Collective entity linking: a random walk-based perspective

Abstract

Facing the large amount of name mentions appearing on the web, entity linking turns to be a hot researching topic recently, in which an entity in a resource is assigned to one name mention to help users grasp the meaning of this name mention. Unfortunately, like word disambiguation, one name mention can refer to several entities without considering its context. Apparently, the name mentions that usually co-occur are related and can be considered together to determine their suitable entities. This approach is called collective entity linking and is often conducted based on entity graph. However, traditional collective entity linking methods either consume much time due to the large scale of entity graph or obtain low accuracy due to simplifying graph to boost speed. To improve both accuracy and efficiency, this paper proposes a novel collective entity linking algorithm. It constructs a complete entity graph by connecting any two related entities, and the relationship between two entities is measured via a random walk-based calculating way. After that the relationships between entities are modeled as a relationship matrix, and a hill-climbing-based algorithm is proposed to change entity linking task to a sub-matrix searching problem. Experimental results demonstrate that our linking algorithm can obtain both accurate linking results and low running time meanwhile.

Appendix

Lemma 3.1

$E\left( {\overline{{\pi_{ij} }} } \right) = \overrightarrow {{P\left( {i,j} \right)}}$, where$\overline{{\pi_{ij} }}$denotes the number of visits on node j by the random walks that all start from node i divided by the number of visits on all the nodes.$\overrightarrow {{P\left( {i,j} \right)}}$denotes the probability that a random walk starts from one node i and ends at another node j.

Proof

Let A denote the transition matrix. $\overrightarrow {{P\left( {i,j} \right)}}$ can be calculated by

$$ \overrightarrow {{P\left( {i,j} \right)}} = \frac{{\sum\limits_{d = 1}^{l} {\left[ {A_{{}}^{d} } \right]_{ij} } }}{l} = \frac{{\left[ {A_{{}}^{1} } \right]_{ij} + \left[ {A_{{}}^{2} } \right]_{ij} + \left[ {A_{{}}^{3} } \right]_{ij} + \cdots + \left[ {A_{{}}^{l} } \right]_{ij} }}{l} $$

(19)

where l denotes the length of path between two nodes i and j. Since we limit the max length of path between two candidates as 5, l is at most 5. A_ij denotes the entry located at the ith row and jth column in A. Since A_ij is the transition probability from node i to node j, as indicated in [42] A ^d _ij is the probability that a random walk starts from node i and visits node j via d steps.

Let VI_ij denote the estimation of the number of visits on node j by a random walk that starts from node i. The expectation of VI_ij is

$$ E\left( {VI_{ij} } \right) = \sum\limits_{d = 1}^{l} {\left[ {A_{{}}^{d} } \right]_{ij} } = \left[ {A_{{}}^{1} } \right]_{ij} + \left[ {A_{{}}^{2} } \right]_{ij} + \left[ {A_{{}}^{3} } \right]_{ij} + \cdots + \left[ {A_{{}}^{l} } \right]_{ij} $$

(20)

Using VI_ij, the estimation in Eq. 13 can be rewritten as

$$ \overline{{\pi_{ij} }} = \frac{{\sum\nolimits_{t = 1}^{m} {VI_{ij} \left( t \right)} }}{ml} $$

(21)

where VI_ij(t) denotes the number of visits on node j by a random walk that starts from node i at tth time.

Due to the fact that the random walks starting from different nodes are independent on each other and the random walks starting from the same node at different times are also independent on each other, we have

$$ E\left( {\overline{{\pi_{ij} }} } \right) = E\left( {\frac{{\sum\nolimits_{t = 1}^{m} {VI_{ij} \left( t \right)} }}{ml}} \right) = \frac{1}{ml}\sum\limits_{t = 1}^{m} {\left( {E\left( {VI_{ij} } \right)} \right)} $$

(22)

From Eqs. 20 and 22, we have

$$ E\left( {\overline{{\pi_{ij} }} } \right) = \frac{1}{ml}\sum\limits_{t = 1}^{m} {\left( {E\left( {VI_{ij} } \right)} \right)} = \frac{1}{ml}\sum\limits_{t = 1}^{m} {\left( {\sum\limits_{d = 1}^{l} {\left[ {A_{{}}^{d} } \right]_{ij} } } \right)} = \frac{1}{l}\sum\limits_{d = 1}^{l} {\left[ {A_{{}}^{d} } \right]_{ij} } $$

(23)

After importing Eq. 19 in Eq. 23, it is easy to obtain that

$$ E\left( {\overline{{\pi_{ij} }} } \right) = \overrightarrow {{P\left( {i,j} \right)}} $$

(24)

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