NERank: Bringing Order to Named Entities from Texts

Abstract

Most entity ranking research aims to retrieve a ranked list of entities from a Web corpus given a query. However, entities in plain documents can be ranked directly based on their relative importance, in order to support entity-oriented Web applications. In this paper, we introduce an entity ranking algorithm NERank to address this issue. NERank first constructs a graph model called Topical Tripartite Graph from a document collection. A ranking function is designed to compute the prior ranks of topics based on three quality metrics. We further propose a meta-path constrained random walk method to propagate prior topic ranks to entities. We evaluate NERank over real-life datasets and compare it with baselines. Experimental results illustrate the effectiveness of our approach.

A preliminary version of this paper has been presented in WWW’16 [6]. This work is partially supported by NSFC under Grant No. 61402180, the Natural Science Foundation of Shanghai under Grant No. 14ZR1412600, Shanghai Agriculture Science Program (2015) Number 3-2 and NSFC-Zhejiang Joint Fund for the Integration of Industrialization and Informatization under Grant No. U1509219.

Appendix: Mathematical Analysis of NERank

We prove that the random walk algorithm of NERank will converge and derive the close-form solution. Let $\mathbf {T_n}$ denote the $|T|\times 1$ matrix which represents the ranks of topics in the $n^{th}$ iteration. Specially, $\mathbf {T_0}$ is the prior rank matrix for topics. Let $\mathbf {E_n}$ denote the $|E|\times 1$ entity rank matrix in the $n^{th}$ iteration. Based on the random walk process, the rank update of topics for TDT meta-path is formulated as: $\mathbf {T_{n}}=\mathbf {\Theta _R}^T\mathbf {\Theta }\cdot \mathbf {T_{n-1}}$ where $\mathbf {\Theta _R}$ is the row-normalized matrix of $\mathbf {\Theta }$. Similarly, for TET meta-path, we have $\mathbf {T_{n}}=\mathbf {\hat{\Phi }_C}\mathbf {\hat{\Phi }_R}^T\cdot \mathbf {T_{n-1}}$ where $\mathbf {\hat{\Phi }_R}$ and $\mathbf {\hat{\Phi }_C}$ are the row-normalized and column-normalized matrices of $\mathbf {\hat{\Phi }}$, respectively. The update rule in one iteration is formulated as:

$$\begin{aligned} \mathbf {T_{n}}=\alpha \cdot \mathbf {\Theta _R}^T\mathbf {\Theta }\cdot \mathbf {T_{n-1}}+\beta \cdot \mathbf {\hat{\Phi }_C}\mathbf {\hat{\Phi }_R}^T\cdot \mathbf {T_{n-1}}+(1-\alpha -\beta )\cdot \mathbf {T_{0}} \end{aligned}$$

For simplicity, we define $\mathbf {M}=\alpha \cdot \mathbf {\Theta _R}^T\mathbf {\Theta }+\beta \cdot \mathbf {\hat{\Phi }_C}\mathbf {\hat{\Phi }_R}^T$. By iteration, we have $\mathbf {T_{n}}=\mathbf {M}^n \cdot \mathbf {T_{0}}+(1-\alpha -\beta )\cdot \sum _{i=0}^{n-1}\mathbf {M}^i\cdot \mathbf {T_{0}}$. Because $\lim _ {n\rightarrow \infty }\mathbf {M}^n=\mathbf {0}$ and $\lim _ {n\rightarrow \infty }\sum _{i=0}^{n-1}\mathbf {M}^i=(\mathbf {I}-\mathbf {M})^{-1}$, the limit of matrix series $\{\mathbf {T_n}\}$ is derived as:

$$\begin{aligned} \lim _ {n\rightarrow \infty }\mathbf {T_{n}} =\lim _ {n\rightarrow \infty }\mathbf {M}^n \cdot \mathbf {T_{0}}+(1-\alpha -\beta )\lim _ {n\rightarrow \infty }\sum _{i=0}^{n-1}\mathbf {M}^i\cdot \mathbf {T_{0}}=(1-\alpha -\beta )(\mathbf {I}-\mathbf {M})^{-1}\mathbf {T_{0}} \end{aligned}$$

where $\mathbf {I}$ is the $|T|\times |T|$ identity matrix. Therefore, the ranks of topics will converge in NERank. Because the rank of entities $\mathbf {E_n}$ can be computed by $\mathbf {E_n}=\mathbf {\hat{\Phi }_R}^T\cdot \mathbf {T_n}$. Denote $\mathbf {E^{*}}$ as the close form solution vector for entity ranks. We have

$$\begin{aligned} \mathbf {E^{*}}=(1-\alpha -\beta )\cdot \mathbf {\hat{\Phi }_R}^T(\mathbf {I}-\alpha \cdot \mathbf {\Theta _R}^T\mathbf {\Theta }-\beta \cdot \mathbf {\hat{\Phi }_C}\mathbf {\hat{\Phi }_R}^T)^{-1}\cdot \mathbf {T_{0}} \end{aligned}$$

where the rank of entity $e_i$ (i.e., $r(e_i)$) is the $i^{th}$ element in $\mathbf {E^{*}}$.