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A Decision Support System For Inbound Marketers: An
Empirical Use of Latent Dirichlet Allocation Topic Model
to Guide Info-Graphic Designers
Meisam Hejazi Nia
University of Texas at Dallas (UTD)
July 9, 2015
Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 1 / 22
Inbound Marketing
Inbound Marketing (Hub Spot):
Promote the company by blogs, podcasts, video,
eBooks, enewsletter white papers, SEO, Social Media
Marketing
Viral Content marketing which serve to attract
customers (Bring visitors in, by making the company
easy to be found,i.e. Pull)
”earn their way in” (via publishing helpful
information): Like Journalists
Especially effective for small businesses that deal with
high dollar values, long research cycles and
knowledge-based products
Outbound Marketing:
Buying attention, cold-calling, direct paper mail, radio,
TV advertisements, sales flyers, spam, telemarketing
and traditional advertising
Go out to get prospects’ attention (Push)
”buy, beg, or bug their way in” (via paid
advertisements, issuing press releases, or paying
commissioned sales people, respectively): Liaison
Info-Graphic is an important tool that inbound
marketers use (Pictorial, Clear)
Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 2 / 22
Info-Graphics
The brain processes visual information 60,000 faster
than text. – 3M Corporation, 2001
(visualteachingalliance.com)
Graphic rep of information, data or knowledge
intended to present info quickly and clearly
Improve cognition by utilizing graphics to enhance
the human visual system’s ability to see patterns and
trends
Businesses that publish infographics grow their traffic
an average of 12% more than those that don’t
(Hubspot.com)
Visual Info design suggestions based on Visual
Psychological Perception Theory: (piktochart.com)
Layout and Design: Relevant text, Meaningful
headline, Expectation
Colors: Contrast, Reduce Color, Harmony, Smart
disharmony
Typography: Easy-to-read font; Spacing
Visuals: Clutter; Icon; Highlight; Sequence; Standard
Colors
You can take something that’s already gone viral,
and piggyback on its success by creating your own
awesome spin on it (Hubspot.com)
Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 3 / 22
Research Questions
Can the low level features of an infographic guide an infographic designer
to design a viral info-graphic?
Can I design a decision support system to allow an info-graphic designer to
measure the effect of her design decision on the probability of the
info-graphic becoming viral?
What are the current viral topics for which the practitioners create
info-graphics?
Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 4 / 22
Overview of this study
Data
355 info-graphics from Pinterest, Hubspot and
InformationIsBeautiful.com
209 Pinterest (Pins and Likes), 64 InformationIsBeautiful (Facebook,
Tweets, and Google+), 82 Hubspot (Pins, LinkedIn, Facebook,
Tweet, Google+)
Methodology: Unsupervised Machine Learning
To extract verbal information by Optimal Character Recognition
(OCR) with dictionary filter and wordNet and Google’s word2vec (bag
of verbal words)
k-mean to extract histogram of five clusters of RGB and HSV of
images (bag of visual words)
Soft clustering generative Latent Dirichlet Allocation (Topic Model),
estimated by Gibbs Sampling
Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 5 / 22
Overview of Results
Results
Info-graphics about world’s top issues and the worlds’ demographics
has significantly higher social media hit than social media and mobile
infographics
Method to allow info-graphic designer to benchmark her design
against the previous viral info-graphics to measure whether a given
design decision can help or hurt the probability of the design
becoming viral
Visual information is more relevant than the the verbal information of
infographics
Identified twelve clusters of infographics named by the word cloud of
their titles
A Machine learning pipeline to summarize big data (i.e. image of
millions of pixels) into the predictive probability of an info-graphic
becoming viral
The first quantitative study to help the design choices of the
info-graphic designers
Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 6 / 22
Data: Pinterest, Information is Beautiful, and HubSpot
Position of This Research in Literature
Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 8 / 22
10 Steps To Design An Infographic
Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 9 / 22
Samples of Infographics - 1
Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 10 / 22
Samples of Infographics - 2
Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 11 / 22
Samples of Infographics - 3
Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 12 / 22
Machine Learning Pipeline
Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 13 / 22
Probability Graphical Model of Latent Dirichlet Allocation
Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 14 / 22
Social Media Hit Statistics of the Latent Infographic Topics
Cluster index Cluster Name Size Average Social
Media Hit
Variance of So-
cial Media Hit
1 Cool info graphics about world’s demographic info-graphics 28 2,303 8,744,003
2 Mobile and Buzz Design Info-graphics 30 924 1,904,941
3 Marketing design and Dashboard Info-graphics 53 1,255 3,987,451
4 Face and Media Info-graphics 9 447 350,812
5 Traditional Marketing Info-graphics 31 2,693 10,011,501
6 Social Media and Decision Making Info-graphics 26 960 869,842
7 General life Info-graphics 39 1,775 5,735,747
8 Online professional design Info-graphics 33 1,414 5,010,189
9 Responsive logos and brands Info-graphics 15 1,195 3,101,275
10 International and online design Info-graphics 35 1,354 6,700,740
11 Interactive Marketing Info-graphics 28 1,031 5,468,611
12 Traditional vs. Online Media Info-graphics 28 1,718 7,377,299
Social Media hit is the sum of the hits of the social media of each
infographic
The name of the clusters are selected based on the word cloud (word
frequency visualization) of the infographic titles
Number of clusters based on the Likelihood model selection measure
suggests twelve distinct clusters (Also CTM vs. LDA)
Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 15 / 22
Social Media Hit Statistics of the Latent Infographic Topics
cluster 2 cluster 3 cluster 4 cluster 5 cluster 6 cluster 7 cluster 8 cluster 9 cluster 10 cluster 11 cluster 12
cluster 1 (2.3,2)* (1.89,1.99)* (1.85,2.03)* (-0.49,2) (2.21,2)* (0.81,2) (1.33,2) (1.33,2.02) (1.36,2) (1.79,2) (0.77,2)
cluster 2 (-0.8,1.99) (1,2.02) (-2.81,2)* (-0.11,2) (-1.74,1.99) (-1.04,2) (-0.57,2.01) (-0.82,2) (-0.21,2) (-1.42,2)
cluster 3 (1.2,2) (-2.56,1.99)* (0.71,1.99) (-1.13,1.99) (-0.34,1.99) (0.11,2) (-0.2,1.99) (0.45,1.99) (-0.87,1.99)
cluster 4 (-2.1,2.02)* (-1.54,2.03) (-1.64,2.01) (-1.27,2.02) (-1.22,2.06) (-1.04,2.02) (-0.73,2.03) (-1.38,2.03)
cluster 5 (2.69,2)* (1.38,1.99) (1.88,2) (1.7,2.01) (1.89,2) (2.27,2) (1.26,2)
cluster 6 (-1.65,2) (-0.97,2) (-0.56,2.02) (-0.74,2) (-0.14,2) (-1.35,2)
cluster 7 (0.66,1.99) (0.85,2) (0.73,1.99) (1.27,2) (0.09,2)
cluster 8 (0.34,2.01) (0.1,2) (0.65,2) (-0.48,2)
cluster 9 (-0.22,2.01) (0.24,2.02) (-0.67,2.02)
cluster 10 (0.51,2) (-0.54,2)
cluster 11 (-1.01,2)
The first element the t-stat, and the second value is the critical value
Cool info graphics about world’s demographic info-graphics are
significantly more viral than mobile and marketing infographics
Traditional marketing infographics are significantly less viral than the
mobile and modern marketing infographics
Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 16 / 22
Findings’ Summary and Conclusion
Info-graphics about world’s top issues and the worlds’ demographics has
significantly higher social media hit than social media and mobile
infographics
Method to allow info-graphic designer to benchmark her design against
the previous viral info-graphics to measure whether a given design decision
can help or hurt the probability of the design becoming viral
Visual information is more relevant than the the verbal information of
infographics
Identified twelve clusters of infographics named by the word cloud of their
titles
A Machine learning pipeline to summarize big data (i.e. image of millions
of pixels) into the predictive probability of an info-graphic becoming viral
The first quantitative study to help the design choices of the info-graphic
designers
Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 17 / 22
Managerial Take Away and Future Research
Infographic designer can create a design and predict its potential virality
by the proposed approach
Visual elements of an infographic is more relevant than its verbal
information, so especial care should be taken to the attractiveness of the
design elements
The proposed approach to summarize the visual information in an image
can be used for summarizing visual information of the viral videos
Future studies might investigate other approaches of data summarization
such as Fourier Transformation and Scale Invariant Feature
Transformation methods
Out of sample prediction of the virality and the dynamics of design pattern
adoptions might be relevant for future studies
Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 18 / 22
Thank You
Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 19 / 22
LDA Generative Model
LDA Generative Model
Choose N ∼ Poisson(ξ), where N is the number of features
Choosing θ ∼ Dirichlet(α),
where θ is the k-dimensional random probability that a given document has primitive topic (k − 1 simplex)
For each of the N features in:
(1) Choose a topic zn ∼ Multinomial(Θ)
(2) Choose a feature in from p(in|zn, β), a multinomial probability conditioned on the topic
θi ≥ 0, k
i=1 θi = 1
P(θ|α) =
Γ( k
i=1 αi
k
i=1 Γ(αi
θα1−1
1 ...θαk −1
k
Likelihood:
p(D|α, β) = M
d=1 p(θd |α)( Nd
n=1 zdn
p(zdn |θd )p(wdn |zdn , β)dθd
Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 20 / 22
Model selection based on log likelihood
Number of clusters (topics) LDA-Gibbs (image) LDA (full) CTM (full)
k = 3 −198757 −1002505 −1002538
k = 4 −176261 −1002539 −1002589
k = 5 −161241 −1002561 −1002642
k = 6 −145156 −1002586 −1002631
k = 7 −133009 −1002610 −1002672
k = 8 −115634 −1002638 −1002712
k = 9 −99629 −1002660 −1002754
k = 10 −93164 −1002505 −1002538
k = 11 −88779 −1002539 −1002589
k = 12 −95304 −1002561 −1002642
k = 13 −97033 −1002586 −1002631
k = 14 −198757 −1002610 −1002672
Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 21 / 22
Estimating LDA model by Gibbs Sampling
Estimation LDA model by Gibbs Sampling: Hornik and Grun
(2011)
p(zi = K|w, z−i ) ∝
n
(i)
−i,K +δ
n
(.)
−i,K +V δ
n
(di )
−i,K +α
n
(di )
−i,.+kα
ˆβ
(j)
K =
n
(i)
−i,K +δ
n
(.)
−i,K +V δ
ˆθ
(d)
K =
n
(di )
−i,K +α
n
(di )
−i,.+kα
Log Likelihood for Gibbs sampling:
log(p(w|z)) = klog(Γ(V δ)
Γ(δ)V + V
K=1{[ V
j=1 log(Γ(n
(j)
k + δ))] − log(Γ(n
(.)
k + V δ))}
Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 22 / 22

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A Decision Support System for Inbound Marketers: An Empirical Use of Latent Dirichlet Allocation Topic Model to Guide Infographic Designers

  • 1. A Decision Support System For Inbound Marketers: An Empirical Use of Latent Dirichlet Allocation Topic Model to Guide Info-Graphic Designers Meisam Hejazi Nia University of Texas at Dallas (UTD) July 9, 2015 Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 1 / 22
  • 2. Inbound Marketing Inbound Marketing (Hub Spot): Promote the company by blogs, podcasts, video, eBooks, enewsletter white papers, SEO, Social Media Marketing Viral Content marketing which serve to attract customers (Bring visitors in, by making the company easy to be found,i.e. Pull) ”earn their way in” (via publishing helpful information): Like Journalists Especially effective for small businesses that deal with high dollar values, long research cycles and knowledge-based products Outbound Marketing: Buying attention, cold-calling, direct paper mail, radio, TV advertisements, sales flyers, spam, telemarketing and traditional advertising Go out to get prospects’ attention (Push) ”buy, beg, or bug their way in” (via paid advertisements, issuing press releases, or paying commissioned sales people, respectively): Liaison Info-Graphic is an important tool that inbound marketers use (Pictorial, Clear) Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 2 / 22
  • 3. Info-Graphics The brain processes visual information 60,000 faster than text. – 3M Corporation, 2001 (visualteachingalliance.com) Graphic rep of information, data or knowledge intended to present info quickly and clearly Improve cognition by utilizing graphics to enhance the human visual system’s ability to see patterns and trends Businesses that publish infographics grow their traffic an average of 12% more than those that don’t (Hubspot.com) Visual Info design suggestions based on Visual Psychological Perception Theory: (piktochart.com) Layout and Design: Relevant text, Meaningful headline, Expectation Colors: Contrast, Reduce Color, Harmony, Smart disharmony Typography: Easy-to-read font; Spacing Visuals: Clutter; Icon; Highlight; Sequence; Standard Colors You can take something that’s already gone viral, and piggyback on its success by creating your own awesome spin on it (Hubspot.com) Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 3 / 22
  • 4. Research Questions Can the low level features of an infographic guide an infographic designer to design a viral info-graphic? Can I design a decision support system to allow an info-graphic designer to measure the effect of her design decision on the probability of the info-graphic becoming viral? What are the current viral topics for which the practitioners create info-graphics? Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 4 / 22
  • 5. Overview of this study Data 355 info-graphics from Pinterest, Hubspot and InformationIsBeautiful.com 209 Pinterest (Pins and Likes), 64 InformationIsBeautiful (Facebook, Tweets, and Google+), 82 Hubspot (Pins, LinkedIn, Facebook, Tweet, Google+) Methodology: Unsupervised Machine Learning To extract verbal information by Optimal Character Recognition (OCR) with dictionary filter and wordNet and Google’s word2vec (bag of verbal words) k-mean to extract histogram of five clusters of RGB and HSV of images (bag of visual words) Soft clustering generative Latent Dirichlet Allocation (Topic Model), estimated by Gibbs Sampling Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 5 / 22
  • 6. Overview of Results Results Info-graphics about world’s top issues and the worlds’ demographics has significantly higher social media hit than social media and mobile infographics Method to allow info-graphic designer to benchmark her design against the previous viral info-graphics to measure whether a given design decision can help or hurt the probability of the design becoming viral Visual information is more relevant than the the verbal information of infographics Identified twelve clusters of infographics named by the word cloud of their titles A Machine learning pipeline to summarize big data (i.e. image of millions of pixels) into the predictive probability of an info-graphic becoming viral The first quantitative study to help the design choices of the info-graphic designers Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 6 / 22
  • 7. Data: Pinterest, Information is Beautiful, and HubSpot
  • 8. Position of This Research in Literature Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 8 / 22
  • 9. 10 Steps To Design An Infographic Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 9 / 22
  • 10. Samples of Infographics - 1 Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 10 / 22
  • 11. Samples of Infographics - 2 Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 11 / 22
  • 12. Samples of Infographics - 3 Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 12 / 22
  • 13. Machine Learning Pipeline Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 13 / 22
  • 14. Probability Graphical Model of Latent Dirichlet Allocation Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 14 / 22
  • 15. Social Media Hit Statistics of the Latent Infographic Topics Cluster index Cluster Name Size Average Social Media Hit Variance of So- cial Media Hit 1 Cool info graphics about world’s demographic info-graphics 28 2,303 8,744,003 2 Mobile and Buzz Design Info-graphics 30 924 1,904,941 3 Marketing design and Dashboard Info-graphics 53 1,255 3,987,451 4 Face and Media Info-graphics 9 447 350,812 5 Traditional Marketing Info-graphics 31 2,693 10,011,501 6 Social Media and Decision Making Info-graphics 26 960 869,842 7 General life Info-graphics 39 1,775 5,735,747 8 Online professional design Info-graphics 33 1,414 5,010,189 9 Responsive logos and brands Info-graphics 15 1,195 3,101,275 10 International and online design Info-graphics 35 1,354 6,700,740 11 Interactive Marketing Info-graphics 28 1,031 5,468,611 12 Traditional vs. Online Media Info-graphics 28 1,718 7,377,299 Social Media hit is the sum of the hits of the social media of each infographic The name of the clusters are selected based on the word cloud (word frequency visualization) of the infographic titles Number of clusters based on the Likelihood model selection measure suggests twelve distinct clusters (Also CTM vs. LDA) Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 15 / 22
  • 16. Social Media Hit Statistics of the Latent Infographic Topics cluster 2 cluster 3 cluster 4 cluster 5 cluster 6 cluster 7 cluster 8 cluster 9 cluster 10 cluster 11 cluster 12 cluster 1 (2.3,2)* (1.89,1.99)* (1.85,2.03)* (-0.49,2) (2.21,2)* (0.81,2) (1.33,2) (1.33,2.02) (1.36,2) (1.79,2) (0.77,2) cluster 2 (-0.8,1.99) (1,2.02) (-2.81,2)* (-0.11,2) (-1.74,1.99) (-1.04,2) (-0.57,2.01) (-0.82,2) (-0.21,2) (-1.42,2) cluster 3 (1.2,2) (-2.56,1.99)* (0.71,1.99) (-1.13,1.99) (-0.34,1.99) (0.11,2) (-0.2,1.99) (0.45,1.99) (-0.87,1.99) cluster 4 (-2.1,2.02)* (-1.54,2.03) (-1.64,2.01) (-1.27,2.02) (-1.22,2.06) (-1.04,2.02) (-0.73,2.03) (-1.38,2.03) cluster 5 (2.69,2)* (1.38,1.99) (1.88,2) (1.7,2.01) (1.89,2) (2.27,2) (1.26,2) cluster 6 (-1.65,2) (-0.97,2) (-0.56,2.02) (-0.74,2) (-0.14,2) (-1.35,2) cluster 7 (0.66,1.99) (0.85,2) (0.73,1.99) (1.27,2) (0.09,2) cluster 8 (0.34,2.01) (0.1,2) (0.65,2) (-0.48,2) cluster 9 (-0.22,2.01) (0.24,2.02) (-0.67,2.02) cluster 10 (0.51,2) (-0.54,2) cluster 11 (-1.01,2) The first element the t-stat, and the second value is the critical value Cool info graphics about world’s demographic info-graphics are significantly more viral than mobile and marketing infographics Traditional marketing infographics are significantly less viral than the mobile and modern marketing infographics Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 16 / 22
  • 17. Findings’ Summary and Conclusion Info-graphics about world’s top issues and the worlds’ demographics has significantly higher social media hit than social media and mobile infographics Method to allow info-graphic designer to benchmark her design against the previous viral info-graphics to measure whether a given design decision can help or hurt the probability of the design becoming viral Visual information is more relevant than the the verbal information of infographics Identified twelve clusters of infographics named by the word cloud of their titles A Machine learning pipeline to summarize big data (i.e. image of millions of pixels) into the predictive probability of an info-graphic becoming viral The first quantitative study to help the design choices of the info-graphic designers Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 17 / 22
  • 18. Managerial Take Away and Future Research Infographic designer can create a design and predict its potential virality by the proposed approach Visual elements of an infographic is more relevant than its verbal information, so especial care should be taken to the attractiveness of the design elements The proposed approach to summarize the visual information in an image can be used for summarizing visual information of the viral videos Future studies might investigate other approaches of data summarization such as Fourier Transformation and Scale Invariant Feature Transformation methods Out of sample prediction of the virality and the dynamics of design pattern adoptions might be relevant for future studies Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 18 / 22
  • 19. Thank You Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 19 / 22
  • 20. LDA Generative Model LDA Generative Model Choose N ∼ Poisson(ξ), where N is the number of features Choosing θ ∼ Dirichlet(α), where θ is the k-dimensional random probability that a given document has primitive topic (k − 1 simplex) For each of the N features in: (1) Choose a topic zn ∼ Multinomial(Θ) (2) Choose a feature in from p(in|zn, β), a multinomial probability conditioned on the topic θi ≥ 0, k i=1 θi = 1 P(θ|α) = Γ( k i=1 αi k i=1 Γ(αi θα1−1 1 ...θαk −1 k Likelihood: p(D|α, β) = M d=1 p(θd |α)( Nd n=1 zdn p(zdn |θd )p(wdn |zdn , β)dθd Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 20 / 22
  • 21. Model selection based on log likelihood Number of clusters (topics) LDA-Gibbs (image) LDA (full) CTM (full) k = 3 −198757 −1002505 −1002538 k = 4 −176261 −1002539 −1002589 k = 5 −161241 −1002561 −1002642 k = 6 −145156 −1002586 −1002631 k = 7 −133009 −1002610 −1002672 k = 8 −115634 −1002638 −1002712 k = 9 −99629 −1002660 −1002754 k = 10 −93164 −1002505 −1002538 k = 11 −88779 −1002539 −1002589 k = 12 −95304 −1002561 −1002642 k = 13 −97033 −1002586 −1002631 k = 14 −198757 −1002610 −1002672 Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 21 / 22
  • 22. Estimating LDA model by Gibbs Sampling Estimation LDA model by Gibbs Sampling: Hornik and Grun (2011) p(zi = K|w, z−i ) ∝ n (i) −i,K +δ n (.) −i,K +V δ n (di ) −i,K +α n (di ) −i,.+kα ˆβ (j) K = n (i) −i,K +δ n (.) −i,K +V δ ˆθ (d) K = n (di ) −i,K +α n (di ) −i,.+kα Log Likelihood for Gibbs sampling: log(p(w|z)) = klog(Γ(V δ) Γ(δ)V + V K=1{[ V j=1 log(Γ(n (j) k + δ))] − log(Γ(n (.) k + V δ))} Meisam Hejazi Nia (UTD) A Decision Support System For Inbound Marketers July 9, 2015 22 / 22