随着文本信息的迅猛增长,数据挖掘已成为知识发现的重要方法。短文本相似性(short text similarity,STSim)度量是数据挖掘研究的重要技术。为了更好的提高短文本相似性度量精度,本文提出了基于加权网络改进的中文短文本相似性度量的一...随着文本信息的迅猛增长,数据挖掘已成为知识发现的重要方法。短文本相似性(short text similarity,STSim)度量是数据挖掘研究的重要技术。为了更好的提高短文本相似性度量精度,本文提出了基于加权网络改进的中文短文本相似性度量的一种新模型。首先,基于词语间的共现频次对语义网络进行加权,利用加权复杂网络表征短文本;其次,考虑短文本加权复杂网络权重识别度低的特点及每个词语节点的位置,计算短文本中每个词语的加权复杂网络综合特征值;最后,根据新模型计算短文本相似性,并通过聚类实验评价其优劣。实验结果表明,新提出的相似性度量模型优于STSim模型。展开更多
We prove that for a compact Finsler manifold M with nonnegative weighted Ricci curvature,if its first closed(resp.Neumann)eigenvalue of Finsler-Laplacian attains the sharp lower bound,then M is isometric to a circle(r...We prove that for a compact Finsler manifold M with nonnegative weighted Ricci curvature,if its first closed(resp.Neumann)eigenvalue of Finsler-Laplacian attains the sharp lower bound,then M is isometric to a circle(resp.a segment).Moreover,a lower bound of the first eigenvalue of Finsler-Laplacian with Dirichlet boundary condition is also estimated.These generalize the corresponding results in recent literature.展开更多
The authors obtain an interlacing relation between the Laplacian spectra of a graph G and its subgraph G-U,which is obtained from G by deleting all the vertices in the vertex subset U together with their incident edge...The authors obtain an interlacing relation between the Laplacian spectra of a graph G and its subgraph G-U,which is obtained from G by deleting all the vertices in the vertex subset U together with their incident edges.Also,some applications of this interlacing property are explored and this interlacing property is extended to the edge weighted graphs.展开更多
In this paper, we work on compact quasi-Einstein metrics and prove several gap results. In the first part, we get a gap estimate for the first nonzero eigenvalue of the weighted Laplacian, by establishing a comparison...In this paper, we work on compact quasi-Einstein metrics and prove several gap results. In the first part, we get a gap estimate for the first nonzero eigenvalue of the weighted Laplacian, by establishing a comparison theorem for the weighted heat kernel. In the second part, we establish two gap results for the Ricci curvature and the scalar curvature, based on which some rigid properties can be derived.展开更多
文摘随着文本信息的迅猛增长,数据挖掘已成为知识发现的重要方法。短文本相似性(short text similarity,STSim)度量是数据挖掘研究的重要技术。为了更好的提高短文本相似性度量精度,本文提出了基于加权网络改进的中文短文本相似性度量的一种新模型。首先,基于词语间的共现频次对语义网络进行加权,利用加权复杂网络表征短文本;其次,考虑短文本加权复杂网络权重识别度低的特点及每个词语节点的位置,计算短文本中每个词语的加权复杂网络综合特征值;最后,根据新模型计算短文本相似性,并通过聚类实验评价其优劣。实验结果表明,新提出的相似性度量模型优于STSim模型。
基金supported by National Natural Science Foundation of China(Grant No.11171253)the Natural Science Foundation of Ministry of Education of Anhui Province(Grant No.KJ2012B197)
文摘We prove that for a compact Finsler manifold M with nonnegative weighted Ricci curvature,if its first closed(resp.Neumann)eigenvalue of Finsler-Laplacian attains the sharp lower bound,then M is isometric to a circle(resp.a segment).Moreover,a lower bound of the first eigenvalue of Finsler-Laplacian with Dirichlet boundary condition is also estimated.These generalize the corresponding results in recent literature.
基金supported by the National Natural Science Foundation of China (No.10731040)the Shanghai Leading Academic Discipline Project (No.S30104)
文摘The authors obtain an interlacing relation between the Laplacian spectra of a graph G and its subgraph G-U,which is obtained from G by deleting all the vertices in the vertex subset U together with their incident edges.Also,some applications of this interlacing property are explored and this interlacing property is extended to the edge weighted graphs.
基金supported by Natural Science Foundation of Jiangsu Province (Grant No. BK20141235)
文摘In this paper, we work on compact quasi-Einstein metrics and prove several gap results. In the first part, we get a gap estimate for the first nonzero eigenvalue of the weighted Laplacian, by establishing a comparison theorem for the weighted heat kernel. In the second part, we establish two gap results for the Ricci curvature and the scalar curvature, based on which some rigid properties can be derived.
