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Navigation behaviour is described by mean of first biological principles: The neurophysiology of decision making.
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11
Web User Behavior Analysis
Doctorado en Sistemas de Ingeniería,
Universidad de Chile. Prof. Guía: Juan D. Velásquez
Pablo E. Romá[email protected]
2
Outline
Motivation, Hypothesis, Achievement The problems & solutions
Pre-processingSimulationCalibration
Conclusions & Future Work
3
Motivation, Hypothesis, Achievement
44
Most famous web companies are analyzing the web user browsing behavior.
Google 2009 net profit: 6,520 Millions US$ Amazon: 902 Millions US$. NetFlix: 116 Millions US$. (Codelco net profit: 1,262 Millions )
AdaptiveWeb Sites
5
Why we study the web user browsing behavior? A web user need to fast information fast
and complete. To enhance a web site
Administrators/owners can only modify:Web Pages’ ContentsWeb Site Links
Hopefully, the modification likes to objective group of members!
6
The main Problem
There are only Heuristics in order to analyze the web user browsing behavior to enhance the contents and structure of a web site
We think we can do it better…
77
Research hypothesis
It is possible to apply neurophysiology’s decision making theories to explain web user navigational behavior by using web data.
8
The Thesis ProposalWeb Intelligence
A.I. in the Web
Web Mining
Knowledge Representation
AdvancedInf Tech. in the Web
AgentUbiquitous Sys.
Wireless Sys.
Grid & Cloud Sys.
Social Network
Web Structure Mining
Web Content Mining
Web Usage Mining
Web user neurocomputing
Neurophysiology model for the analysis of the behavior
discovering pattern of web user navigational behavior from the set of user’ trails
99
Web user neurocomputing in Brief
We use a brain model of decision making to study how people browse a web site.
Based on neurophysiology first principles.
1010
Machine learning vs. First principle model
Traditional Web Mining: Machine Learning (ML) Generic algorithm that can found or be trained to reproduce data regularities.
First principle models (FPP): e.g. Newton’s Law.
1. Can we use ML or FPP to build trajectories of the Apollo mission?
2. One million dollar Netflix contest: achieve a 10% improvement to the accuracy of customer movie preference. 4 years without a winner!!!
3. If conditions of the problem change, then ML system’s must be recalibrated.
Proposed Solution
1111
Thesis dissertation: Main Contributions Novel mechanism for web session extraction from
web log based on Integer Programming. 2008, WI-IAT Int. Conf. R. Dell, P. Román, J. Velásquez. Using a linear objective function.
2010, Submitted to IDA Journal. P. Román, R. Dell, J. Velásquez. Using a network model.
Application of a Psychology model for describing web user navigation. 2009, AWIC Int. Conf. P. Román, J. Velásquez.
Simulation of decision’s making Neurophysiology. Calibration and simulation of Psychology based
stochastic model. 2009, IAAA BICA Symposium, P. Román, J. Velásquez. 2010, WI-IAT Int. Conf. , P. Román, J. Velásquez.
12
First problem: Pre-processing
13
Web basic operationWeb basic operation
14
Web data: Web logs (Usage)Web data: Web logs (Usage)# IP Id Acces Time Method/URL/Protocol Status Bytes Referer Agent
1 165.182.168.101 - - 16/06/2002:16:24:06 GET p1.htm HTTP/1.1 200 3821 out.htm Mozilla/4.0 (MSIE 5.5; WinNT 5.1)2 165.182.168.101 - - 16/06/2002:16:24:10 GET A.gif HTTP/1.1 200 3766 p1.htm Mozilla/4.0 (MSIE 5.5; WinNT 5.1)3 165.182.168.101 - - 16/06/2002:16:24:57 GET B.gif HTTP/1.1 200 2878 p1.htm Mozilla/4.0 (MSIE 5.5; WinNT 5.1)4 204.231.180.195 - - 16/06/2002:16:32:06 GET p3.htm HTTP/1.1 304 0 - Mozilla/4.0 (MSIE 6.0; Win98)5 204.231.180.195 - - 16/06/2002:16:32:20 GET C.gif HTTP/1.1 304 0 - Mozilla/4.0 (MSIE 6.0; Win98)6 204.231.180.195 - - 16/06/2002:16:34:10 GET p1.htm HTTP/1.1 200 3821 p3.htm Mozilla/4.0 (MSIE 6.0; Win98)7 204.231.180.195 - - 16/06/2002:16:34:31 GET A.gif HTTP/1.1 200 3766 p1.htm Mozilla/4.0 (MSIE 6.0; Win98)8 204.231.180.195 - - 16/06/2002:16:34:53 GET B.gif HTTP/1.1 200 2878 p1.htm Mozilla/4.0 (MSIE 6.0; Win98)9 204.231.180.195 - - 16/06/2002:16:38:40 GET p2.htm HTTP/1.1 200 2960 p1.htm Mozilla/4.0 (MSIE 6.0; Win98)
10 165.182.168.101 - - 16/06/2002:16:39:02 GET p1.htm HTTP/1.1 200 3821 out.htm Mozilla/4.0 (MSIE 5.01; WinNT 5.1)11 165.182.168.101 - - 16/06/2002:16:39:15 GET A.gif HTTP/1.1 200 3766 p1.htm Mozilla/4.0 (MSIE 5.01; WinNT 5.1)12 165.182.168.101 - - 16/06/2002:16:39:45 GET B.gif HTTP/1.1 200 2878 p1.htm Mozilla/4.0 (MSIE 5.01; WinNT 5.1)13 165.182.168.101 - - 16/06/2002:16:39:58 GET p2.htm HTTP/1.1 200 2960 p1.htm Mozilla/4.0 (MSIE 5.01; WinNT 5.1)14 165.182.168.101 - - 16/06/2002:16:42:03 GET p3.htm HTTP/1.1 200 4036 p2.htm Mozilla/4.0 (MSIE 5.01; WinNT 5.1)15 165.182.168.101 - - 16/06/2002:16:42:07 GET p2.htm HTTP/1.1 200 2960 p1.htm Mozilla/4.0 (MSIE 5.5; WinNT 5.1)16 165.182.168.101 - - 16/06/2002:16:42:08 GET C.gif HTTP/1.1 200 3423 p2.htm Mozilla/4.0 (MSIE 5.01; WinNT 5.1)17 204.231.180.195 - - 16/06/2002:17:34:20 GET p3.htm HTTP/1.1 200 2342 out.htm Mozilla/4.0 (MSIE 6.0; Win98)18 204.231.180.195 - - 16/06/2002:17:34:48 GET C.gif HTTP/1.1 200 3423 p2.htm Mozilla/4.0 (MSIE 6.0; Win98)19 204.231.180.195 - - 16/06/2002:17:35:45 GET p4.htm HTTP/1.1 200 3523 p3.htm Mozilla/4.0 (MSIE 6.0; Win98)20 204.231.180.195 - - 16/06/2002:17:35:56 GET D.gif HTTP/1.1 200 3231 p4.htm Mozilla/4.0 (MSIE 6.0; Win98)21 204.231.180.195 - - 16/06/2002:17:36:06 GET E.gif HTTP/1.1 404 0 p4.htm Mozilla/4.0 (MSIE 6.0; Win98)
15
Web data: Content (text, object,..)Web data: Content (text, object,..)
You can put anything you want on a Web page, from family to business info….
You can put anything you want on a Web page, from family to business info….
Hyperlink structureHyperlink structure
16
Web Data: Hyperlink structure
1717
Proposal: Data sources
Neurophysiology commonly uses data obtained from neural-cabled subjects or psychological tests (surveys).
I use web data for the study of human behavior using the web
1818
Problem: Web data pre-processing Hyperlink graph, Web page content, Web user session
(sequence of pages). Web Logs do not directly capture sessions How to reconstruct sessions? SESSIONIZATION : process for obtaining sessions. If invasive methods are used privacy right are violated
(forbidden by law in several countries). Cookies Spyware Tracking applications
19
Traditional approach for sessionization1. Proactive: direct tracking of the web user
a) Privacy issueb) The most exact
2. Reactive: reconstruction of web user’s page sequence heuristically.
a) Only an approximation (40% noise)b) Use anonymous activity data sources like web logs.c) Models of behavior are sensitive to noise in data.
20
Traditional heuristic for sessionization
Filtering: IP+Browser(Agent)
Timeout of 30 minute
Path completion: shortest path backward
How to identify individual web users?
2121
Sessionization: The proposal
Incorporate all restrictions as a combinatorial optimization problem. Two formulation: Maximization of a linear reward, network flow model.
2222
Integer Programming for sessionization (WI-IAT08 R. Dell, P.Roman, J. Velasquez)
Xros : 1 if log register “r” is assigned as the “o-th” request during session “s” and zero otherwise.
It is a labeling problem!
Index r IP Time Method/URL/Protocol Status Bytes Agent1 "165.182.168.101" 16/04/2008:16:24:06 GET index.htm HTTP/1.1 200 3821 Mozilla/4.02 "165.182.168.101" 16/04/2008:16:24:07 GET /informacion/academicos/index.htm HTTP/1.1 200 1345 Mozilla/4.03 "165.182.168.101" 16/04/2008:16:24:08 GET /informacion/academicos/Profesores_Titulares/index.htm HTTP/1.1 200 2567 Mozilla/4.04 "190.20.216.76" 16/04/2008:16:24:09 GET /images/borde_titulos.jpg HTTP/1.1 200 4678 Mozilla/4.05 "190.44.161.57" 16/04/2008:16:24:10 / HTTP/1.1 200 3821 Mozilla/4.06 "165.182.168.101" 16/04/2008:16:24:11 GET index.htm HTTP/1.1 200 3821 Mozilla/4.07 "165.182.168.101" 16/04/2008:16:24:12 GET informacion/academicos/index.htm HTTP/1.1 200 1345 Mozilla/4.08 "165.182.168.101" 16/04/2008:16:24:13 GET index.htm HTTP/1.1 200 3821 Mozilla/4.09 "165.182.168.101" 16/04/2008:16:24:14 GET index.htm HTTP/1.1 200 3821 Mozilla/4.0
10 "165.182.168.101" 16/04/2008:16:24:15 GET /exalumnos_empresas/index.htm HTTP/1.1 200 4563 Mozilla/4.011 "165.182.168.101" 16/04/2008:16:24:16 GET /proyectos_investigacion/index.htm HTTP/1.1 200 1224 Mozilla/4.012 "165.182.168.101" 16/04/2008:16:24:17 GET /publicaciones/index.htm HTTP/1.2 200 2543 Mozilla/4.013 "165.182.168.101" 16/04/2008:16:24:18 GET /~cea/ index.html 200 1924 Mozilla/4.0
1 2 3 4 5 . . .o1 5 6 8 92 7 12 133 104 11...
s
123
Log register
Sessions
2323
Integer Program ~ Maximize the number of sessions. (WI-IAT08, KES09 P. Roman et al)
Register used once
One register on o
Structure and time
2424
Network model: Minimize number of session.(IDA10 P. Roman et al)
Source Sink
…
Z=3
1
0
0
(1,1)
00
0
1
: flow of a session1
(1,1)
1’
2(1,1)
2’
3(1,1)
3’1
0
Now is feasibleN
N’
(1,1)
4
4’
1
1
1
0
0
• Edge indicates register precedence• Node is a register (duplicated) • Flow = Number of sessions
25
Experiment: Large scale (15 month)DII departmental web site.
~4000 pages ~17000 links ~15000 visits per month Simple: precise information Content mainly based on text Objective: Academics, Study
programs, Projects, … Session size distribution (1 Year)
0
1
2
3
4
5
6
0 0,5 1 1,5 2 2,5
Log Size
Log
N
http://www.dii.uchile.cl/
2626
A large scale experiment evaluation: F-Score over cookie retrieved sessions. (IDA10 P. Roman et al)
• 0<F<1• Higher F is better
Traditional sessionization
Both proposal
2727
A large scale experiment evaluation: F-Score over cookie retrieved sessions.Method Precision Recall F-Score TimeSessionization Integer Programming (SIP)
0.7788 0.6696 0.7201 6 Hour
Network Flow (BCM)
0.7777 0.6671 0.7182 4 Min
Canonical Sessionization
0.5091 0.6996 0.5993 1 Min
Compared with 15 months of cookie retrieval
28
Summary: Pre-processing It is possible to ensure data quality using
optimality Even in the worst scenario when only web logs
are available. Main Achievement: F=0.72 In acceptable processing time 4min/month
Ready for Neurocomputing!
29
Second problem: Simulation
3030
Strong Regularities:Distribution of sessions(WI-IAT08 P. Roman et al)
•Empirical power rule for session size has been observed in the literature [Huberman et al. 1998, Science]. Web Surfer Law.
•The correlation coefficient and standard error of fitting to a power law gives us a sense of the quality of the sessions.
•Our correlation coefficient is 0.94 and our standard error is 0.3817. A common heuristic has a correlation coefficient of 0.91 and a standard error of 0.64.
3131
Regularity presence of internal rule (2008, CLAIO P. Roman et al.)
Law of surfing Machine learning algorithm has been applied
in order to capture such regularities. Today new directions based on the brain’s
informatics are used to explains navigation.
What we need isa theory for
explaining such regularities!
3232
Proposal: To adapt Psychological theory to web navigation, using web data.
Human behavior on the web is the result of brain neural network processing.
Require historical data of individual’s trajectories on a web site.
Difficult to calculate or predict the calculation of 1011 neuron and 1014 Interconnection.
Diffusion process -> average at mesoscopic level This is the point of view of this thesis.
3333
Biological experiment (1970-2005)
Rhesus monkey with sensor placed on Lateral intra-parietal (LIP) cortex (2002-2008)
Screen with moving dots, the decision is to select the correct direction of motion.
Monkeys are trained to receive a reward if they answer the correctly.
Possible options map on the LIP cortex and the point with higher neural activity will correspond to the decision of the subject.
3434
Neurophysiology of decision making: First Principles
First hitting time -> time to decide. First hitting coordinate -> the choice
X1
X2
It decides option 1.
Two options0
3535
LCA Model (Leacky Competing Accumulator) [M. Usher et al, 2001]
X>0 → Biological condition: Neural activity is positive II is considered exogenous and constant Others parameters (k,λ,σ) in the model are positives The stochastic equation:
jjl jljj dWdtIXkXdX
X
I
IIjj : Likelihood to make choice j. It drives the decision! Result from other area processing (e.g. Visual Cortex).
Important parameter!!
3636
Application: The browsing process Arrivals (first page) are
exogenous to this model. Based on historic sessions,
the model predicts probability of following a link.
Web users are information seeker and respond according to text.
3737
Modeling the likelihood of choosing each option (vector I)
Ij considered a probability of choosing option j.
Discrete choice theory Text must be represented as numeric
entities -> Bag of words model with TF-IDF (~ vector of frequency of appearance of word).
3838
Likelihood of a decision and web user utility
Random Utility Model (Economy): Individuals decide within discrete options {j} with utility Vj with probability Pj of choice j.
The likelihood of taking decision j should be proportional to Pj
Web user objectives are modeled as a text vector µ. Web users are information (TEXT) seeker.
Similarity between text is measured as the cosine between both vectors.
j
jj
L
LV
k
V
V
j k
j
e
eI
),...](09.0),(1.0),(3.0[ diimgomba
3939
Assumption & Approximation
Web browsing is characterized only by jumps.
Independence of available choices.
Utility only depends on text.
Independent of the past visited trail.
No information Satiety Rational web user Correctness of web site
information Web pages with little
content. Web page with simple
content. Web user information
processing time is negligible.
40
jDj
jkk
Cj
jDj
jEj
Cj
Djj
IF
XF
XF
dWdtFFFdX
)(
40
Adaptation of the LCA model (WI-IAT10, P. Roman et al)
• It is a Langevin’s equation.• force interpretation of the stochastic neural activity evolution.• Open the way for improving the dynamic system: Adding forces.
jjl jljj dWdtIXkXdX
Evidence
Inhibition
Dissipation
Noise
4141
)()0,(
)(ˆ,,0)),(2
()(ˆ
0,,0),(
)],(2
),()([),(
2
2
XX
XnXtXFXn
tXtX
tXtXXIt
tX
41
The Fokker-Planck equation: probability density of not reaching a decision (AWIC09 P. Roman et al).
Never reach a decision in t’<t
Neural activity is positive
Neural activity is initially near to 0
Probability density jl ljljj dWdtXIdX
4242
The probability of reaching a decision in time t.
The probability of deciding option “j” in time “t”
jl ljljj dWdtXIdX
1
0
1
1
0
21
0
1
1
0
|2
|),(jk
kXjjk
kXj dXX
dXJdSJtjpjjj
434343
Unconstrained exact solution
Hermite PolinomialsExact solution
jl ljljj dWdtXIdX (Ornstein-Uhlenbeck)
44
Exact unconstrained solution evolution Nearly a delta in t=0, X=0 Large time solution 0 No border condition
But in t=0 the delta values on border are nearly 0
(Ornstein-Uhlenbeck)
4545
This approach is threefold
1. Stochastic equation allows simulations for finding probabilities given a web site. But parameters need to be calibrated. Approximation: constant for all users.
2. Calibration of the model is performed by maximum likelihood. But requires web data (session set). Requires approximation of the density φ
3. Session needs to be obtained with higher accuracy.
jl ljljj dWdtXIdX
4646
Simulation: Monte Carlo simulation
Euler approximation
Exact simulation
),(
),(
),(,1
Xtb
IXkXXta
WXtbtXtatXtX
j
lj jljj
jkjkjkjkj
jl ljljj dWdtXIdX
47
Simulation algorithm: Deciding which link to follows.
4848
Results: Simulated session length distribution (BICA08, AWIC09, BAO10).
Empirical result: Session length [1] distribution follows a power law [4,5].
j
jj
L
LV
• Kind of average web user• u contains all text in the web site• Sessions L>20 diverge: users that performs more elaborate processing?• Session L=1: users that have others text interest?
4949
Results: Number of visits per page. Fuzzy, but averages remain similar.
5050
Adjustment of distribution of time used per session.
Log scale time spend per session
y = -0,3968x + 6,8958
R 2 = 0,9573
012
3456
789
0 2 4 6 8 10
Number of session
Tim
e u
sed
Simulated session
• Same power law than real case.
• Shift in time, change time scale that is used for adjusting white noise variance.
• Slope represent more structural behavior. Intended to adjust other scalar parameters.
51
In Summary
With only an estimation of the parameter, simulation shows result that are close to real.
Calibrating the model should produce better simulation.
52
Third problem: Calibration
5353
Calibration (WI-IAT 2010, P. Roman et al) Parameters :
Should correspond to properties of neural tissue.Approximation: constant for all users.
Parameter : The evidence vector ICorresponds to the intention of the web user It is distributed
The density must be approximated!!!
,,,
54
SESSION DATA: • (i,j) : Hyperlink from i to j.• k: numerate the time distribution.• nijk : The number of observed transitions• tijk: The observed time used on this observation
Parameter Inference
ijk ijkijkI
ItjiPLognSMax )),,,|,,((,,,
Maximum log-likelihood:
• Approximate P by a linear combination of unconstrained exact solutions.
• The approximated probability function must agree restriction of LCA model.
j
i
55
Curse of dimensionality
Many numerical methods for solving differential equations require a partition of the space.
Discretization involves: Any coordinate partition in 100. A typical number of links on a page is 20 Then the total number of points of the discretization is
about 1040
unmanageable
56
Distribution of number of links per page.
0
20
40
60
80
100
120
140
0 10 20 30 40 50 60 70
Number of Link
Num
ber o
f Pag
e
5757
Proposal (1): To use symbolic processing Explicit expression are not manageable
by hand. Operation involved: Integration,
differentiation, product, … Φ is based on polynomials Instead of evaluating at each step, it
is better to perform symbolic manipulation until evaluation is needed.
Grid is not necessary for intermediate step.
/
1 -
1 ^
X 2
21
1
x
5858
Proposal (2):Use the time propagator of the Cauchi problem
Initial condition is concentrated on 0.
But L must ensure border condition!!!!
00| t
443322 24/16/12/11 LtLtLttLetL
]2
)([2
XIL
595959
Proposal (3):Penalization method for ensuring border condition A force FP on boundary that is added to
ensure reflection and adsorption
jP
l ljljj dWdtFXIdX
FFPP(x)(x)=(1-x)2n+x2n
]2
)([~ 2
pFXIL
6060
Approximating the probability distribution Φ Unconstrained case involves polynomial solution. Propagator takes Φ on a small t to a t’. Propagator involves only derivatives. Symbolic processing of the solution could be performed
for building solutions for the required time t’. Probability P is built on a derivative of a definite integral that are
easily calculated by symbolic processing. A solution for the dimensionality problem!!!
61
Experiment: DII departmental web site. ~4000 pages ~17000 links ~15000 visits per month Simple: concise and
precise information. Content mainly based on
text. Objective: Academics,
Study programs, Projects, …
Session size distribution (1 Year)
0
1
2
3
4
5
6
0 0,5 1 1,5 2 2,5
Log Size
Log
N
62
Calibration of parameter
Neurophisiology = 0.4 = 0.2 = 0.03
Text vector preference 1 vector: Most ranked words
Mba Syllabus Project
A distribution of Gaussian vector 3 main clusters related to : study programs, academics, economics.
λ
κ
σ
63
Simulation of in the DII site
Average error of only 5% in distribution of session size precision: 0.8, recall 0.74 by number of specific sessions
Empirical vs simulated web user session
-8
-7
-6
-5
-4
-3
-2
-1
0
0 0,5 1 1,5 2 2,5 3 3,5
Log(Session Length)
Log(
Fre
quen
cy n
umer
of s
essi
on)
Simulation
Experimental
64
Comparing with ML approach
ML Algorithm based on clustering session with text measured.
Simulation approximates 70% of reality.
ML reachs 60% [J. Borges, 2007, IEEE Trans.] [Ghorbani, 2007, WI-IAT][J. Velasquez et Al., 2007, International Journal of Artificial Intelligence Tools ][J. Velasquez et Al., 2007, Journal of Knowledge-Based Systems (Elsevier)]
65
Situation after 1 month: stability of the calibration. 5% of links were modified 2% of pages are new or deleted 30% of words in documents have
changed.
Simulation reach an F-score of 0.7
66
In Summary In spite of changing web site configuration
(after 1 month) simulation returns similar session distribution.
Complexity of calibration process is improved by symbolic calculation.
Density of session length is matched in 95%. But Distribution of sessions is matched in 70%.
67
Conclusions & Future Work
68
Conclusion (1) In spite of the anonymous character of a
web log, It is possible to extract sessions in good agreement with an empirical statistical law.
~70% F-score Quick pre-processing can be obtained with
the use of network models. Further explorations using combinatorial
model leads us to retrieve other likely values.
69
Conclusions (2) Web users are shown to behave like text
information seeker using simulation. Simulation of a web user is a straightforward
algorithm if parameters are known. Distribution of web user sessions are obtained with notable precision.
Calibration is notably difficult due to the dimensionality. A method based on symbolic manipulation and semi-group propagation was proposed for density estimation.
70
Conclusion (3)
The model is robust to changes to the web site maintaining 70% accuracy in predicting distribution of sessions.
Compared with traditional data mining methods that have only 60-70% only one step prediction.
71
Future Work Web personalization
Simulation is cheap and parallelizable, once it is trained (expansion coefficients are fitted).
Small changes (same semantic) in web site (hyperlink and structure) produce changes on web user trails on the web site.
Simulation predict web usage! Since assuming same users with the same fitted behaviour will visit the web site.
Iteration on changes and simulation could find better changes given a measure of quality.
72
Publications: Book Chapters
1. 2010. Web Usage Mining, P. Román, G. L’Huillier, J. Velásquez, in Advanced Techniques in Web Intelligence – 1. J. Velásquez, L. Jain, Springer.
2. 2010. Advanced Techniques in Web Data Pre-Processing and Cleaning, P. Román, R. F. Dell, J. Velásquez, in Advanced Techniques in Web Intelligence – 1. J. Velásquez, L. Jain, Springer.
Publications: International Journal1. 2010, Optimization Models For Sessionization, Submitted to Journal of Intelligent Data
Analysis.
2. 2011, Simulation of web user navigation. In preparation.
73
International Conferences1. 2006.Improving a Web Site using Keywords, P. Román, J. Velásquez, CLAIO
XIII, Int. Conf. Uruguay.2. 2008.Markov Chain for modeling the Web User Behavior, P. Román, J.
Velásquez, Infomrs, CLAIO XIV, Int. Conf. Colombia.3. 2008. Identifying Web User Session using an Integer programming Approach,
R. Dell, P. Román, J. Velásquez, CLAIO XIV, Int. Conf. Colombia.4. 2008. Web User Session Reconstruction Using Integer Programming, R. Dell,
P. Román, J. Velásquez, IEEE/ACM, WI-IAT Int. Conf. Australia.5. 2009. A Dynamic Stochastic Model Applied to the Analysis of the Web User
Behavior, P. Román, J. Velásquez, IEEE, AWIC Int. Conf. Czech Republic.6. 2009. Fast Combinatorial Algorithm for Web User Session Reconstruction, R.
Dell, P. Román, J. Velásquez, the 24th IFIP TC7 Int. Conf., Argentina.7. 2009. Analysis of the Web User Behavior with a Psychologically-Based
Diffusion Model, P. Román, J. Velásquez, AAAI BICA Int. Conf., USA.8. 2009. Web User Session Reconstruction with Back Button Browsing, P. Román,
R. Dell, J. Velásquez, IEEE LNAI 5711, KES Int. Conf. Chile.9. 2010. Stochastic Simulation of Web Users, P. Román, J. Velásquez,
IEEE/ACM, WI-IAT Int. Conf. Canada.
74
Publications: National Conferences1. 2010. Ant Colony Surfer: Discovering the Distribution of Text
Preferences from Web Usage, P. Loyola, P.E. Román and J.D. Velásquez, BAO.
2. 2010. Best Web Site Structure for Users Based on a Genetic Algorithm Approach, E. Andaur, S. Rios, P.E. Román and J.D. Velásquez, BAO.
3. 2010. Artificial Web User Simulation and Web Usage Mining, P.E. Román and J.D. Velásquez, BAO.
4. 2010. Time Course of the Web User, P.E. Román and J.D. Velásquez, TUO2.
Publications: National review1. 2009, ; Un método de optimización lineal entera para el análisis de
sesiones de usuarios web, Revista de Ingenieria de Sistemas; Vol. 23.
75
Thanks youfor your attention.