Effective Latent Space Graph-based Re-ranking Model with Global Consistency

Hongbo Deng, Michael R. Lyu and Irwin King

Department of Computer Science and Engineering

The Chinese University of Hong Kong

Feb. 12, 2009

WSDM 2009

2Hongbo Deng, Michael R. Lyu and Irwin KingDepartment of Computer Science and Engineering

The Chinese University of Hong Kong WSDM 2009

Outline

Introduction Related work Methodology

Graph-based re-ranking model Learning a latent space graph A case study and the overall algorithm

Experiments Conclusions and Future Work

Introduction

Problem definition Given a set of documents D A term vector di = xi

Relevance scores using VSM or LM A connected graph

Explicit link (e.g., hyperlinks) Implicit link (e.g., inferred from the content information)

Many other features

How to leverage the interconnection between documents/entities to improve the

ranking of retrieved results

with respect to the query?

Introduction

Initial ranking scores: relevance Graph structure: centrality (importance, authority) Simple method: Combine those two parts linearly Limitations:

Do not make full use of the information Treat each of them individually

What we have done? Propose a joint regularization framework Combine the content with link information in a latent

space graph

Related work

Using some variations of PageRank and HITS Centrality within graphs (Kurland

and Lee, SIGIR’05 & SIGIR’ 06) Improve Web search results using

affinity graph (Zhang et al., SIGIR’05)

Improve an initial ranking by random walk in entity-relation networks (Minkov et al., SIGIR’06)

Structural re-ranking model

Regularization framework

Learning a latent space

Linear combination, treat the content and link individually

Structural re-ranking model

Regularization framework Graph Laplacians for label propagation

(two classes) (Zhu et al., ICML’03, Zhou et al., NIPS’03)

Extent the graph harmonic function to multiple classes (Mei et al., WWW’08)

Score regularization to adjust ad-hoc retrieval scores (Diaz, CIKM’05)

Enhance learning to rank with parameterized regularization models (Qin et al., WWW’08)

Query-independent settingsDo not consider multiple relationships between objects.

Learning a latent space Latent Semantic Analysis (LSA)

(Deerwester et al., JASIS’90) Probabilistic LSI (pLSI) (Hofmann,

SIGIR’99) pLSI + PHITS (Cohn and Hofmann,

NIPS’00) Combine content and link for

classification using matrix factorization (Zhu et al., SIGIR’07)

Learning a latent space

Regularization framework

Use the joint factorization to learning the latent feature.

Difference: leverage the latent feature for building a latent space graph.

Methodology

Graph-based re-ranking model

Learning a latent space graph

Case study:Expert finding

Intuition: Global consistency: similar documents are most likely

to have similar ranking scores with respect to a query. The initial ranking scores provides invaluable

information Regularization framework

Global consistency Fit initial scores

Parameter

III. Methodology

Optimization problem

A closed-form solution

Connection with other methods μα 0, return the initial scores μα 1, a variation of PageRank-based model μα (0, 1), combine both information simultaneously∈

Graph-based re-ranking modelIII. Methodology

Methodology

Objective: incorporate the content with link information (or relational data) simultaneously Latent Semantic Analysis Joint factorization

Combine the content with relational data Build latent space graph

Calculate the weight matrix W

III. Methodology

Latent Semantic Analysis

Map documents to vector space of reduced dimensionality

SVD is performed on the matrix

The largest k singular values

Reformulated as an optimization problem

III. Methodology - Learning a latent space graph

Embedding multiple relational data Taking the papers as an

example Paper-term matrix C Paper-author matrix A

A unified optimization problem

X VC VA

A NxMNxL Conjugate Gradient

Build latent space graph

The edge weight wij is defined

Methodology

Case study: Application to expert finding

Utilize statistical language model to calculate the initial ranking scores The probability of a query given a document

Infer a document model θd for each document The probability of the query generated by the document

model θd

The product of terms generated by the document model (Assumption: each term are independent)

III. Methodology

Case study: Application to expert finding

Expert Finding: Identify a list of experts in the academic field for a given

query topic (e.g., “data mining” “Jiawei Han, etc”) Publications as representative of their expertise Use DBLP dataset to obtain the publications

Authors have expertise in the topic of their papers Overall aggregation of their publications

Refine the ranking scores of papers, then aggregate the refined scores to re-rank the experts

III. Methodology

Case study: Application to expert findingIII. Methodology

Experiments

DBLP Collection A subset of the DBLP records (15-CONF) Statistics of the 15-CONF collection

Benchmark Dataset

A benchmark dataset with 16 topics and expert lists

IV. Experiments

Evaluation Metrics

Precision at rank n (P@n):

Mean Average Precision (MAP):

Bpref: The score function of the number of non-relevant candidates

IV. Experiments

Preliminary Experiments

Evaluation results (%)

PRRM may not improve the performance GBRM achieve the best results

IV. Experiments

Details of the resultsIV. Experiments

Effect of parameter μα

μα 0, return the initial scores (baseline)

μα 1, discard the initial scores, consider the global consistency over the graph

IV. Experiments

Effect of parameter μα

Robust, achieve the best results when μα (0.5, 0.7)

IV. Experiments

Effect of graph construction

Different dimensionality (kd) of the latent feature, which is used to calculate the weight matrix W

Become better for greater kd, because higher dimensional space can better capture the similarities

kd, = 50 achieve better results than tf.idf

IV. Experiments

Effect of graph construction

Different number of nearest neighbors (knn)

Tends to degrade a little with increasing knn knn = 10 achieve the best results Average processing time: increase linearly with the

increase of knn

IV. Experiments

Conclusions and Future Work

Conclusions Leverage the graph-based model for the query-dependent

ranking problem Integrate the latent space with the graph-based re-ranking

model Address expert finding task in a the academic field using the

proposed method The improvement in our proposed model is promising

Future work Extend our framework to consider more features Apply the framework to other applications and large-scale

dataset

Thanks!

Effective Latent Space Graph-based Re-ranking Model with Global Consistency

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