Transcript Document

Google搜索与
Inter网的信息检索
马志明
May 16, 2008
Email: [email protected]
http://www.amt.ac.cn/member/mazhiming/index.html
约有626,000项符合中国科学院数
学与系统科学研究院的查询结果，
以下是第1-100项。
(搜索用时 0.45 秒）
How can google make a
ranking of 626,000 pages
in 0.45 seconds?
A main task of
Internet (Web)
Information Retrieval
= Design and Analysis of
Search Engine (SE) Algorithm
involving
plenty of Mathematics
 HITS
1998 Jon Kleinberg Cornell University
 PageRank
1998 Sergey Brin and Larry Page
Stanford University
Nevanlinna Prize（2006)
Jon Kleinberg
• One of Kleinberg‘s most important research achievements
focuses on the internetwork structure of the World Wide Web.
• Prior to Kleinberg‘s work, search engines focused only on
the content of web pages，not on the link structure.
• Kleinberg introduced the idea of
• “authorities” and “hubs”:
• An authority is a web page that contains information on a
particular topic,
• and a hub is a page that contains links to many authorities.
Zhuzihu thesis.pdf
Page Rank, the ranking system
Google search engine.
• Query independent
• content independent.
• using only the web graph
structure
used by the
Page Rank, the ranking system used
by the Google search engine.
WWW 2005 paper
PageRank as a Function of the Damping Factor
Paolo Boldi Massimo Santini Sebastiano Vigna
DSI, Università degli Studi di Milano
3 General Behaviour
3.1 Choosing the damping factor
3.2 Getting close to 1
  lim  ( )
*
 1
 can we somehow characterise the properties of  ?
*
 what makes  different from the other (infinitely
many, if P is reducible) limit distributions of P?
*
Conjecture 1 :
 is the limit distribution of P when the starting
*
distribution is uniform, that is,
1 n
lim  ( )  lim P .
n  N
 1
Website provide plenty of information:
pages in the same website may share the same IP, run
on the same web server and database server, and be
authored / maintained by the same person or organization.
there might be high correlations between pages in the
same website, in terms of content, page layout and
hyperlinks.
websites contain higher density of hyperlinks inside
them (about 75% ) and lower density of edges in between.
HostGraph loses much
transition information
Can a surfer jump from page 5 of site 1 to
a page in site 2 ?
From: [email protected] [mailto:s06-pc-chairsSent: 2006年4月4日 8:36
To: Tie-Yan Liu; [email protected]; [email protected];
[email protected]; [email protected]
Subject: [SIGIR2006] Your Paper #191
Title: AggregateRank:
Congratulations!!
Bring Order to Web Sites
29th Annual International Conference on Research & Development
on Information Retrieval (SIGIR’06, August 6–11, 2006, Seattle,
Washington, USA).
Ranking Websites,
a Probabilistic View
Internet Mathematics, Volume 3
(2007), Issue 3
Ying Bao, Gang Feng, Tie-Yan Liu,
Zhi-Ming Ma, and Ying Wang
- --- We
suggest evaluating the importance of a
website with the mean frequency of visiting the
website for the Markov chain on the Internet
Graph describing random surfing.
---We show that this mean frequency is
equal to the sum of the PageRanks of all the
webpages in that website
(hence is referred as PageRankSum )
---We propose a novel algorithm
(AggregateRank Algorithm)
based on the
theory of stochastic complement
to calculate the rank of a website.
---The AggregateRank Algorithm can
approximate the PageRankSum accurately,
while the corresponding computational
complexity is much lower than
PageRankSum
--- By constructing return-time Markov chains
restricted to each website, we describe also the
probabilistic relation between PageRank and
AggregateRank.
---The complexity and the error bound of
AggregateRank Algorithm with experiments
of real dada are discussed at the end of the
paper.
• n webs in N sites,
n  n1  n2    nN
The stationary distribution, known as the
PageRank vector, is given by
We may rewrite the stationary distribution as
with
as a row vector of length
ni
We define the one-step transition probability
from the website Si to the website S j by
where e is an n j dimensional column
vector of all ones
The N×N matrix C(α)=(cij(α)) is referred to as
the coupling matrix, whose elements represent
the transition probabilities between websites. It
can be proved that C(α) is an irreducible
stochastic matrix, so that it possesses a unique
stationary probability vector. We use ξ(α) to
denote this stationary probability, which can be
gotten from
   C       with    e  1
Since
One can easily check that
is the unique solution to
   C       with    e  1
We shall refer
as the AggregateRank
That is, the probability of visiting a
website is equal to the sum of PageRanks
of all the pages in that website. This
conclusion is consistent to our intuition.
the transition probability from Si to Sj actually
summarizes all the cases that the random surfer
jumps from any page in Si to any page in Sj within
one-step transition. Therefore, the transition in this
new HostGraph is in accordance with the real
behavior of the Web surfers. In this regard, the socalculated rank from the coupling matrix C(α) will
be more reasonable than those previous works.
Let
denote the number of
visiting the website
during the n times
,
that is
We have
Assume a starting state in website A, i.e.
We define
and inductively
It is clear that all the variables
are stopping times for X.
Let
denote the transition matrix of
the return-time Markov chain for site
Similarly, we have
Suppose that AggregateRank, i.e.
the stationary distribution of
Since
Therefore
is
• Based on the above discussions, the direct
approach of computing the AggregateRank ξ(α) is
to accumulate PageRank values (denoted by
PageRankSum).
• However, this approach is unfeasible because the
computation of PageRank is not a trivial task
when the number of web pages is as large as
several billions. Therefore,
Efficient computation becomes a
significant problem .
AggregateRank
1.
Divide the n × n matrix
into
N × N blocks according to the N sites.
2. Construct the stochastic matrix
for
by changing the diagonal elements of
to make each raw sum up to 1.
3. Determine
from
4. Form an approximation
matrix
, by evaluating
to the coupling
5. Determine the stationary distribution of
and denote it
, i.e.,
Experiments
• In our experiments, the data corpus is the
benchmark data for the Web track of TREC
2003 and 2004, which was crawled from
the .gov domain in the year of 2002.
• It contains 1,247,753 webpages in total.
we get 731 sites in the .gov dataset. The largest website
contains 137,103 web pages while the smallest one
contains only 1 page.
Performance Evaluation of Ranking Algorithms based
on Kendall's distance
Similarity between PageRankSum and
other three ranking results.
• From: [email protected]
Sent: Thursday, April 03, 2008 9:48 AM
Dear Yuting Liu, Bin Gao, Tie-Yan Liu, Ying Zhang,
• Zhiming Ma, Shuyuan He, Hang Li
• We are pleased to inform you that your paper
Title: BrowseRank: Letting Web Users
Vote
for Page Importance
has been accepted for oral presentation as a full paper and
for publication as an eight-page paper in the proceedings of
• the 31st Annual International ACM SIGIR
Conference on Research & Development on Information
Retrieval.
Congratulations!!
Building model
• Properties of Q process:
– Stationary distribution:
•
   P(t )
– Jumping probability:
•
– Embedded Markov chain:
•
is a Markov chain with the transition probability
matrix
Main conclusion 1
•
–
is the mean of the staying time on page i.
The more important a page is, the longer
staying time on it is.
–
is the mean of the first re-visit time at page i.
The more important a page is, the smaller the
re-visit time is, and the larger the visit frequency is.
Main conclusion 2
•
–
is the stationary distribution of
– The stationary distribution of discrete model is
easy to compute
• Power method for
• Log data for
Further questions
• How about inhomogenous process?
– Statistic result show: different period of time
possesses different visiting frequency.
– Poisson processes with different intensity.
• Marked point process
– Hyperlink is not reliable.
– Users’ real behavior should be considered.
Relevance
Ranking
• Many features
for measuring
relevance
– Term distribution (anchor, URL, title, body,
proximity, ….)
– Recommendation & citation (PageRank, clickthrough data, …)
– Statistics or knowledge extracted from web data
• Questions
– What is the optimal ranking function to combine
different features (or evidences)?
– How to measure relevance?
Learning to Rank
• What is the optimal weightings for
combining the various features
– Use machine learning methods to learn the ranking
function
– Human relevance system (HRS)
– Relevance verification tests (RVT)
Wei-Ying Ma, Microsoft Research Asia
Learning to Rank
(1)
q (m)
d1(1)
d1( m )
q
d 2(1)

d
(1)
n (1 )
 d (m)
2


Learning
System
Model
d n( m( m))
d1( m1)
q ( m1)
Ranking
System
d 2( m1)

d n( m( m11))
Wei-Ying Ma, Microsoft Research Asia
66
q (i )
d1( i )
Learning
to
Rank
(Cont)
d
(i )
2

Break down
d
q (i )
(i )
j
, d k(i )

1 j , k  n ( i )
d n( i( i))
• State-of-the-art algorithms for learning
to rank take the pairwise approach
– Ranking SVM
– RankBoost
– RankNet (employed at Live Search)
Wei-Ying Ma, Microsoft Research Asia
67
learning to rank
• The goal of learning to rank is to construct
a real-valued function that can generate a
ranking on the documents associated with
the given query. The state-of-the-art
methods transforms the learning problem
into that of classification and then performs
the learning task:
• For each query, it is assumed that there are
two categories of documents: positive and
negative (representing relevant and
irreverent with respect to the query). Then
document pairs are constructed between
positive documents and negative documents.
In the training process, the query
information is actually ignored.
[5] Y. Cao, J. Xu, T.-Y. Liu, H. Li, Y. Huang, and H.-W. Hon.
Adapting ranking svm to document retrieval.
In Proc. of SIGIR’06, pages 186–193, 2006.
[11] T. Qin, T.-Y. Liu, M.-F. Tsai, X.-D. Zhang, and H. Li.
Learning to search web pages with query-level
loss functions. Technical Report MSR-TR-2006-156, 2006.
As case studies, we investigate Ranking SVM and RankBoost.
We show that after introducing query-level normalization to its
objective function, Ranking SVM will have query-level stability.
For RankBoost, the query-level stability can be achieved if we
introduce both query-level normalization and regularization to its
objective function.
• We re-represent the learning to rank problem by
introducing the concept of
• ‘query’ and ‘distribution given query’
• into its mathematical formulation.
• More precisely, we assume that queries are drawn
independently from a query space Q according to
an (unknown) probability distribution
It should be noted that if
, then the bound makes
sense. This condition can be satisfied in many practical cases.
As case studies, we investigate Ranking SVM and RankBoost.
We show that after introducing query-level normalization to its
objective function, Ranking SVM will have query-level stability.
For RankBoost, the query-level stability can be achieved if we
introduce both query-level normalization and regularization to its
objective function.
These analyses agree largely with our experiments and the
experiments in [5] and [11].
Rank aggregation
• Rank aggregation is to combine ranking
results of entities from multiple ranking
functions in order to generate a better one.
The individual ranking functions are
referred to as base rankers, or simply
rankers.
Score-based aggregation
• Rank aggregation can be classified into
two categories [2]. In the first category,
the entities in individual ranking lists
are assigned scores and the rank
aggregation function is assumed to use
the scores (denoted as score-based
aggregation) [11][18][28].
order-based aggregation
• In the second category, only the orders of
the entities in individual ranking lists are
used by the aggregation function (denoted
as order-based aggregation). Order-based
aggregation is employed at meta-search,
for example, in which only order (rank)
information from individual search engines
is available.
• Previously order-based aggregation was
mainly addressed with the unsupervised
learning approach, in the sense that no
training data is utilized; methods like
•
•
•
•
•
Borda Count [2][7][27],
median rank aggregation [9],
genetic algorithm [4],
fuzzy logic based rank aggregation [1],
Markov Chain based rank aggregation [7]
and so on were proposed.
i5  i4  i3  i2  i1
It turns out that the optimization problems for the
Markov Chain based methods are hard, because
they are not convex optimization problems.
We are able to develop a method for the
optimization of one Markov Chain based method,
called Supervised MC2.
We prove that we can transform the optimization
problem into that of Semidefinite Programming. As
a result, we can efficiently solve the issue.
Next Generation Web Search ?
(Web Search 2.0 --> 3.0)
• Directions for new innovations
– Process-centric vs. data-centric
– Infrastructure for Web-scale data mining
– Intelligence & knowledge discovery
Wei-Ying Ma, Microsoft Research Asia
Web Search –
Past, Present, and Future
Wei-Ying Ma
Web Search and Mining Group
Microsoft Research Asia
next generation.ppt
Web Search - Past Present and Future - public.ppt