We propose a context-sensitive topical PageRank method for keyword ranking and a probabilistic scoring function that considers both relevance and interestingness of keyphrases for keyphrase ranking.

For keyword ranking, we modify the Topical PageRank method proposed by Liu et al.

Next for each topic, we run a topical PageRank algorithm to rank keywords and then generate candidate keyphrases using the top ranked keywords (Section 3.3).

3.3 Topical PageRank for Keyword Ranking

Topical PageRank was introduced by Liu et al.

Mihalcea and Tarau (2004) proposed to use TextRank, a modified PageRank algorithm to extract keyphrases.

We set the damping factor ,u to 0.15 following the standard PageRank paradigm.

PageRank 0.493 0.481 0.509 0.536 0.604 PersRank 0.501 0.542 0.558 0.560 0.611 DivRank 0.487 0.505 0.518 0.523 0.585 CoRank 0.519 0.546 0.550 0.585 0.617

PageRank 0.557 0.549 0.623 0.559 0.588 PersRank 0.571 0.595 0.655 0.613 0.601 DivRank 0.538 0.591 0.594 0.547 0.589 CoRank 0.637 0.644 0.715 0.643 0.628

Tables 3 and 4 show how the performance of our co-ranking algorithm varies when considering only tweet popularity using the standard PageRank algorithm, personalization (PersRank), and diversity (DivRank).

Popularity We rank the tweet network following the PageRank paradigm (Erin and Page, 1998).

Personalization The standard PageRank algorithm performs a random walk, starting from any node, then randomly selects a link from that node to follow considering the weighted matrix M, or jumps to a random node with equal probability.

In contrast to PageRank , DivRank assumes that the transition probabilities change over time.

On the other hand, we apply the PageRank algorithm to rank important words in each document.

Whereas, we apply the PageRank algorithm (Brin et al., 1998) for the issue, because the algorithm scores the centrality of a node in a graph, and important words should be regarded as having the centrality (Hassan et al., 2007).

ment for text classification, there are many studies which use the PageRank algorithm.

They apply topic-specific PageRank to a graph of both words and documents, and introduce Polarity PageRank , a new semi-supervised sentiment classifier that integrates lexicon induction with document classification.

As a study related to topic detection by important words obtained by the PageRank algorithm, Kubek et al.

In particular, (Hassan et al., 2007) shows that the PageRank score is more clear to rank important words rather than tfidf.

In this study, we refer to their method and use PageRank algorithm to decide important words.

We present equivalent formalizations that show CoSimRank’s close relationship to Personalized PageRank and SimRank and also show how we can take advantage of fast matrix multiplication algorithms to compute CoSimRank.

We first first give an intuitive introduction of CoSimRank as a Personalized PageRank (PPR) derivative.

3.1 Personalized PageRank

Haveliwala (2002) introduced Personalized PageRank — or topic-sensitive PageRank — based on the idea that the uniform damping vector 19(0) can be replaced by a personalized vector, which depends on node i.

The use of weighted edges was first proposed in the PageRank patent.

These algorithms are often based on PageRank (Erin and Page, 1998) and other centrality measures (e.g., (Erkan and Radev, 2004)).

This paper introduces CoSimRank,1 a new graph-theoretic algorithm for computing node similarity that combines features of SimRank and PageRank .

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

LexRank (Erkan and Radev, 2004) is similar to PPR+cos in that it combines PageRank and cosine; it initializes the sentence similarity matrix of a document using cosine and then applies PageRank to compute lexical centrality.

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

Besides, the PageRank algorithm (Page et al., 1998) is adopted to optimize the graph model.

Finally, the weights of word nodes are calculated using the PageRank algorithm as follows:

where d is the damping factor as in the PageRank algorithm.

Besides, the standard PageRank algorithm is employed to optimize the graph model.

We develop induction algorithms based on three distinct types of algorithmic framework that have been shown successful for the analogous task of sentiment lexicon induction: HITS & PageRank (§2.1), Label/Graph Propagation (§2.2), and Constraint Optimization via Integer Linear Programming (§2.3).

2.1 HITS & PageRank

(2011) explored the use of HITS (Kleinberg, 1999) and PageRank (Page et al., 1999) to induce the general connotation of words hinging on the linguistic phenomena of selectional preference and semantic prosody, i.e., connotative predicates influencing the connotation of their arguments.

We find that the use of label propagation alone [PRED-ARG (CP)] improves the performance substantially over the comparable graph construction with different graph analysis algorithms, in particular, HITS and PageRank approaches of Feng et al.

To construct each semantic signature, we use the iterative method for calculating topic-sensitive PageRank (Haveliwala, 2002).

The PageRank may then be computed using:

For our semantic signatures we used the UKB2 off-the-shelf implementation of topic-sensitive PageRank .

As our WSD system, we used UKB, a state-of-the-art knowledge-based WSD system that is based on the same topic-sensitive PageRank algorithm used by our approach.

After creating the graph, PageRank is run to rank sentences.

Finally, instead of PageRank , we used SimRank (Haveliwala, 2002) to identify the nodes most similar to the query node and not only the central sentences in the graph.

After the graph is generated, the PageRank algorithm (Page et al., 1999) is used to determine the most central linguistic units in the graph.

PageRank spreads the query similarity of a vertex to its close neighbors, so that we rank higher sentences that are similar to other sentences which are similar to the query.

Standard features for learning to rank include various query-document features, e. g., BM25 (Robertson, 1997), as well as query-independent features, e. g., PageRank (Erin and Page, 1998).

These include sets of measures such as BM25, language-model-based IR score, and PageRank .

PageRank PageRank score (Brin and Page, 1998)

To do that, we employ a variant of the PageRank algorithm (Erin and Page, 1998).

Inline with the PageRank algorithm, we define the authority of user as

Considering the semantic similarity between nodes, we use another variant of the PageRank algorithm to calculate the weight of comment

When using the user graph as feature, we compute the authority score for each user with PageRank as shown in Equation 1.

PageRank Score: We employ the PageRank (Page et al., 1999) score of each URL as popularity score.

We compute the user’s authority score (AS) based on the link analysis algorithm PageRank:

We set the damping factor ,u to 0.85, following the standard PageRank paradigm.

The standard PageRank algorithm starts from an arbitrary node and randomly selects to either follow a random outgoing edge (considering the weighted transition matrix) or to jump to a random node (treating all nodes with equal probability).

where 1 is a vector with all elements equaling to l and the size is correspondent to the size of V0 or VT. ,u is the damping factor usually set to 0.85, as in the PageRank algorithm.