1. Yi-Chia Wang LTI 2nd year Master student
Analysis of Social Media
Trend Analysis
Yi-Chia Wang
LTI 2nd year Master student

2. Analysis of Social Media 2007
Introduction
Document streams
Arrive continuously over time
, news articles, search engine query logs, …
Identify topics in document streams
Topic detection and tracking
Text mining
Visualization …
Is there a better organizing principle for the enormous archives of document streams?
Temporal information in document streams
Trausan-Matu et al., 2007
Oct-30
Analysis of Social Media 2007

3. Analysis of Social Media 2007
“Burst of activity”
Topics appear, grow in intensity for a period of time, and then fade away.
Bursts correspond to points at which the intensity of message arrivals increases sharply
Problems with naive identification of bursts
Easily identifying large numbers of short bursts
Fragmenting long burst into many smaller ones
Goal: identifying bursts only when they have sufficient intensity
Oct-30
Analysis of Social Media 2007

4. Bursty and Hierarchical Structure in Streams
Jon Kleinberg Department of Computer Science Cornell University SIGKDD ‘02
My advisor is Carolyn Rose
This work is funded by PSLC
The project name is TagHelper

5. Two-state Automaton (A) Model
Idea: periods of lower message intensity interleave with periods of higher message intensity
A begins in state q0
A changes state with probability p
When in state q0, messages are emitted at a slow rate; when in state q1, messages are emitted at a faster rate
time
intensity q0 q1 q0 q1 p
1-p
States correspond to higher and higher message intensities
State transitions signal bursts
Emissions decide arrival times of next messages
Oct-30
Analysis of Social Media 2007

6. Exponential Distribution
Modeling the message emission rate
Modeling the time gap between messages and
Modeling by exponential distribution with parameter being the rate of message arrivals
Wikipedia
Oct-30
Analysis of Social Media 2007

7. Two-state Automaton (A) Model
Formally, given:
messages with specified arrival times
: inter-arrival gaps
We want to determine the conditional probability of a state sequence
Given a set of messages, one can find a likely state sequence based on the model
Oct-30
Analysis of Social Media 2007

8. Two-state Automaton (A) Model
Finding a state sequence q maximizing the probability
Equivalently, minimizing the following cost function:
Favoring state sequences that conform well to the sequence x of gap values
Favoring sequences with a small number of state transitions
Oct-30
Analysis of Social Media 2007

9. Infinite-state Automata Model
Cost Function
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Analysis of Social Media 2007

10. Computing a minimum-cost state sequence
THEOREM: If q* is an optimal state sequence in , then it is also an optimal state sequence in
Dynamic programming is used for searching an optimal state sequence
Oct-30
Analysis of Social Media 2007

11. Bursts exhibit a natural nested structure
A burst of intensity j is a maximal interval over which a part of state sequence is in a state of index j or higher
Bursts can also be represented as a tree. Each burst is a node in the tree
Oct-30
Analysis of Social Media 2007

12. Analysis of Social Media 2007
Experiments
The model makes sense for many datasets (of an analogous flavor)
Titles of conference papers
U.S. Presidential State of the Union Addresses
Web clickstreams
Oct-30
Analysis of Social Media 2007

13. Analysis of Social Media 2007
Dataset
Is the appearance of messages containing particular words exhibits a burst in the vicinity of significant times such as deadlines?
Author’s own collection of
June 9, 1997 – August 23, 2001
34344 messages (41.7 MB)
Focusing on the response set
Oct-30
Analysis of Social Media 2007

14. Results for the Word - ITR
ITR is the name of a large NSF program
The author wrote 2 proposals for it in ; one is a small proposal while another is a large one
The intervals are annotated with the first and last dates of the messages
The first subtree splits further into 2 subtrees
For the 2nd subtree, there is no burst since the author did not continue the submission
The figure shows the resulting bursts for the optimal state sequence
The intervals are annotated with the first and last dates of the messages
Oct-30
Analysis of Social Media 2007

15. Results for the Word - prelim
Prelim is the term used at Cornell for non-final exams
The author taught courses in 4 of the 8 semesters covered by the collection of , and each of these courses had 2 prelims
For the first of these courses, there was a special course account
For remaining 3 courses, each corresponds to a long burst and 2 shorter, more intense bursts for the particular prelims
The 2 structures suggest how a large folder of might naturally be divided into a hierarchical set of sub-folders around certain key events, based only on the rate of message arrivals
Oct-30
Analysis of Social Media 2007

16. Titles of Conference Papers
Goal: extracting bursts in term usage from the titles of conference papers over the past several decades
Problem: conference papers arrive in discrete batches every half or one year  no message inter-arrivals gaps
Modified automaton model:
Generating batched arrivals
For each state, there is an expected fraction of relevant documents
Bursty is identified if the fraction of relevant documents increases
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Analysis of Social Media 2007

17. Titles of Conference Papers
Cost function for each arrival batch:
The weight of the burst : the improvement in cost by using state q1 rather than state q0
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Analysis of Social Media 2007

18. Analysis of Social Media 2007
SIGMOD & VLDB,
Considering each word in paper titles
The 30 bursts of highest weight
The bursts with no ending date  the interval extends to the most recent conference
These bursty words are different from a list of common words
The bursts are picking up trend in language use
Oct-30
Analysis of Social Media 2007

19. Analysis of Social Media 2007
STOC & FOCS,
The 30 bursts of highest weight
Particular titling conventions that were in fashion for certain periods
“How to construct random functions” …
Oct-30
Analysis of Social Media 2007

20. U.S. Presidential State of the Union Addresses
Kleinbergh, SIGKDD ‘02
Oct-30
Analysis of Social Media 2007

21. Web usage data – clickstreams
Settings:
80 undergraduate students
Two and a half months in Spring 2000
For every URL w, all bursts in the stream of visits to w are determined
Focusing on high-weighted bursts as well as those that involve at least 10 distinct users
Results:
High-ranked bursts involve the URLs of the online class reading assignments, centered on intervals shortly before and during the weekly sessions at which they were discussed
Oct-30
Analysis of Social Media 2007

22. Analysis of Social Media 2007
Conclusions
Modeling streams using an infinite-state automaton
State transitions lead to bursts
First story detection: a single message on which the associated state transition occurred
The model offers a means of structuring the information from our patterns of interacting and communicating
Document streams have a strong temporal character
In many domains, we are accumulating detailed records of our own communication and behavior
Oct-30
Analysis of Social Media 2007