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The 2015 ACM International Conference on Bioinformatics, Computational Biology, and Health Informatics
Ontology-based Deep Learning
for Human Behavior Prediction
in Health Social Networks
NhatHai Phan1, Dejing Dou1, Hao Wang1, Brigitte Piniewski2,
and David Kil3
1 Computer and Information Science Department,
University of Oregon, Eugene, OR, USA
2 PeaceHealth Laboratories, Vancouver, WA, USA
3 HealthMantic Inc. Los Altos, CA, USA
1
Outline
• Overweight/Obesity, YesiWell Health Social
Network
• Motivation of the SMASH project
• Human Behavior Prediction
– Ontology-based Restricted Boltzmann Machine
• Experimental Results
• Conclusions and Future Works
2
Obesity and Physical Activity Interventions
• 18 states (30% - <35%), 2 states (>= 35%)
• Medical cost:
– $147 billion
in 2008
• 30 minutes, 5 days
• Interventions
– Telephone (16)
– Website (15)
– Effective in
short term
3
Prevalence* of Self-Reported Obesity Among U.S. Adults
CDC, http://www.cdc.gov/obesity/data/prevalence-maps.html-2014
Overweight and Obesity
• The prevalence of Obesity has increased
from 23% to 31% over the recent past, and
66% of adults are overweight. Why?
• It cannot be explained only by genetics and
has occurred among all socioeconomic
groups. Weight gain in one person might
influence weight gain in others.
4
12,067 people for 32 years (Christakis-Fowler 2007)
N. Christakis and J. Fowler. “The spread of obesity in a large social network
over 32 years.” New England Journal of Medicine, 357(4), 2007. 5
Motivation of Our Research
• Can healthy behaviors, e.g., physical
exercise, also spread in the social networks?
• Can we design a social network to help the
spread of healthy behaviors better?
6
7
YesiWell Health Social Network
(2010-2011)
Clear Correlations (254 users)
8
SPD (Steps per Day) vs. SN size
The larger your social network,
the more active you are?
SN size
SPD
Impact of Online Social Network
• Increase weekly leisure walking from 129 to 341
minutes, on average, a 164% increase over the 6-
month study period, compared with a 47% increase
for the control group (i.e., ~250 non-users).
9
J. Greene, R. Sacks, B. Piniewski, D. Kil, and J.S. Hahn "The Impact of an Online Social Network
with Wireless Monitoring Devices on Physical Activity and Weight Loss." Journal of Primary
Care and Community Health, 4(3): 189-194, 2013.
Semantic Mining of Activity, Social, and Health Data
(NIH/NIGMS Funded in 2013, R01 Grant) (PI: Dou)
10
Research Aims
• Understand key factors that enable spread of healthy
behaviors in a social network. (ICDM’12, CIKM’14,
ASONAM’15)
• Develop Formal Semantic Web Ontologies for
Healthcare Social Networks. (BCB’15)
• Identify social network structures that maximally
enable spreading of wellness with recommendations.
(CIKM’14)
11
Detected Communities for Influence
Propagation (CIKM’14)
• Influencers: circle nodes
• Influenced users: rectangle nodes
• Non-Influenced users: triangle nodes
12
N. Phan , D. Dou, X. Xiao, B. Piniewski, and D. Kil, “Analysis of physical activity propagation in a health social network,” in
CIKM’14, pp. 1329–1338.
Outline
• YesiWell Health Social Network and SMASH
• Motivation of the SMASH project
• Human Behavior Prediction
– Ontology-based Restricted Boltzmann Machine
• Experimental Results
• Conclusions and Future Works
13
Human Behavior Prediction
1
2
3
4
5
6
7
1
2
3
4
5
6
7
1
2
3
4
5
6
7
t1t 1t
Decrease exercise Increase exercise 14
Dataset, Features, and Task
• YesiWell dataset
– 254 users
– Oct 2010 – Aug 2011
• BMI
• Wellness score
• Prediction Task: Try to predict whether a YesiWell user will
increase or decrease exercises in the next week compared
with the current week.
15
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cHbAULDLU
HDLTGUBMIUy
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Challenging for Existing Models
Existing Models for Prediction
• Logistic Auto-Regression (LAR),
Socialized Logistic Auto-Regression
(SLAR), Behavior Pattern Search (BPS),
Gaussian Process Model (GP), Socialized
Gaussian Process (SGP, ICDM’12)
Challenges for Existing Models
• Unobserved (hidden) social
relationships/events
• Evolving of the social network
– Temporal effects
• (Explicit & implicit) Social influences
16
Social Restricted Boltzmann Machine (ASONAM’15)
t
……………
…………………………
Hidden
layer
Visible layer
t
iv
jh
W
A
B
u
t
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…..……...………………
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Historical layer
t-1t-2
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A
Self-Motivation
Implicit Social Influence
Environmental Events
Explicit Social Influence
j
17N. Phan , D. Dou, B. Piniewski, and D. Kil, “Social Restricted Boltzmann Machine: Human Behavior Prediction in Health Social
Networks ,” in ASONAM’15.
Biomedical Ontologies
• The Gene Ontology (GO): to standardize the formal representation
of gene and gene product attributes across all species and gene
databases (e.g., zebrafish, mouse)
– Classes: cellular component, molecular function, biological process, …
– Properties: is_a, part_of
• UMLS, SNOMED CT, ICD-9/10/11, NDFRT: comprehensive
dictionaries and ontologies for medical terms, diseases, and drugs.
• The National Center of Biomedical Ontology (NCBO) at Stanford
University
– >300 ontologies (hundreds to thousands concepts each one) 4 millions
of mappings.
18
SMASH Ontology and Its Hidden
Variables
• Ontology development
– Biomarkers: a collection of
biomedical indicators health
conditions
– Social Activities: a set of
interactions between social
entities, either persons or social
communities
– Physical Activities: any bodily
activity involved in daily life.
• Represent concepts by
– their own properties
– the properties of its related
concepts
– the representation of their sub-
concepts
19
http://bioportal.bioontolo
gy.org/ontologies/SMASH
NCBO BioPortal
Ontology-based Restricted Boltzmann
Machine (ORBM)
20
ORBM Model Learning
• Minimize the energy function
21
Performance of the ORBM Model
• ORBM: 85.9%, and SRBM: 83%
• Previous State-of-the-art: 75.21% (the SGP
model in our ICDM’12 work)
22
Y. Shen, R. Jin, D. Dou, N. Chowdhury, J. Sun, B. Piniewski, and D. Kil. “Socialized gaussian process model for human
behavior prediction in a health social network.” In ICDM’12, pages 1110–1115.
Synthetic Health Social Network
• Pajek to generate graphs under the Scale-
Free/Power Law Model
– 254 nodes, and the average node degree is 5.4
• Map pair-wise vertices between the synthetic
social network and the YesiWell health social
network
– by applying PATH
23
M. Zaslavskiy, F. Bach, and J.-P. Vert. “A path following algorithm for graph matching.” In IEEE
Transactions on Pattern Analysis and Machine Intelligence, volume 5099, pages 329–337, 2008.
Performance of ORBM on the Synthetic Data
• ORBM model also outperforms state-of-the-
art models
24
Conclusions and Future Works
• Propose Ontology-based Restricted Boltzmann
Machine (ORBM) model
– Self-motivation, social influence, environmental events
– Extend traditional deep learning framework to ontology-
based deep learning
• Human behavior prediction
– ORBM: 85.9%, SRBM: 83%
– Previous State-of-the-art: 75.21%
• The ORBM model can be applied on different datasets
• Try other Deep Learning models like CNN, etc. in the
near future works
25
The 2015 ACM International Conference on Bioinformatics, Computational Biology, and Health Informatics
{haiphan, dou}@cs.uoregon.edu
SMASH Project: http://aimlab.cs.uoregon.edu/smash/
26
YesiWell Health Social Network
Thank you!

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Ontology-based Deep Learning for Human Behavior Prediction in Health Social Networks

  • 1. The 2015 ACM International Conference on Bioinformatics, Computational Biology, and Health Informatics Ontology-based Deep Learning for Human Behavior Prediction in Health Social Networks NhatHai Phan1, Dejing Dou1, Hao Wang1, Brigitte Piniewski2, and David Kil3 1 Computer and Information Science Department, University of Oregon, Eugene, OR, USA 2 PeaceHealth Laboratories, Vancouver, WA, USA 3 HealthMantic Inc. Los Altos, CA, USA 1
  • 2. Outline • Overweight/Obesity, YesiWell Health Social Network • Motivation of the SMASH project • Human Behavior Prediction – Ontology-based Restricted Boltzmann Machine • Experimental Results • Conclusions and Future Works 2
  • 3. Obesity and Physical Activity Interventions • 18 states (30% - <35%), 2 states (>= 35%) • Medical cost: – $147 billion in 2008 • 30 minutes, 5 days • Interventions – Telephone (16) – Website (15) – Effective in short term 3 Prevalence* of Self-Reported Obesity Among U.S. Adults CDC, http://www.cdc.gov/obesity/data/prevalence-maps.html-2014
  • 4. Overweight and Obesity • The prevalence of Obesity has increased from 23% to 31% over the recent past, and 66% of adults are overweight. Why? • It cannot be explained only by genetics and has occurred among all socioeconomic groups. Weight gain in one person might influence weight gain in others. 4
  • 5. 12,067 people for 32 years (Christakis-Fowler 2007) N. Christakis and J. Fowler. “The spread of obesity in a large social network over 32 years.” New England Journal of Medicine, 357(4), 2007. 5
  • 6. Motivation of Our Research • Can healthy behaviors, e.g., physical exercise, also spread in the social networks? • Can we design a social network to help the spread of healthy behaviors better? 6
  • 7. 7 YesiWell Health Social Network (2010-2011)
  • 8. Clear Correlations (254 users) 8 SPD (Steps per Day) vs. SN size The larger your social network, the more active you are? SN size SPD
  • 9. Impact of Online Social Network • Increase weekly leisure walking from 129 to 341 minutes, on average, a 164% increase over the 6- month study period, compared with a 47% increase for the control group (i.e., ~250 non-users). 9 J. Greene, R. Sacks, B. Piniewski, D. Kil, and J.S. Hahn "The Impact of an Online Social Network with Wireless Monitoring Devices on Physical Activity and Weight Loss." Journal of Primary Care and Community Health, 4(3): 189-194, 2013.
  • 10. Semantic Mining of Activity, Social, and Health Data (NIH/NIGMS Funded in 2013, R01 Grant) (PI: Dou) 10
  • 11. Research Aims • Understand key factors that enable spread of healthy behaviors in a social network. (ICDM’12, CIKM’14, ASONAM’15) • Develop Formal Semantic Web Ontologies for Healthcare Social Networks. (BCB’15) • Identify social network structures that maximally enable spreading of wellness with recommendations. (CIKM’14) 11
  • 12. Detected Communities for Influence Propagation (CIKM’14) • Influencers: circle nodes • Influenced users: rectangle nodes • Non-Influenced users: triangle nodes 12 N. Phan , D. Dou, X. Xiao, B. Piniewski, and D. Kil, “Analysis of physical activity propagation in a health social network,” in CIKM’14, pp. 1329–1338.
  • 13. Outline • YesiWell Health Social Network and SMASH • Motivation of the SMASH project • Human Behavior Prediction – Ontology-based Restricted Boltzmann Machine • Experimental Results • Conclusions and Future Works 13
  • 15. Dataset, Features, and Task • YesiWell dataset – 254 users – Oct 2010 – Aug 2011 • BMI • Wellness score • Prediction Task: Try to predict whether a YesiWell user will increase or decrease exercises in the next week compared with the current week. 15 2 ))(( )( mheight kgmass  )1()( )/()( 3423 121 cHbAULDLU HDLTGUBMIUy    
  • 16. Challenging for Existing Models Existing Models for Prediction • Logistic Auto-Regression (LAR), Socialized Logistic Auto-Regression (SLAR), Behavior Pattern Search (BPS), Gaussian Process Model (GP), Socialized Gaussian Process (SGP, ICDM’12) Challenges for Existing Models • Unobserved (hidden) social relationships/events • Evolving of the social network – Temporal effects • (Explicit & implicit) Social influences 16
  • 17. Social Restricted Boltzmann Machine (ASONAM’15) t …………… ………………………… Hidden layer Visible layer t iv jh W A B u t i …..……...……………… ..……..….......…….. …………………….… …..…….....…….. …..………..………….. …..………..………….. …..………..………….. …..………..………….. …..………..………….. …..…….…..….. Historical layer t-1t-2 U 1u mu …..………..………….. ..……..........…..…….. …..………..………….. A Self-Motivation Implicit Social Influence Environmental Events Explicit Social Influence j 17N. Phan , D. Dou, B. Piniewski, and D. Kil, “Social Restricted Boltzmann Machine: Human Behavior Prediction in Health Social Networks ,” in ASONAM’15.
  • 18. Biomedical Ontologies • The Gene Ontology (GO): to standardize the formal representation of gene and gene product attributes across all species and gene databases (e.g., zebrafish, mouse) – Classes: cellular component, molecular function, biological process, … – Properties: is_a, part_of • UMLS, SNOMED CT, ICD-9/10/11, NDFRT: comprehensive dictionaries and ontologies for medical terms, diseases, and drugs. • The National Center of Biomedical Ontology (NCBO) at Stanford University – >300 ontologies (hundreds to thousands concepts each one) 4 millions of mappings. 18
  • 19. SMASH Ontology and Its Hidden Variables • Ontology development – Biomarkers: a collection of biomedical indicators health conditions – Social Activities: a set of interactions between social entities, either persons or social communities – Physical Activities: any bodily activity involved in daily life. • Represent concepts by – their own properties – the properties of its related concepts – the representation of their sub- concepts 19 http://bioportal.bioontolo gy.org/ontologies/SMASH NCBO BioPortal
  • 21. ORBM Model Learning • Minimize the energy function 21
  • 22. Performance of the ORBM Model • ORBM: 85.9%, and SRBM: 83% • Previous State-of-the-art: 75.21% (the SGP model in our ICDM’12 work) 22 Y. Shen, R. Jin, D. Dou, N. Chowdhury, J. Sun, B. Piniewski, and D. Kil. “Socialized gaussian process model for human behavior prediction in a health social network.” In ICDM’12, pages 1110–1115.
  • 23. Synthetic Health Social Network • Pajek to generate graphs under the Scale- Free/Power Law Model – 254 nodes, and the average node degree is 5.4 • Map pair-wise vertices between the synthetic social network and the YesiWell health social network – by applying PATH 23 M. Zaslavskiy, F. Bach, and J.-P. Vert. “A path following algorithm for graph matching.” In IEEE Transactions on Pattern Analysis and Machine Intelligence, volume 5099, pages 329–337, 2008.
  • 24. Performance of ORBM on the Synthetic Data • ORBM model also outperforms state-of-the- art models 24
  • 25. Conclusions and Future Works • Propose Ontology-based Restricted Boltzmann Machine (ORBM) model – Self-motivation, social influence, environmental events – Extend traditional deep learning framework to ontology- based deep learning • Human behavior prediction – ORBM: 85.9%, SRBM: 83% – Previous State-of-the-art: 75.21% • The ORBM model can be applied on different datasets • Try other Deep Learning models like CNN, etc. in the near future works 25
  • 26. The 2015 ACM International Conference on Bioinformatics, Computational Biology, and Health Informatics {haiphan, dou}@cs.uoregon.edu SMASH Project: http://aimlab.cs.uoregon.edu/smash/ 26 YesiWell Health Social Network Thank you!

Notes de l'éditeur

  1. Good morning everyone! My name is Nhathai Phan. I am a Research Associate at Computer and Information Science Department, University of Oregon. I work with Prof. Dejing Dou, and PhD student Hao Wang. Our collaborators are Dr. Brigitte Piniewski, Chief Medical Officer at PeaceHealth Lab, and David Kil, Co-founder and CEO of HealthMantic. Today, my talk will focus on Ontology-based Deep Learning for Human Behavior Prediction in Health Social Networks.
  2. I will talk about overweight/obesity and introduce our YesiWell health social network. Then, I will talk about the motivation of our SMASH project. I will introduce our novel Ontology-based Restricted Boltzmann Machine for human behavior prediction. Experimental results, conclusions and our future works.
  3. This is the Prevalence of self-reported obesity among US adults in 2014. Obesity is everywhere, there are 18 states with the proportions are from 30 – 35%, 2 states are larger than 35%. Medical treatment cost $147 billion dollars in 2008, perhaps it costs more money today. To reduce the risk of overweigh and obesity-related disease, regular exercise is recommended. We need to exercise at least 39 minutes everyday, in at least 5 days per week. However, not so many people can satisfy this requirements, especially for overweight and obese individuals. Therefore, many intervention systems have been developed, as far as we known, they are effective only in a short term.
  4. The prevalence of Obesity has increased from 23% to 31% over the recent past, and 66% of adults are overweight. Why? It cannot be explained only by genetics and has occurred among all socioeconomic groups. Weight gain in one person might influence weight gain in others.
  5. In 2007, by analyzing the data collected from over 12,000 people for 32 years, Christakis and Fowler discovered that Mutual Friend relationship has significant higher risk to spread obesity. In their series of research, they also showed that non-healthy behaviors such as smoking, alcohol, depression also spread in social networks.
  6. Different from them, instead of non-healthy behaviors, our motivation is to answer whether healthy behaviors such as physical exercise can also spread in social networks or not?, whether we can design a social network to help the spread of healthy behaviors better?
  7. We design YesiWell health social network in 2010 to 2011. What we did is recruiting 254 overweight and obese individuals. Each person will carried a mobile device which keep tracking numbers of walking/running/jogging steps every 15 minutes. We also measure biomarkers and biometric measures such as BMI, cholesterol, etc. The novel part of our research is that all the users enrolled in an online social network so that they can make friend, interact with each other, and form some competitions in different groups.
  8. By analyzing the YesiWell data, we found a very clear positive correlation between # of friends and the level of physical exercises. The social network size is basically determined by the number of friends. So, the larger your social network, the more active you are? Or, the more active you are, the larger your social network? Causality is difficult to be determined here.
  9. To illustrate the impact of online social network on physical activity, we compare the YesiWell users with a control group who did not use YesiWell. We can see that, the YesiWell users have increased their number of leisure time walking from 129 to 341 minutes per week after 6 months. This is significantly different from the control group and within the YesiWell users as well.
  10. Our project named Semantic Mining of Activity, Social, and Health Data has been funded by NIH NIGMS since 2013 as a R01 grant. We collect multi-dimensional data from biomarkers, social activities, and physical activities. We then design a Health Ontology to represent the data. We apply different techniques such as data mining, intervention approaches, and privacy preserving models to extract knowledge based on our health ontology and data.
  11. These are three of five research aims of our project. For instance, understanding key factors that enable spread of healthy behaviors in a social network, and Developing Formal Ontologies for Healthcare Social Networks, and Identifying social network structures that maximally enable spreading of wellness with recommendations.
  12. In our paper published in CIKM 2014. We discover that there are three communities of users in our YesiWell social network. Some users influence others in terms of physical activity, some users have been influenced, some have not been influenced.
  13. In this paper, we focus on a new research problem for human behavior prediction. I am going to introduce our novel Ontology-based Restricted Boltzmann Machine model.
  14. Human behavior prediction is a general problem in social network analysis. Given the social network at a specific timestamp, each node is a user, there is an edge between 2 nodes if they are socially connected. For instance, friend connections. Different colors are used to denote different behaviors of users. In YesiWell social network, the blue nodes indicate that the users increase their exercise compared with the previous timestamp, the orange nodes indicate that the users decrease their exercise compared with the previous timestamp. Given the social network in M timestamps, we would like to predict the status of users in the next timestamp.
  15. We have 254 users. We consider 30 individual features in total including physical activities, social communications, and biomarkers. In this study, We try to predict whether a YesiWell user will increase or decrease exercises in the next week compared with the current week.
  16. We first try state-of-the-art human behavior prediction models including logistic auto-regression, Gaussian process model, socialized Gaussian process model, some add-hoc model like Behavior Pattern Search. Here is the results, we can see that the baseline approaches work somehow but not `perfectly. They have low prediction accuracy in the middle weeks. There are several challenging issues with the existing models: for instance unobserved or hidden social relationships/events since the users join a lot of offline activities. In addition, the network’s evolving over time. We can see the number of active users change over time in this diagram. Also, we need to capture explicit and implicit social influences in social networks. Existing models cannot handle all the challenges together.
  17. In ASONAM 2015 Conference, We proposed the social RBM model to address all Challenges together. First of all, the traditional RBM has two layers, visible layer and hidden layer which are fully bi-partite connected. The visible layer takes the individual features as inputs, and the hidden layer will learn hidden features from the visible layer. To model self-motivation, we add another layer called historical layer. The historical layer contains the individual features in the past as additional observed variables. The historical layer will be fully bi-partite connected to visible and hidden layers. The probability of hidden and visible variables are given as the formulas. The assumption behind this is that the behaviors in the past can influence the current behaviors. To model implicit social influences and environmental events, we add all the users in the social network into the historical layer. To integrate the explicit social influences, we add eta^u_t into dynamic biases with beta_i is a linear parameter.
  18. There is a drawback of our previous social RBM model. The input of the model is a flat setting. All the attributes are treated the same that might not reflect the domain knowledge of their difference. In biomedical domain, domain knowledge can be defined as formal ontologies. For instance, Gene Ontology, UMLS, SNOMED. NCBO (the national center of biomedical ontology) has stored more than 300 biomedical ontologies.
  19. In our study, we design the Smash ontology using Protégé and submitted to the NCBO BioPortal. We have focused on defining concepts that are associated with sustained weight loss. There are three modules, biomarker measures, physical activities, and social activities. This is a small portion of our SMASH ontology. We have the concept person, then a person has biological measure, physical activity, social activity. There would be some attributes such as BMI, cholesterol, Competition, etc. We design the structure of RBMs with multiple layers of hidden variables based on the hierarchy of concepts, the properties of its related concepts, and their sub-concepts. Then we can learn the weights of the RBMs.
  20. Now, we are ready to present our novel Ontology-based RBM (ORBM). The representation of the root node (Person) is used to feed into the human behavior model. On top of the ORBM model, we use a binomial softmax layer for human behavior prediction.
  21. After designing the structure of RBMs based on the ontology, we can learn the weights of RBMs by minimizing this energy function.
  22. The ORBM outperforms other algorithms including SRBM, our most recent model, and the previous state-of-the-art SGP. Overall, the ORBM model achieves 88.7%, the best so far.
  23. To illustrate that our model can be applied in different datasets. We applied Pajek to generate synthetic social network under the Scale-Free/Power Law Model, 254 nodes, and the average node degree is 5.4. To assign individual attributes to the synthetic social network, we then use PATH to map pairwise vertices between the synthetic and the YesiWell health social networks.
  24. The ORBM models still outperforms state-of-the-art models. This shows that our ORBM model can be applied on different datasets. The fluctuation of the models are because the friend connections are randomly generated.
  25. We have proposed a novel Ontology-based Deep Learning model for human behavior prediction in health social networks. The model integrates human behavior determinants such as self-motivation, social influence, and environmental events. The model also extends the traditional deep learning framework to hierarchical deep learning based on ontology. Our proposed model outperforms existing models. We will Try other Deep Learning models like CNN in the near future works
  26. Now, we propose the social Restricted Boltzmann Machine to model human behaviors. First of all, the traditional RBM has two layers, visible layer and hidden layer which are fully bi-partite connected. The visible layer takes the individual features as inputs, and the hidden layer will learn hidden features from the visible layer. To model self-motivation, we add another layer called historical layer. The historical layer contains the individual features in the past as additional observed variables. The historical layer will be fully bi-partite connected to visible and hidden layers. The probability of hidden and visible variables are given as the formulas. b^hat and a^hat are dynamic biases which contains static biases and the contributions from the past. The assumption behind this is that the behaviors in the past can influences the current behaviors. To model implicit social influences and environmental events, we add all the users in the social network into the historical layer. Now, one user can be influenced by any other users and the social context. To integrate the explicit social influences, called eta^u_t, into the model, we add eta^u_t into dynamic biases with beta_i is a linear parameter. Now, we need to figure how to evaluate the explicit social influence eta^u_t.
  27. To estimate the explicit social influence, we consider homophily principle “love the same” and a physical activity-based social influence which assumes that users will tend to follow authorities or strong influential users. This physical activity-based social influence is derived from our previous work at CIKM’14. Homophily principle is the cosine similarity between two users given visible layer and hidden layer. L_t and cosine similarity is combined into a temporal smoothing function with alpha and tau are parameters to control the smoothness. The indicator function Psi is 1 if user u is connected to user m until time t, and 0 otherwise. 1 means increase the exercise and 0 means decrease.
  28. We train the model by minimizing the energy function. Well known contrastive divergence algorithm can be used. Furthermore, we apply back-propagation to train the binomial softmax layer for human behavior prediction. C(\theta) is the cross-entropy error function. y_t is the actual behavior of a user, y_t^hat is the probability that y_t will be 1.
  29. Given a week if a user does exercise more than the previous N (i.e., 3) week, he/she is considered increasing exercise in that week. Otherwise, the user will be considered decreasing exercise. We compare with previous 3 weeks to determine whether a user will increase or decrease the exercises this week. Given 10 (M) weeks data, try to predict whether a user will increase the exercise next week compared with previous 3 (N) weeks?