued cosine similarity over a pair of document vectors.

To illustrate how the model described above can learn geographically-informed semantic representations of words, table 1 displays the terms with the highest cosine similarity to wicked in Kansas and Massachusetts after running our joint model on the full 1.1 billion words of Twitter data; while wicked in Kansas is close to other evaluative terms like evil and pure and religious terms like gods and spirit, in Massachusetts it is most similar to other intensifiers like super, ridiculously and insanely.

Table 2 likewise presents the terms with the highest cosine similarity to city in both California and New York; while the terms most evoked by city in California include regional locations like Chinatown, Los Angeles’ South Bay and San Francisco’s East Bay, in New York the most similar terms include hamptons, upstate and borough

Table 1: Terms with the highest cosine similarity to wicked in Kansas and Massachusetts.

The edges between corresponding nodes (dz) represent the cosine similarity between them is above a threshold (0.10 following (Erkan and Radev, 2004)).

Maximal Marginal Relevance (MMR) (Carbonell and Goldstein, 1998) uses the pairwise cosine similarity matrix and greedily chooses sentences that are the least similar to those already in the summary.

C-LexRank is a clustering-based model in which the cosine similarities of document pairs are used to build a network of documents.

Once a lexical similarity graph is built, they modify the graph based on cluster information and perform LexRank on the modified cosine similarity graph.

Focus, coherence and referential clarity are best evaluated by a class of features measuring local coherence on the basis of cosine similarity between sentences, coreference information, and summarization specific features.

Cosine similarity We use cosine similarity to compute the overlap of words in adjacent sentences s,- and 3H1 as a measure of continuity.

We compute the min, max, and average value of cosine similarity over the entire summary.

Cosine similarity is thus indicative of both continuity and redundancy.

For all four other questions, the best feature set is Continuity, which is a combination of summarization specific features, coreference features and cosine similarity of adjacent sentences.

We now investigate to what extent each of its components—summary-specific features, coreference, and cosine similarity between adjacent sentences—contribute to performance.

The word similarity is based on cosine similarity of TF/IDF weighted vectors.

- Cosine similarity with the question

- Cosine similarity between contiguous sentences

(2006a) used cosine similarity to match students’ query with reply posts for discussion-bot.

For clustering we use a number of word similarities like cosine similarity among words and co-occurrence, along with the k-means clustering algorithm.

3.1 Cosine Similarity based on Sentence Level Co-occurrence

Then we measure cosine similarity between the word vectors.

The cosine similarity between two word vectors (fl and E”) with dimension d is measured as:

We computed the similarity between co-occurrence vectors using different metrics: Cosine Similarity , Dice coefficient (Curran, 2004), Kullback—Leibler divergence or KL divergence or relative entropy (Kullback and Leibler, 1951) and the J enson-Shannon divergence (Lee, 1999).

One year data (1991) were used to extract the “noun wo verb” tuples to compute word similarity (using cosine similarity metric) and collocation scores.

These data are necessary to compute the word similarity (using cosine similarity metric) and collocation scores.

To measure the latent similarity among documents, we construct topic vectors with the topic probabilistic distribution, and then adopt the Jensen-Shannon divergence to measures it, on the other hand, in the case of using document vectors we adopt cosine similarity .

Table 1: Extracting important sentences Methods Measure Accuracy F-value PageRank J enshen-Shannon 0.567 0.485 Cosine similarity 0.287 0.291 tf.

idf J enshen-Shannon 0.550 0.43 5 Cosine similarity 0.275 0.270

As a similarity function, we use cosine similarity weighted with TF*IDF.

We define sim(efl, ej/lx) as the cosine similarity between excerpts 63-; from topic 253- and ej/l/ from topic if.

If excerpts ejl and ej/l/ have cosine similarity

For each topic present in the human-authored article, the Oracle selects the excerpt from our full model’s candidate excerpts with the highest cosine similarity to the human-authored text.

Our experiments show that both methods are able to improve the baseline approach, and we find that the cosine similarity between utterances or between an utterance and the whole document is not as useful as in other document summarization tasks.

0 sim(s, D) is the cosine similarity between DA 3 and all the utterances in the dialogue from the same speaker, D. It measures the relevancy of s to the entire dialogue from the target speaker.

For cosine similarity measure, we use TF*IDF (term frequency, inverse document frequency) term weighting.

is modeled as an adjacency matrix, where each node represents a sentence, and the weight of the edge between each pair of sentences is their similarity ( cosine similarity is typically used).

Of all the methods in isolation, the simple approach of Section 4.1 — to use the total cosine similarity between a potential answer and the other words in the sentence — has performed best.

For the LSA model, the linear combination has three inputs: the total word similarity, the cosine similarity between the sum of the answer word vectors and the sum of the rest of sentence’s word vectors, and the number of out—of—vocabulary terms in the answer.

An important property of SVD is that the rows of US — which represents the words — behave similarly to the original rows of W, in the sense that the cosine similarity between two rows in US approximates the cosine similarity between the corre—

sponding rows in W. Cosine similarity is defined as

Let m be the smallest cosine similarity between h and any word in the vocabulary V: m = minwev sim(h, w).

We use cosine similarity , which

As described in Section 3.2, we find paraphrases of a phrase p,- by finding its nearest neighbors based on cosine similarity between the feature vector of pi and other phrases.

If n is the number of vectors and d is the dimensionality of the vector space, finding cosine similarity between each pair of vectors has time complexity 0(n2 d).

The data was generated by clustering similar news stories from Gigaword using TF-IDF cosine similarity of their headlines.

Doc-pair Cosine Similarity

The x-axis represents the cosine similarity between the document pairs.

Additionally, there is more data in the MTC dataset which has low cosine similarity than in RF.

cos: The cosine similarity between the named entity textual mention and the KB entry title.

ijim: While the cosine similarity between a textual mention in the document and the candidate

The cosine similarity between “Essex” and “Danbury, Essex” is higher than that between “Essex” and “Essex County Cricket Club”, which is not helpful in the NED setting.

Cosine similarity between the document vector representations is probably the easiest and most commonly used among the various similarity measures.

The cosine similarity between two (document representation) vectors v1 and 212 is given by 0036 = W. A value of 0 indicates that the vectors are orthogonal and dissimilar, a value of 1 indicates perfectly similar documents in terms of the words con-

To compute the cosine overlap features, we find the pairwise cosine similarity between each two documents in an input set and compute their average.

Cosine similarity with previous sentence.

Here we use the cosine similarity between sentences, where each sentence is represented as a vector of words, with term weight calculated using TD-IDF (term frequency times inverse document frequency).

* Cosine similarity with previous sentence.

Cohesiveness Score: Mean of the cosine similarities between each pair of definitions of w.

Average Number of Null Similarities: The number of definition pairs that have zero cosine similarity score (no word overlap).

The last feature sorts the pairwise cosine similarity scores in ascending order, prunes the top n% of the scores, and uses the maximum remaining score as the feature value.

1) Cosine- 1 st: we rank the utterances in the chat log based on the cosine similarity between the utterance and query.

2) Cosine-all: we rank the utterances in the chat log based on the cosine similarity between the utterance and query and then select the utterances with a cosine similarity greater than 0;

Query Relevance: another interesting observation is that relying only on the cosine similarity (i.e., cosine-all) to measure the query relevance presents a quite strong baseline.

We use the K-mean clustering algorithm by cosine similarity as a distance function between sentence vectors composed of tfidf scores.

The similarity between a test response and a score-specific vector is then calculated by a cosine similarity metric.

Although a total of 4 cosine similarity scores (one per score group) were generated, only 0034from among the four similarity scores, and cosmazc,

0 0034: the cosine similarity score between the test response and the vector of POS bigrams for the highest score class (level 4); and,

We used the cosine similarity , longest common subsequence, and word n- gram similarity measures.

Cosine similarity was applied on binary weighted term vectors (L2 norm).

Cosine similarity , longest common subsequence, and word n-gram similarity were also applied to measure the similarity between the edit comment and the turn text as well as the similarity between the edit comment and the turn topic name.

One of the most effective similarity measures is the cosine similarity , which is a normalized dot product.

Indeed, taking Hp as above, and cosine similarity as the only feature (i.e., w E R), yields the distribution

These measures give complementary perspectives on the similarity between the predicates, as the cosine similarity is symmetric between the LHS and RHS predicates, while BInc takes into account the directionality of the inference relation.

Evaluation: The similarity between a tweet and a news article is measured by cosine similarity .

4 The cosine similarity

In the WTMF model, we would like the latent vectors of two text nodes Q.,j1,Q.,j-2 to be as similar as possible, namely that their cosine similarity to be close to 1.

o 31(mi, mj): The cosine similarity of 75071;) and t(mj); and tweets are represented as TF-IDF vectors;

0 32(mi, mj): The cosine similarity of 75071;) and t(mj); and tweets are represented as topic distribution vectors;

SemTag uses the TAP knowledge base5, and employs the cosine similarity with TF-IDF weighting scheme to compute the match degree between a mention and an entity, achieving an accuracy of around 82%.

Cosine Similarity Word overlap is admittedly a naive measure of similarity, based on lexical identity.

We compare four extractive models based on word overlap, cosine similarity , and two probabilistic similarity measures, namely KL and JS divergence and two abstractive models based on words (see equation (8)) and phrases (see equation (15)).

As can be seen the probabilistic models (KL and J S divergence) outperform word overlap and cosine similarity (all differences are statistically significant, p < 0.01).6 They make use of the same topic model as the image annotation model, and are thus able to select sentences that cover common content.

Borrowing this idea, for each sub-summary in a human-generated summary, we find its most matched sub-summary (judged by the cosine similarity measure) in the corresponding system-generated summary and then define the correlation according to the concordance between the two

For the semantic-based approach, we compare three different approaches to defining the subtopic number K: (1) Semantic-based 1: Following the approach proposed in (Li et al., 2007), we first derive the matrix of tweet cosine similarity .

For a tweet in a peak area, the linear combination of two measures is considered to evaluate its significance to be a sub-summary: (l) subtopic representativeness measured by the cosine similarity between the tweet and the centroid of all the tweets in the same peak area; (2) crowding endorsement measured by the times that the tweet is re-tweeted normalized by the total number of re-tweeting.

We can then estimate the topical similarity of two article sets by calculating the cosine similarity of their category frequency vectors C712=Aand6722= Bas

Table 3: Cosine similarity scores between the category frequency vectors of the flawed article sets and the respective random or reliable negatives

The nearest neighbors of a word are computed by comparing the cosine similarity between the center word and all other words in the dictionary.

Table 1: Nearest neighbors of words based on cosine similarity .

Table 2: Nearest neighbors of word embeddings learned by our model using the multi-prototype approach based on cosine similarity .

Vector-based approaches are often adopted to represent words as feature vectors and compute their distance with cosine similarity .

Distance is the cosine similarity between bag-of-words vector representations.

We measure similarity using cosine similarity between the vectors in both approaches.

An alternative to structural distance measures would be distance measures between the genres based on pairwise cosine similarities between them.

To assess this, we aggregated all character 4-gram training vectors of each genre and calculated standard cosine similarities .

Inspecting the distance matrix visually, we determined that the cosine similarity could clearly distinguish between Fiction and NonFiction texts but not between any other genres.

The WordNet senses are then ranked according to the cosine similarity between their sense vector and the contextually constrained target verb vector.

Therefore the choice of which word is contextualized does not strongly influence their cosine similarity , and contextualizing both should not add any useful information.

we compute [[swapOBmeadfl and compare it to the lifted first-order vectors of all paraphrase candidates, LOBJ([hint]) and LOBJ([star]), using cosine similarity .

LexRank is a multidocument summarization system, which first builds a cosine similarity graph of all the candidate sentences.

To formalize this assumption we use the sigmoid of the cosine similarity of two sentences to build it.

Intuitively, if a sentence has higher similarity with the reference paper, it should have a higher potential of being in class 1 or C. The flag of each sentence here is a value between 0 and l and is determined by its cosine similarity to the reference.

During classification cosine similarity is measured between the feature vector of the classified document and the expanded vectors of all categories.

The first avoids any expansion, classifying documents based on cosine similarity with category names only.

We also examined another filtering score, the cosine similarity between the vectors representing the two rule sides in LSA (Latent Semantic Analysis) space (Deerwester et al., 1990).