RecSys'19 SMORe

CLIP Lab, National Chengchi University CFDA Lab, Academia Sinica
Ting-HsiangWang,TexasA&MUniversity
SMORe :
Modularize Graph Embedding for Recommendation
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13TH ACM CONFERENCE ON RECOMMENDER SYSTEMS
COPENHAGEN, DENMARK. 16-20 SEPTEMBER 2019

TUTORIAL: GRAPH EMBEDDING (11:00-12:30)
Chih-Ming Chen

(CM)
Ting-Hsiang Wang

(Sean)
Chuan-Ju Wang

(Jennifer)
Ming-Feng Tsai

(Victor)

Lecture (Sean & CM, 65 minutes)
Hands-on (CM, 15 minutes)
Q&A (Sean & CM, 10 minutes)
2
QR to Slides, Codes, Abstract
Tutorial Agenda

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DeepWalk: Online Learning of Social Representations
Bryan Perozzi
Stony Brook University
Department of Computer
Science
Rami Al-Rfou
Science
Steven Skiena
Science
{bperozzi, ralrfou, skiena}@cs.stonybrook.edu
ABSTRACT
We present DeepWalk, a novel approach for learning la-
tent representations of vertices in a network. These latent
representations encode social relations in a continuous vector
ace, which is easily exploited by statistical models. Deep-
eralizes recent advancements in language mod-
ised feature learning (or deep learning)
graphs.
obtained from trun-
tions by treat-
trate
(a) Input: Karate Graph
(b) Output: Representation
Figure 1: Our proposed method learns a latent space rep-
resentation of social interactions in R
d . The learned rep-
resentation encodes community structure so it can be eas-
oited by standard classiﬁcation methods. Here, our
on Zachary’s Karate network [44] to gen-
tion in R
2 . Note the correspon-
re in the input graph and
odularity-based
1
?
?
?
?

Lecture Agenda
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Q0. Recommendation (REC) and challenges
Q1. Why graph embedding (GE) for REC
Q2. SMORe modularization of GE and benefits
Q3. Exemplar structural modeling for REC
Q4. REC using SMORe
(Sean)
(Sean)
(Sean)
(CM)
(CM)

Lecture Agenda
5
Q4. REC using SMORe
(Sean)
(Sean)
(Sean)
(CM)
(CM)

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REC systems are everywhere !
Movie
Music
Book, Toy, Electronics, etc. Friend, Interest Group
Recruiter, Job Seeker
Local Business
Trend, Following
News, Ad, Media, etc.
And many more …

• REC center around users to provide customized results
• CF assumes people agree on things are likely to agree on other things
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Let’s start with Collaborative Filtering (CF)
User Item
Sam
Liz
Derek
5
4
3
5
4
Song A
Song B
Song A Song B Song C
Sam 5 4 4
Derek 4 5 ?
Liz - 3 ?
Roger - - ?
☞
→ Sam and Derek have similar tastes; therefore,
if Sam likes Song C, it is likely Derek does, too

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User Item
Sam
Liz
Derek
5
4
3
5
4
Song A
Song B
Sam 5 4 4
Derek 4 5 ?
Liz - 3 ?
Roger - - ?
☞
Collaborate

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User Item
Sam
Liz
Derek
5
4
3
5
4
Song A
Song B
4
Song C
Sam 5 4 4
Derek 4 5 ?
Liz - 3 ?
Roger - - ?
☞
Collaborate
Filter

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User Item
Sam
Liz
Derek
5
4
3
5
4
Song A
Song B
Sam 5 4 4
Derek 4 5 ?
Liz - 3 ?
Roger - - ?
☞
4
Song C
Collaborate
Filter
Recommend

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Challenge (1) : Data Sparsity
User Item
Sam
Liz
Derek
5
4
3
5
4
Song A
Song B
• When data sparsity occurs, it is difficult to make accurate REC with CF
Sam 5 4 4
Derek 4 5 ?
Liz - 3 ?
Roger - - ?
☞
→ Data sparsity occurs to Liz as there is insufﬁcient
ratings from Liz to compare her taste with others’
Collaborate

12
User Item
Sam
Liz
Derek
5
4
3
5
4
Song A
Song B
4
Song C
Sam 5 4 4
Derek 4 5 ?
Liz - 3 ?
Roger - - ?
☞
Collaborate
Filter

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User Item
Sam
Liz
Derek
5
4
3
5
4
Song A
Song B
4
Song C
Sam 5 4 4
Derek 4 5 ?
Liz - 3 ?
Roger - - ?
☞
Collaborate
Filter
Recommend

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Challenge (2) : Cold Start
User Item
Sam
Liz
Derek
5
4
3
5
4
Song A
Song B
• When cold start occurs, it is impossible to conduct CF since there is no context 
for comparison
Sam 5 4 4
Derek 4 5 ?
Liz - 3 ?
Roger - - ?☞
→ Cold Start occurs to Roger as there is NO song
rating from Roger to compare his taste with others’
Roger
?
?
?

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Challenge (3) : Constant Cold Start
• Some Cold Start situations are constant, i.e., never warm up
• E.g., event tickets are sold before user-event interactions can occur
November 2, 2019 November 16, 2019 October 16, 2019
→ Today is September 19, 2019

16

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Common Solution : Add Attributes
→ REC systems often mitigate Complete
Cold Start problems by requiring new
users to specify interests and items
be labeled using tags
→ By requiring user interests and item tags
to come from predeﬁned label set, users
and items share context for comparison

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To enrich context for comparison …
Derek
User Item
Sam
Liz
5
4
3
5
4
Song A
Song B
• For additional context for comparison, REC systems often borrow auxiliary 
information, such as item content and user and item attributes
• This forms a Heterogeneous Information Network (HIN)

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Derek
User Item Attribute
Sam
Liz Singer A
5
4
3
5
4
Song A
Song B
Metal
Rock
Genre, Artist
Add auxiliary information …
→ Item attributes are added to improve
item comparison, e.g., music genre, 
artist, metadata, etc.

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Metal
User Item AttributeAttribute
Sam
Liz
Rock
Working
Student
Singer A
5
4
3
5
4
Song A
Song B
Derek
Social NetworkOccupation
Genre, Artist
And more auxiliary information !
artist, metadata, etc. 
→ User attributes are added to improve
user comparison, e.g., social network, 
occupation, favorite artist & genre, etc.

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Metal
User Item AttributeAttribute
Sam
Liz
Rock
Working
Student
Singer A
5
4
3
5
4
Song A
Song B
artist, metadata, etc. 
→ User attributes are added to improve
user comparison, e.g., social network, 
occupation, favorite artist & genre, etc.
→ HIN gives holistic view of complex systems
Derek
Graph coordinates all relations !

Lecture Agenda
22
Q4. REC using SMORe
(Sean)
(Sean)
(Sean)
(CM)
(CM)

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Why Graph ?
1. Universal language for describing complex data [1]
• Many fields have all chosen graph to depict entity interactions
Twitter Ego-Network
Delta Airline Route Map NetworkCore Sound Food Web

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2. Shared vocabulary (therefore ideas) between fields [1]
• E.g., distributional hypothesis in linguistics vs. CF in REC systems
User Item
Why Graph ?

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3. Holistic view of complex systems of interactions
• Different domains can easily connect and be jointly mined
User Item Attribute
→ HINs easily integrates information
from different domains
Why Graph ?

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4. General deﬁnition of contexts used for entity comparison
• Model graph structure instead specific types of relations
User Item Attribute
→ Different REC approaches, similar
structure
CF CBF
Why Graph ?

5. Sophisticated models available from network-related researches
• Network schema, meta-path, subgraph matching, information propagation, etc.
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(a) ACM data (b) DBLP data
Figure 3: Examples of bibliographic network
schema.
distinct semantics under diﬀerent paths will lead to diﬀerent
relatedness. The relatedness under APVC path emphasizes
on the conferences that authors participated, while the relat-
edness under APSPVC path emphasizes on conferences pub-
lishing the papers that have the same subjects with authors’
papers. For example, assume most papers of an author are
published in the KDD, SIGMOD, and VLDB. However, the
papers having the same subjects with the author’s papers
may be published in more wide conferences, such as ICDM,
Figu
In m
jects
lar p
As a
ence
gene
to th
resea
man
mor
Star-schema [2]
Meta-path [3]
Why Graph ?

5. Sophisticated models available from network-related researches
• Network schema, meta-path, subgraph matching, information propagation, etc.
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Why Graph ?

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REC as Link Prediction on Graphs
?
?
?
?
✘
✔
✔
✘
Machine Learning
Algorithm
• Many ways to compare node similarity: entity types, shared neighbors, distance, etc.
• Early REC models, e.g., CF and CBF, define intuitive relations for similarity measurement
• As models mature and data diversity skyrockets nowadays, designing features 
for REC becomes increasingly challenging

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Graph Embedding Pipeline
Hidden layer
Input layer Output layer
Supply Graph Return Embeddings (from hidden Layer)Train Neural Network
eepWalk: Online Learning of Social Representations
Bryan Perozzi
Science
Rami Al-Rfou
Science
Steven Skiena
Science
{bperozzi, ralrfou, skiena}@cs.stonybrook.edu
ABSTRACT
We present DeepWalk, a novel approach for learning la-
tent representations of vertices in a network. These latent
representations encode social relations in a continuous vector
space, which is easily exploited by statistical models. Deep-
k generalizes recent advancements in language mod-
supervised feature learning (or deep learning)
ds to graphs.
mation obtained from trun-
esentations by treat-
emonstrate
el
(a) Input: Karate Graph
(b) Output: Representation
resentation of social interactions in R
d . The learned rep-
ly exploited by standard classiﬁcation methods. Here, our
used on Zachary’s Karate network [44] to gen-
resentation in R
2 . Note the correspon-
tructure in the input graph and
ent a modularity-based
Rami Al-Rfou
y Brook University
tment of Computer
Science
Steven Skiena
Science
u, skiena}@cs.stonybrook.edu
ing la-
latent
vector
Deep-
e mod-
rning)
m trun-
y treat-
nstrate
ti-label
s Blog-
Deep-
allowed
ence of
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(a) Input: Karate Graph (b) Output: Representation
resentation of social interactions in Rd
. The learned rep-
ily exploited by standard classiﬁcation methods. Here, our
method is used on Zachary’s Karate network [44] to gen-
erate a latent representation in R2
. Note the correspon-
dence between community structure in the input graph and
• GE for REC exploits observed links as graph structures to predict unobserved links
• Entities are converted into spatial features (embeddings) in the hidden layer and 
iteratively updated such that their interactions approximate values in the output layer
• Entity relatedness is preserved as spatial properties, e.g., distance and angle

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Why Embedding ?
1. Efﬁcient retrieval from approximate nearest neighbor (ANN) search methods
• E.g., Spotify ANNOY reduces curse of dimensionality during online search by maintaining 
a binary tree of subdivisions such that good enough results can be found in [4]
❌Query
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→ Brute force exhaustive search finds the closest nearest neighbors in
❌Query
Why Embedding ?
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33
❌Query
Why Embedding ?
→ Brute force exhaustive search finds the closest nearest neighbors in O(log n!)<latexit sha1_base64="ZUjF3udMHzVYQ9q9OFGt0N8yXiQ=">AAAB+3icbZC7TsMwFIZPyq2UWygji6FBKkuVdIGxEgsbRaIXqY0qx3Vaq44T2Q6iivoqLAwgxMqLsPE2uG0GaPklS5/+c47O8R8knCntut9WYWNza3unuFva2z84PLKPy20Vp5LQFol5LLsBVpQzQVuaaU67iaQ4CjjtBJObeb3zSKVisXjQ04T6ER4JFjKCtbEGdrkfhJlz51R5PEKOOHMuZwO74tbchdA6eDlUIFdzYH/1hzFJIyo04Vipnucm2s+w1IxwOiv1U0UTTCZ4RHsGBY6o8rPF7TN0YZwhCmNpntBo4f6eyHCk1DQKTGeE9Vit1ubmf7VeqsNrP2MiSTUVZLkoTDnSMZoHgYZMUqL51AAmkplbERljiYk2cZVMCN7ql9ehXa95hu/rlUYjj6MIp3AOVfDgChpwC01oAYEneIZXeLNm1ov1bn0sWwtWPnMCf2R9/gA8KZKY</latexit><latexit sha1_base64="ZUjF3udMHzVYQ9q9OFGt0N8yXiQ=">AAAB+3icbZC7TsMwFIZPyq2UWygji6FBKkuVdIGxEgsbRaIXqY0qx3Vaq44T2Q6iivoqLAwgxMqLsPE2uG0GaPklS5/+c47O8R8knCntut9WYWNza3unuFva2z84PLKPy20Vp5LQFol5LLsBVpQzQVuaaU67iaQ4CjjtBJObeb3zSKVisXjQ04T6ER4JFjKCtbEGdrkfhJlz51R5PEKOOHMuZwO74tbchdA6eDlUIFdzYH/1hzFJIyo04Vipnucm2s+w1IxwOiv1U0UTTCZ4RHsGBY6o8rPF7TN0YZwhCmNpntBo4f6eyHCk1DQKTGeE9Vit1ubmf7VeqsNrP2MiSTUVZLkoTDnSMZoHgYZMUqL51AAmkplbERljiYk2cZVMCN7ql9ehXa95hu/rlUYjj6MIp3AOVfDgChpwC01oAYEneIZXeLNm1ov1bn0sWwtWPnMCf2R9/gA8KZKY</latexit><latexit sha1_base64="ZUjF3udMHzVYQ9q9OFGt0N8yXiQ=">AAAB+3icbZC7TsMwFIZPyq2UWygji6FBKkuVdIGxEgsbRaIXqY0qx3Vaq44T2Q6iivoqLAwgxMqLsPE2uG0GaPklS5/+c47O8R8knCntut9WYWNza3unuFva2z84PLKPy20Vp5LQFol5LLsBVpQzQVuaaU67iaQ4CjjtBJObeb3zSKVisXjQ04T6ER4JFjKCtbEGdrkfhJlz51R5PEKOOHMuZwO74tbchdA6eDlUIFdzYH/1hzFJIyo04Vipnucm2s+w1IxwOiv1U0UTTCZ4RHsGBY6o8rPF7TN0YZwhCmNpntBo4f6eyHCk1DQKTGeE9Vit1ubmf7VeqsNrP2MiSTUVZLkoTDnSMZoHgYZMUqL51AAmkplbERljiYk2cZVMCN7ql9ehXa95hu/rlUYjj6MIp3AOVfDgChpwC01oAYEneIZXeLNm1ov1bn0sWwtWPnMCf2R9/gA8KZKY</latexit><latexit sha1_base64="ZUjF3udMHzVYQ9q9OFGt0N8yXiQ=">AAAB+3icbZC7TsMwFIZPyq2UWygji6FBKkuVdIGxEgsbRaIXqY0qx3Vaq44T2Q6iivoqLAwgxMqLsPE2uG0GaPklS5/+c47O8R8knCntut9WYWNza3unuFva2z84PLKPy20Vp5LQFol5LLsBVpQzQVuaaU67iaQ4CjjtBJObeb3zSKVisXjQ04T6ER4JFjKCtbEGdrkfhJlz51R5PEKOOHMuZwO74tbchdA6eDlUIFdzYH/1hzFJIyo04Vipnucm2s+w1IxwOiv1U0UTTCZ4RHsGBY6o8rPF7TN0YZwhCmNpntBo4f6eyHCk1DQKTGeE9Vit1ubmf7VeqsNrP2MiSTUVZLkoTDnSMZoHgYZMUqL51AAmkplbERljiYk2cZVMCN7ql9ehXa95hu/rlUYjj6MIp3AOVfDgChpwC01oAYEneIZXeLNm1ov1bn0sWwtWPnMCf2R9/gA8KZKY</latexit>

34
❌Query
→ Spotify ANNOY builds binary tree of subdivisions to quickly find closest neighbors
Why Embedding ?

35
❌Query
Why Embedding ?
→ Spotify ANNOY builds binary tree of subdivisions to quickly find closest neighbors

36
2. Efﬁcient pairwise comparison due to dimensionality reduction (DR)
• Lower dimension costs less to calculate feature similarity
O(log n)<latexit sha1_base64="CpYTxtDU/JE+emzgwPLx6uI+9ck=">AAAB+nicdVDLTsJAFL3FF+Kr6NLNRGqCG9KyUJckbtyJiYAJNGQ6TGHCdNrMTDWk8iluXGiMW7/EnX/jFDDxeZKbe3LOvZk7J0g4U9p1363C0vLK6lpxvbSxubW9Y5d32ypOJaEtEvNYXgdYUc4EbWmmOb1OJMVRwGknGJ/lfueGSsVicaUnCfUjPBQsZARrI/Xtci8IM+fCqfJ4iBzhHE37dsWtHbs50G/i1WbdrcACzb791hvEJI2o0IRjpbqem2g/w1Izwum01EsVTTAZ4yHtGipwRJWfzU6fokOjDFAYS1NCo5n6dSPDkVKTKDCTEdYj9dPLxb+8bqrDUz9jIkk1FWT+UJhypGOU54AGTFKi+cQQTCQztyIywhITbdIqmRA+f4r+J+16zTP8sl5pNBZxFGEfDqAKHpxAA86hCS0gcAv38AhP1p31YD1bL/PRgrXY2YNvsF4/APp4kn8=</latexit><latexit sha1_base64="CpYTxtDU/JE+emzgwPLx6uI+9ck=">AAAB+nicdVDLTsJAFL3FF+Kr6NLNRGqCG9KyUJckbtyJiYAJNGQ6TGHCdNrMTDWk8iluXGiMW7/EnX/jFDDxeZKbe3LOvZk7J0g4U9p1363C0vLK6lpxvbSxubW9Y5d32ypOJaEtEvNYXgdYUc4EbWmmOb1OJMVRwGknGJ/lfueGSsVicaUnCfUjPBQsZARrI/Xtci8IM+fCqfJ4iBzhHE37dsWtHbs50G/i1WbdrcACzb791hvEJI2o0IRjpbqem2g/w1Izwum01EsVTTAZ4yHtGipwRJWfzU6fokOjDFAYS1NCo5n6dSPDkVKTKDCTEdYj9dPLxb+8bqrDUz9jIkk1FWT+UJhypGOU54AGTFKi+cQQTCQztyIywhITbdIqmRA+f4r+J+16zTP8sl5pNBZxFGEfDqAKHpxAA86hCS0gcAv38AhP1p31YD1bL/PRgrXY2YNvsF4/APp4kn8=</latexit><latexit sha1_base64="CpYTxtDU/JE+emzgwPLx6uI+9ck=">AAAB+nicdVDLTsJAFL3FF+Kr6NLNRGqCG9KyUJckbtyJiYAJNGQ6TGHCdNrMTDWk8iluXGiMW7/EnX/jFDDxeZKbe3LOvZk7J0g4U9p1363C0vLK6lpxvbSxubW9Y5d32ypOJaEtEvNYXgdYUc4EbWmmOb1OJMVRwGknGJ/lfueGSsVicaUnCfUjPBQsZARrI/Xtci8IM+fCqfJ4iBzhHE37dsWtHbs50G/i1WbdrcACzb791hvEJI2o0IRjpbqem2g/w1Izwum01EsVTTAZ4yHtGipwRJWfzU6fokOjDFAYS1NCo5n6dSPDkVKTKDCTEdYj9dPLxb+8bqrDUz9jIkk1FWT+UJhypGOU54AGTFKi+cQQTCQztyIywhITbdIqmRA+f4r+J+16zTP8sl5pNBZxFGEfDqAKHpxAA86hCS0gcAv38AhP1p31YD1bL/PRgrXY2YNvsF4/APp4kn8=</latexit><latexit sha1_base64="CpYTxtDU/JE+emzgwPLx6uI+9ck=">AAAB+nicdVDLTsJAFL3FF+Kr6NLNRGqCG9KyUJckbtyJiYAJNGQ6TGHCdNrMTDWk8iluXGiMW7/EnX/jFDDxeZKbe3LOvZk7J0g4U9p1363C0vLK6lpxvbSxubW9Y5d32ypOJaEtEvNYXgdYUc4EbWmmOb1OJMVRwGknGJ/lfueGSsVicaUnCfUjPBQsZARrI/Xtci8IM+fCqfJ4iBzhHE37dsWtHbs50G/i1WbdrcACzb791hvEJI2o0IRjpbqem2g/w1Izwum01EsVTTAZ4yHtGipwRJWfzU6fokOjDFAYS1NCo5n6dSPDkVKTKDCTEdYj9dPLxb+8bqrDUz9jIkk1FWT+UJhypGOU54AGTFKi+cQQTCQztyIywhITbdIqmRA+f4r+J+16zTP8sl5pNBZxFGEfDqAKHpxAA86hCS0gcAv38AhP1p31YD1bL/PRgrXY2YNvsF4/APp4kn8=</latexit>
Why Embedding ?

37
3. Reduced space complexity due to DR
• Lower dimension costs less storage space
Why Embedding ?

38
3. Reduced space complexity due to DR
• Lower dimension costs less storage space
4. Transfer learning with pertained embeddings
• Pretrained embeddings are better guesses than randomly initialized vectors
Why Embedding ?

39
GE for REC : Challenges
• So graph embedding is GREAT for recommendation :
• Reduces data sparsity and cold start via integrating auxiliary information
• Provides holistic view of REC problem and jointly mines different relations in
terms of graph structures
• Trains fast, compares fast, and retrieves fast while taking less space

40
• So graph embedding is GREAT for recommendation :
• Reduces data sparsity and cold start via integrating auxiliary information
• Provides holistic view of REC problem and jointly mines different relations in
terms of graph structures
• Trains fast, compares fast, and retrieves fast while taking less space 
• What’s the catch ?
GE for REC : Challenges

Lecture Agenda
41
Q4. REC using SMORe
(Sean)
(Sean)
(Sean)
(CM)
(CM)

42
Embedding space
Let’s look at GE process …

43
…
Graph structures
Embedding space

…
44
Samples relation
A
B
BA
Graph structures
A B
Embedding space

…
B
A
45
Samples relation
A
B
BA
Graph structures
Maps entities to space
Embedding space

…
46
Samples relation
A
B
BA
Embedding space
Graph structures
A
B
Optimizes distance

Challenge (1) : Select structure is HARD
A
B
47
Embedding space
Graph structures
Maps entities to spaceB
Samples relation
A
BA
…
→ Unsure which graph structures
best model current REC task
Optimizes distance

A
B
48
Embedding space
Graph structures
Samples relation
A
BA
…
5
8 7
6
2
3
1
4
In bipartite, model & by
neighborhood is intuitive; but in
planar, & are also shown
similar in betweenness
g j
5 7
Optimizes distance

A
B
49
Embedding space
Graph structures
Samples relation
A
BA
…
5
8 7
6
2
3
1
4
In bipartite, model & by
neighborhood is intuitive; but in
planar, & are also shown
similar in betweenness
g j
5 7
Optimizes distance

Challenge (2) : Customize GE model
A
B
50
Embedding space
Graph structures
Samples relation
A
BA
…
→ Wanna customize GE methods
during each stage of training
Optimizes distance

Challenge (3) : Make fair comparison
A
B
51
Embedding space
Graph structures
Samples relation
A
BA
…
→ Wanna customize GE methods
during each stage of training
→ Difﬁcult to compare models as
their implementations often vary
Optimizes distance

Solution : Modularize GE for adaptability !
52
…
Samples relation
BA
Embedding space
Graph structures
A
B
Optimizes distance

…
Samples relation
BA
Embedding space
Graph structures
A
B
Optimizes distance
53
Sampler
Mapper
Optimizer

A
B
54
…
Samples relation
BA
Embedding space
Graph structures
Optimizes distance
Sampler
Mapper
Optimizer
•Extracts graph structures from dataset
while remains type-agnostic to sampled
entities, i.e., nodes & edges
E : {(v1, v2)|(v1, v2) 2 V ⇥ V }<latexit sha1_base64="Tguco8yNKzLzF1xI2NN30+8zm+U=">AAACIHicbZBNS8NAEIY39avWr6hHL4utUEFK0kvFU1EEjxXsBzQhbLabdulmE3Y3hRLzU7z4V7x4UERv+mvctjlodWDZh3dmmJnXjxmVyrI+jcLK6tr6RnGztLW9s7tn7h90ZJQITNo4YpHo+UgSRjlpK6oY6cWCoNBnpOuPr2b57oQISSN+p6YxcUM05DSgGCkteWajcn3hpNWJl9rZGdRfPTuF93BJcCiHHegoGhI5g6zimWWrZs0D/gU7hzLIo+WZH84gwklIuMIMSdm3rVi5KRKKYkaykpNIEiM8RkPS18iRHuWm8wMzeKKVAQwioR9XcK7+7EhRKOU09HVliNRILudm4n+5fqKCczelPE4U4XgxKEgYVBGcuQUHVBCs2FQDwoLqXSEeIYGw0p6WtAn28sl/oVOv2Zpv6+XmZW5HERyBY1AFNmiAJrgBLdAGGDyAJ/ACXo1H49l4M94XpQUj7zkEv8L4+gaxJqAz</latexit><latexit sha1_base64="Tguco8yNKzLzF1xI2NN30+8zm+U=">AAACIHicbZBNS8NAEIY39avWr6hHL4utUEFK0kvFU1EEjxXsBzQhbLabdulmE3Y3hRLzU7z4V7x4UERv+mvctjlodWDZh3dmmJnXjxmVyrI+jcLK6tr6RnGztLW9s7tn7h90ZJQITNo4YpHo+UgSRjlpK6oY6cWCoNBnpOuPr2b57oQISSN+p6YxcUM05DSgGCkteWajcn3hpNWJl9rZGdRfPTuF93BJcCiHHegoGhI5g6zimWWrZs0D/gU7hzLIo+WZH84gwklIuMIMSdm3rVi5KRKKYkaykpNIEiM8RkPS18iRHuWm8wMzeKKVAQwioR9XcK7+7EhRKOU09HVliNRILudm4n+5fqKCczelPE4U4XgxKEgYVBGcuQUHVBCs2FQDwoLqXSEeIYGw0p6WtAn28sl/oVOv2Zpv6+XmZW5HERyBY1AFNmiAJrgBLdAGGDyAJ/ACXo1H49l4M94XpQUj7zkEv8L4+gaxJqAz</latexit><latexit sha1_base64="Tguco8yNKzLzF1xI2NN30+8zm+U=">AAACIHicbZBNS8NAEIY39avWr6hHL4utUEFK0kvFU1EEjxXsBzQhbLabdulmE3Y3hRLzU7z4V7x4UERv+mvctjlodWDZh3dmmJnXjxmVyrI+jcLK6tr6RnGztLW9s7tn7h90ZJQITNo4YpHo+UgSRjlpK6oY6cWCoNBnpOuPr2b57oQISSN+p6YxcUM05DSgGCkteWajcn3hpNWJl9rZGdRfPTuF93BJcCiHHegoGhI5g6zimWWrZs0D/gU7hzLIo+WZH84gwklIuMIMSdm3rVi5KRKKYkaykpNIEiM8RkPS18iRHuWm8wMzeKKVAQwioR9XcK7+7EhRKOU09HVliNRILudm4n+5fqKCczelPE4U4XgxKEgYVBGcuQUHVBCs2FQDwoLqXSEeIYGw0p6WtAn28sl/oVOv2Zpv6+XmZW5HERyBY1AFNmiAJrgBLdAGGDyAJ/ACXo1H49l4M94XpQUj7zkEv8L4+gaxJqAz</latexit><latexit sha1_base64="Tguco8yNKzLzF1xI2NN30+8zm+U=">AAACIHicbZBNS8NAEIY39avWr6hHL4utUEFK0kvFU1EEjxXsBzQhbLabdulmE3Y3hRLzU7z4V7x4UERv+mvctjlodWDZh3dmmJnXjxmVyrI+jcLK6tr6RnGztLW9s7tn7h90ZJQITNo4YpHo+UgSRjlpK6oY6cWCoNBnpOuPr2b57oQISSN+p6YxcUM05DSgGCkteWajcn3hpNWJl9rZGdRfPTuF93BJcCiHHegoGhI5g6zimWWrZs0D/gU7hzLIo+WZH84gwklIuMIMSdm3rVi5KRKKYkaykpNIEiM8RkPS18iRHuWm8wMzeKKVAQwioR9XcK7+7EhRKOU09HVliNRILudm4n+5fqKCczelPE4U4XgxKEgYVBGcuQUHVBCs2FQDwoLqXSEeIYGw0p6WtAn28sl/oVOv2Zpv6+XmZW5HERyBY1AFNmiAJrgBLdAGGDyAJ/ACXo1H49l4M94XpQUj7zkEv8L4+gaxJqAz</latexit>
: E ! R<latexit sha1_base64="j+ipPQXWS0Htqsw+lExijt/CRa0=">AAACAXicbZDLSgMxFIYz9VbrbdSN4CbYCq7KTDeKq6IILqvYC3SGkkkzndBMMiQZpQx146u4caGIW9/CnW9j2s5CW38IfPznHE7OHySMKu0431ZhaXllda24XtrY3NresXf3WkqkEpMmFkzIToAUYZSTpqaakU4iCYoDRtrB8HJSb98Tqajgd3qUED9GA05DipE2Vs8+qHhJROE5vIKepINIIynFA7yt9OyyU3Wmgovg5lAGuRo9+8vrC5zGhGvMkFJd10m0nyGpKWZkXPJSRRKEh2hAugY5ionys+kFY3hsnD4MhTSPazh1f09kKFZqFAemM0Y6UvO1iflfrZvq8MzPKE9STTieLQpTBrWAkzhgn0qCNRsZQFhS81eIIyQR1ia0kgnBnT95EVq1qmv4plauX+RxFMEhOAInwAWnoA6uQQM0AQaP4Bm8gjfryXqx3q2PWWvBymf2wR9Znz87EpV0</latexit><latexit sha1_base64="j+ipPQXWS0Htqsw+lExijt/CRa0=">AAACAXicbZDLSgMxFIYz9VbrbdSN4CbYCq7KTDeKq6IILqvYC3SGkkkzndBMMiQZpQx146u4caGIW9/CnW9j2s5CW38IfPznHE7OHySMKu0431ZhaXllda24XtrY3NresXf3WkqkEpMmFkzIToAUYZSTpqaakU4iCYoDRtrB8HJSb98Tqajgd3qUED9GA05DipE2Vs8+qHhJROE5vIKepINIIynFA7yt9OyyU3Wmgovg5lAGuRo9+8vrC5zGhGvMkFJd10m0nyGpKWZkXPJSRRKEh2hAugY5ionys+kFY3hsnD4MhTSPazh1f09kKFZqFAemM0Y6UvO1iflfrZvq8MzPKE9STTieLQpTBrWAkzhgn0qCNRsZQFhS81eIIyQR1ia0kgnBnT95EVq1qmv4plauX+RxFMEhOAInwAWnoA6uQQM0AQaP4Bm8gjfryXqx3q2PWWvBymf2wR9Znz87EpV0</latexit><latexit sha1_base64="j+ipPQXWS0Htqsw+lExijt/CRa0=">AAACAXicbZDLSgMxFIYz9VbrbdSN4CbYCq7KTDeKq6IILqvYC3SGkkkzndBMMiQZpQx146u4caGIW9/CnW9j2s5CW38IfPznHE7OHySMKu0431ZhaXllda24XtrY3NresXf3WkqkEpMmFkzIToAUYZSTpqaakU4iCYoDRtrB8HJSb98Tqajgd3qUED9GA05DipE2Vs8+qHhJROE5vIKepINIIynFA7yt9OyyU3Wmgovg5lAGuRo9+8vrC5zGhGvMkFJd10m0nyGpKWZkXPJSRRKEh2hAugY5ionys+kFY3hsnD4MhTSPazh1f09kKFZqFAemM0Y6UvO1iflfrZvq8MzPKE9STTieLQpTBrWAkzhgn0qCNRsZQFhS81eIIyQR1ia0kgnBnT95EVq1qmv4plauX+RxFMEhOAInwAWnoA6uQQM0AQaP4Bm8gjfryXqx3q2PWWvBymf2wR9Znz87EpV0</latexit><latexit sha1_base64="j+ipPQXWS0Htqsw+lExijt/CRa0=">AAACAXicbZDLSgMxFIYz9VbrbdSN4CbYCq7KTDeKq6IILqvYC3SGkkkzndBMMiQZpQx146u4caGIW9/CnW9j2s5CW38IfPznHE7OHySMKu0431ZhaXllda24XtrY3NresXf3WkqkEpMmFkzIToAUYZSTpqaakU4iCYoDRtrB8HJSb98Tqajgd3qUED9GA05DipE2Vs8+qHhJROE5vIKepINIIynFA7yt9OyyU3Wmgovg5lAGuRo9+8vrC5zGhGvMkFJd10m0nyGpKWZkXPJSRRKEh2hAugY5ionys+kFY3hsnD4MhTSPazh1f09kKFZqFAemM0Y6UvO1iflfrZvq8MzPKE9STTieLQpTBrWAkzhgn0qCNRsZQFhS81eIIyQR1ia0kgnBnT95EVq1qmv4plauX+RxFMEhOAInwAWnoA6uQQM0AQaP4Bm8gjfryXqx3q2PWWvBymf2wR9Znz87EpV0</latexit>
G = (V, E, R, )<latexit sha1_base64="hfH2qiOkdhHaLO2qsmwczf37cp4=">AAAB/nicbZDLSgMxFIbPeK31Niqu3ARboUIpM93oRiiK6LKKvUA7lEyatqGZzJBkhDIUfBU3LhRx63O4821M21lo6w+Bj/+cwzn5/YgzpR3n21paXlldW89sZDe3tnd27b39ugpjSWiNhDyUTR8rypmgNc00p81IUhz4nDb84dWk3nikUrFQPOhRRL0A9wXrMYK1sTr2Yf4GXaBCvYiui+i+iNrRgJ3mO3bOKTlToUVwU8hBqmrH/mp3QxIHVGjCsVIt14m0l2CpGeF0nG3HikaYDHGftgwKHFDlJdPzx+jEOF3UC6V5QqOp+3siwYFSo8A3nQHWAzVfm5j/1Vqx7p17CRNRrKkgs0W9mCMdokkWqMskJZqPDGAimbkVkQGWmGiTWNaE4M5/eRHq5ZJr+K6cq1ymcWTgCI6hAC6cQQVuoQo1IJDAM7zCm/VkvVjv1sesdclKZw7gj6zPH/r0kkY=</latexit><latexit sha1_base64="hfH2qiOkdhHaLO2qsmwczf37cp4=">AAAB/nicbZDLSgMxFIbPeK31Niqu3ARboUIpM93oRiiK6LKKvUA7lEyatqGZzJBkhDIUfBU3LhRx63O4821M21lo6w+Bj/+cwzn5/YgzpR3n21paXlldW89sZDe3tnd27b39ugpjSWiNhDyUTR8rypmgNc00p81IUhz4nDb84dWk3nikUrFQPOhRRL0A9wXrMYK1sTr2Yf4GXaBCvYiui+i+iNrRgJ3mO3bOKTlToUVwU8hBqmrH/mp3QxIHVGjCsVIt14m0l2CpGeF0nG3HikaYDHGftgwKHFDlJdPzx+jEOF3UC6V5QqOp+3siwYFSo8A3nQHWAzVfm5j/1Vqx7p17CRNRrKkgs0W9mCMdokkWqMskJZqPDGAimbkVkQGWmGiTWNaE4M5/eRHq5ZJr+K6cq1ymcWTgCI6hAC6cQQVuoQo1IJDAM7zCm/VkvVjv1sesdclKZw7gj6zPH/r0kkY=</latexit><latexit sha1_base64="hfH2qiOkdhHaLO2qsmwczf37cp4=">AAAB/nicbZDLSgMxFIbPeK31Niqu3ARboUIpM93oRiiK6LKKvUA7lEyatqGZzJBkhDIUfBU3LhRx63O4821M21lo6w+Bj/+cwzn5/YgzpR3n21paXlldW89sZDe3tnd27b39ugpjSWiNhDyUTR8rypmgNc00p81IUhz4nDb84dWk3nikUrFQPOhRRL0A9wXrMYK1sTr2Yf4GXaBCvYiui+i+iNrRgJ3mO3bOKTlToUVwU8hBqmrH/mp3QxIHVGjCsVIt14m0l2CpGeF0nG3HikaYDHGftgwKHFDlJdPzx+jEOF3UC6V5QqOp+3siwYFSo8A3nQHWAzVfm5j/1Vqx7p17CRNRrKkgs0W9mCMdokkWqMskJZqPDGAimbkVkQGWmGiTWNaE4M5/eRHq5ZJr+K6cq1ymcWTgCI6hAC6cQQVuoQo1IJDAM7zCm/VkvVjv1sesdclKZw7gj6zPH/r0kkY=</latexit><latexit sha1_base64="hfH2qiOkdhHaLO2qsmwczf37cp4=">AAAB/nicbZDLSgMxFIbPeK31Niqu3ARboUIpM93oRiiK6LKKvUA7lEyatqGZzJBkhDIUfBU3LhRx63O4821M21lo6w+Bj/+cwzn5/YgzpR3n21paXlldW89sZDe3tnd27b39ugpjSWiNhDyUTR8rypmgNc00p81IUhz4nDb84dWk3nikUrFQPOhRRL0A9wXrMYK1sTr2Yf4GXaBCvYiui+i+iNrRgJ3mO3bOKTlToUVwU8hBqmrH/mp3QxIHVGjCsVIt14m0l2CpGeF0nG3HikaYDHGftgwKHFDlJdPzx+jEOF3UC6V5QqOp+3siwYFSo8A3nQHWAzVfm5j/1Vqx7p17CRNRrKkgs0W9mCMdokkWqMskJZqPDGAimbkVkQGWmGiTWNaE4M5/eRHq5ZJr+K6cq1ymcWTgCI6hAC6cQQVuoQo1IJDAM7zCm/VkvVjv1sesdclKZw7gj6zPH/r0kkY=</latexit>

55
…
Samples relation
BA
Embedding space
Graph structures
A
B
Sampler
Mapper
Optimizer
•Converts entities into spatial features
via embedding stacking operations, 
e.g, lookup, pooling (average, etc.)
f : (p) ! Rd
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f : (p, q) ! Rd
<latexit sha1_base64="w+fc6rCobrgHcpaEWRxxo2tpDbs=">AAACFHicbZC7TsMwFIadcivlFmBksWiRikBV0gXEVMHCWBC9SE2oHMdprToXbAdURXkIFl6FhQGEWBnYeBucNgO0/JKlT/85Rz7ndyJGhTSMb62wsLi0vFJcLa2tb2xu6ds7bRHGHJMWDlnIuw4ShNGAtCSVjHQjTpDvMNJxRhdZvXNPuKBhcCPHEbF9NAioRzGSyurrR5bjJRXvDFaj47tDaHE6GErEefgALR/JoeMk1+lt4qawkvb1slEzJoLzYOZQBrmaff3LckMc+ySQmCEheqYRSTtBXFLMSFqyYkEihEdoQHoKA+QTYSeTo1J4oBwXeiFXL5Bw4v6eSJAvxNh3VGe2qJitZeZ/tV4svVM7oUEUSxLg6UdezKAMYZYQdCknWLKxAoQ5VbtCPEQcYalyLKkQzNmT56Fdr5mKr+rlxnkeRxHsgX1QBSY4AQ1wCZqgBTB4BM/gFbxpT9qL9q59TFsLWj6zC/5I+/wBMe6drA==</latexit><latexit sha1_base64="w+fc6rCobrgHcpaEWRxxo2tpDbs=">AAACFHicbZC7TsMwFIadcivlFmBksWiRikBV0gXEVMHCWBC9SE2oHMdprToXbAdURXkIFl6FhQGEWBnYeBucNgO0/JKlT/85Rz7ndyJGhTSMb62wsLi0vFJcLa2tb2xu6ds7bRHGHJMWDlnIuw4ShNGAtCSVjHQjTpDvMNJxRhdZvXNPuKBhcCPHEbF9NAioRzGSyurrR5bjJRXvDFaj47tDaHE6GErEefgALR/JoeMk1+lt4qawkvb1slEzJoLzYOZQBrmaff3LckMc+ySQmCEheqYRSTtBXFLMSFqyYkEihEdoQHoKA+QTYSeTo1J4oBwXeiFXL5Bw4v6eSJAvxNh3VGe2qJitZeZ/tV4svVM7oUEUSxLg6UdezKAMYZYQdCknWLKxAoQ5VbtCPEQcYalyLKkQzNmT56Fdr5mKr+rlxnkeRxHsgX1QBSY4AQ1wCZqgBTB4BM/gFbxpT9qL9q59TFsLWj6zC/5I+/wBMe6drA==</latexit><latexit sha1_base64="w+fc6rCobrgHcpaEWRxxo2tpDbs=">AAACFHicbZC7TsMwFIadcivlFmBksWiRikBV0gXEVMHCWBC9SE2oHMdprToXbAdURXkIFl6FhQGEWBnYeBucNgO0/JKlT/85Rz7ndyJGhTSMb62wsLi0vFJcLa2tb2xu6ds7bRHGHJMWDlnIuw4ShNGAtCSVjHQjTpDvMNJxRhdZvXNPuKBhcCPHEbF9NAioRzGSyurrR5bjJRXvDFaj47tDaHE6GErEefgALR/JoeMk1+lt4qawkvb1slEzJoLzYOZQBrmaff3LckMc+ySQmCEheqYRSTtBXFLMSFqyYkEihEdoQHoKA+QTYSeTo1J4oBwXeiFXL5Bw4v6eSJAvxNh3VGe2qJitZeZ/tV4svVM7oUEUSxLg6UdezKAMYZYQdCknWLKxAoQ5VbtCPEQcYalyLKkQzNmT56Fdr5mKr+rlxnkeRxHsgX1QBSY4AQ1wCZqgBTB4BM/gFbxpT9qL9q59TFsLWj6zC/5I+/wBMe6drA==</latexit><latexit sha1_base64="w+fc6rCobrgHcpaEWRxxo2tpDbs=">AAACFHicbZC7TsMwFIadcivlFmBksWiRikBV0gXEVMHCWBC9SE2oHMdprToXbAdURXkIFl6FhQGEWBnYeBucNgO0/JKlT/85Rz7ndyJGhTSMb62wsLi0vFJcLa2tb2xu6ds7bRHGHJMWDlnIuw4ShNGAtCSVjHQjTpDvMNJxRhdZvXNPuKBhcCPHEbF9NAioRzGSyurrR5bjJRXvDFaj47tDaHE6GErEefgALR/JoeMk1+lt4qawkvb1slEzJoLzYOZQBrmaff3LckMc+ySQmCEheqYRSTtBXFLMSFqyYkEihEdoQHoKA+QTYSeTo1J4oBwXeiFXL5Bw4v6eSJAvxNh3VGe2qJitZeZ/tV4svVM7oUEUSxLg6UdezKAMYZYQdCknWLKxAoQ5VbtCPEQcYalyLKkQzNmT56Fdr5mKr+rlxnkeRxHsgX1QBSY4AQ1wCZqgBTB4BM/gFbxpT9qL9q59TFsLWj6zC/5I+/wBMe6drA==</latexit>
Optimizes distance

BA
56
…
Samples relation
Embedding space
Graph structures
A
B
Sampler
Mapper
Optimizer
•Preserves entity relatedness as spatial
properties with customizable similarity
metrics and loss functions
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Matrix Factorization Collaborative Metric Learning
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$%
$"
$#
$%
$"
&# &"
$#
$"
$%
Figure 3: Example latent vector assignments for ma-
trix factorization and CML. The table on the right
shows user/item’s preference relationships.
3.5 Training Procedure
The complete objective function of the proposed model is
g
&# &"
$#
$"
$%
s for ma-
Dot Product Euclidean Distance
→ Euclidean distance keeps triangular
inequality; dot product does not [5] Optimizes distance

B
A
57
…
Samples relation
BA
Embedding space
Graph structures
Sampler
Mapper
for
Recommendation
Optimizer
Optimizes distance

SMORe : Modular GE toolkit for REC
B
A
58
…
Samples relation
BA
Embedding space
Graph structures
Sampler
Mapper
for
Recommendation
Optimizer
Optimizes distance

59
SMORe is a modular GE toolkit for REC S’more is a campfire treat with layers
SMORe : Modular GE toolkit for REC

60
Beneﬁts of SMORe
Performance levelSampler
Mapper
for
Recommendation
Optimizer
Modules contribute different
levels of performance during
different REC tasks
Model A
Model B
Model C

61
Beneﬁts of SMORe
Sampler
Mapper
for
Recommendation
Optimizer
SMORe enables combining
the most suitable modules
for given REC task

62
Beneﬁts of SMORe
Sampler
Mapper
for
Recommendation
Optimizer
SMORe enables combining
the most suitable modules
for given REC task

63
Beneﬁts of SMORe
Best THEN!
Best NOW!
As toolkit for research:
1. Baseline comparison
2. Ballpark approaches
3. One module at a time
As framework for development:
1. Reduces development time
2. Raises performance limit
3. Adapts to new tasks

References
64
1. Hamilton, William L., et al. “Representation on Networks”, WWW 2018 Tutorial
2. Shi, Chuan, et al. “Relevance Search in Heterogeneous Networks”, ACM EDBT 2012
3. Shi, Chuan, et al. “A Survey of Heterogeneous Information Network Analysis”, 
IEEE TKDE 2016
4. Bernhardsson, Erik “ANNOY library”, https://github.com/spotify/annoy
5. Hsieh, Cheng-Kang, et al. “Collaborative Metric Learning”, WWW 2017

Lecture Agenda
65
Q4. REC using SMORe
(Sean)
(Sean)
(Sean)
(CM)
(CM)

CLIP Lab, National Chengchi University CFDA Lab, Academia Sinica66
Example Graph
vertex
edge

Vertex Structure
• Adjacency 
- vertices which share the same edge
• Neighborhood 
- vertices which share similar connections
• Community 
- vertices which share similar communities
• Centrality 
- vertices which share similar properties

1. Adjacency
DB
A EC
F
EDGE EDGE
EDGE

Adjacency
user item
user-item preference
vertices share the same edge are treated as similar pairs

Matrix Factorization
r = ? ? ? ?
?
?
?
?
x
p1 p2 p3
U1
U2
U3
I1 I2 I3 I4
IEEE Computer’09
Yehuda Koren, Robert M. Bell, Chris Volinsky: Matrix Factorization
Techniques for Recommender Systems. IEEE Computer 42(8): 30-37 (2009)
might distort the data considerably. Hence, more r
works3-6
suggested modeling directly the observe
ings only, while avoiding overfitting through a regula
model. To learn the factor vectors (pu
and qi
), the s
minimizes the regularized squared error on the
known ratings:
min
* *,q p
( , )u i
(rui
qi
T
pu
)2
+ (|| qi
||2
+ || pu
||2
)
Here, is the set of the (u,i) pairs for which rui
is k
q1
q2
q3
(rating - item*user)
p4

Graph
user-item graph
Matrix Factorization in SMORe

( , )
(user, item)
72
SamplerGraph
user-item graph

( , )
(user, item)
73
SamplerGraph
Mapper
user-item graph
~v<latexit sha1_base64="m1L29Cxyzv4kq0gD0isZHiqvweE=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lqQY8FLx4r2A9oQ9lsJ+3SzSbsbgol9Ed48aCIV3+PN/+N2zYHbX0w8Hhvhpl5QSK4Nq777RS2tnd294r7pYPDo+OT8ulZW8epYthisYhVN6AaBZfYMtwI7CYKaRQI7AST+4XfmaLSPJZPZpagH9GR5CFn1Fip058iy6bzQbniVt0lyCbxclKBHM1B+as/jFkaoTRMUK17npsYP6PKcCZwXuqnGhPKJnSEPUsljVD72fLcObmyypCEsbIlDVmqvycyGmk9iwLbGVEz1uveQvzP66UmvPMzLpPUoGSrRWEqiInJ4ncy5AqZETNLKFPc3krYmCrKjE2oZEPw1l/eJO1a1bup1h7rlUYzj6MIF3AJ1+DBLTTgAZrQAgYTeIZXeHMS58V5dz5WrQUnnzmHP3A+fwC0XY/a</latexit>
Embedding Lookup

( , )
(user, item)
74
OptimizerSamplerGraph
Mapper
user-item graph
Square Error
(~v · ~v y)2
<latexit sha1_base64="uQdhOq3LVxgk6wWspOVfIsBCS58=">AAACBnicbVDLSgMxFM34rPU16lKEYBHqwjJTBV0W3LisYB/QGUsmk2lDM8mQZApl6MqNv+LGhSJu/QZ3/o1pO4K2Hrhwcs695N4TJIwq7Thf1tLyyuraemGjuLm1vbNr7+03lUglJg0smJDtACnCKCcNTTUj7UQSFAeMtILB9cRvDYlUVPA7PUqIH6MepxHFSBupax+VvSHB2XAMPRwKDX9eZ3B0el/t2iWn4kwBF4mbkxLIUe/an14ocBoTrjFDSnVcJ9F+hqSmmJFx0UsVSRAeoB7pGMpRTJSfTc8YwxOjhDAS0hTXcKr+nshQrNQoDkxnjHRfzXsT8T+vk+roys8oT1JNOJ59FKUMagEnmcCQSoI1GxmCsKRmV4j7SCKsTXJFE4I7f/IiaVYr7nmlentRqtXzOArgEByDMnDBJaiBG1AHDYDBA3gCL+DVerSerTfrfda6ZOUzB+APrI9vpWyX/A==</latexit>
Embedding Lookup

Sparse LInear Method (SLIM) ICDM’11, RecSys’16
= 1 0 1 0
0 ?
0
? 0
- 0
x
I1 I2 I3
I1
I2
I3
I4
I4I1 I2 I3 I4
U1
U2
U3
1. Xia Ning, George Karypis: SLIM: Sparse Linear Methods for Top-N Recommender Systems. ICDM 2011: 497-506
2. Evangelia Christakopoulou, George Karypis: Local Item-Item Models For Top-N Recommendation. RecSys 2016: 67-74
nd MF. In
y with a
methods.
ed as a
Bayesian
maximum
sures the
ems and
n method
objective
o denote
nd items
in ˜aT
i in decreasing order and recommending the top-N items.
B. Learning W for SLIM
We view the purchase/rating activity of user ui on item tj in
A (i.e., aij) as the ground-truth item recommendation score.
Given a user-item purchase/rating matrix A of size m⇥n, we
learn the sparse n⇥n matrix W in Equation 2 as the minimizer
for the following regularized optimization problem:
minimize
W
1
2
kA AWk2
F +
2
kWk2
F + kWk1
subject to W 0
diag(W) = 0,
(3)
where kWk1 =
Pn
i=1
Pn
j=1 |wij| is the entry-wise `1-norm
of W, and k · kF is the matrix Frobenius norm. In Equa-
1 - 1 -
I1 I2 I3 I4
U1
U2
U3
Transition Matrix W

( , )
(user, item)
76
SamplerGraph
user-item graph
SLIM in SMORe

( , )
(user, item)
77
SamplerGraph
Mapper
user-item graph
SLIM in SMORe
space such that the co-occurrence of users and items (i.e.,
a certain user has purchased a certain item) can be rendered
conditionally independent. Koren [10] proposed an intersect-
ing approach between neighborhood-based method and MF. In
his approach, item similarity is learned simultaneously with a
matrix factorization so as to take advantages of both methods.
Top-N recommendation has also been formulated as a
ranking problem. Rendle et al [11] proposed a Bayesian
Personalized Ranking (BPR) criterion, which is the maximum
posterior estimator from a Bayesian analysis and measures the
difference between the rankings of user-purchased items and
the rest items. BPR can be well adopted for item knn method
(BPRkNN) and MF methods (BPRMF) as a general objective
function.
III. DEFINITIONS AND NOTATIONS
In this paper, the symbols u and t will be used to denote
the users and items, respectively. Individual users and items
will be denoted using different subscripts (i.e., ui, tj). The
set of all users and items in the system will be denoted by U
represents the recommendation s
ui. Top-N recommendation for ui
purchased/-rated items based on t
in ˜aT
i in decreasing order and rec
B. Learning W for SLIM
We view the purchase/rating act
A (i.e., aij) as the ground-truth i
Given a user-item purchase/rating
learn the sparse n⇥n matrix W in
for the following regularized opti
minimize
W
1
2
kA AWk2
F +
subject to W 0
diag(W) = 0,
where kWk1 =
Pn
i=1
Pn
j=1 |wij
of W, and k · kF is the matrix
tion 3, AW is the estimated matri
(i.e., ˜A) by the sparse linear mo
1 2
A 
(fixed)
W
(trainable)

( , )
(user, item)
78
Mapper
user-item graph
SLIM in SMORe
Square Error
(~v · ~v y)2
<latexit sha1_base64="uQdhOq3LVxgk6wWspOVfIsBCS58=">AAACBnicbVDLSgMxFM34rPU16lKEYBHqwjJTBV0W3LisYB/QGUsmk2lDM8mQZApl6MqNv+LGhSJu/QZ3/o1pO4K2Hrhwcs695N4TJIwq7Thf1tLyyuraemGjuLm1vbNr7+03lUglJg0smJDtACnCKCcNTTUj7UQSFAeMtILB9cRvDYlUVPA7PUqIH6MepxHFSBupax+VvSHB2XAMPRwKDX9eZ3B0el/t2iWn4kwBF4mbkxLIUe/an14ocBoTrjFDSnVcJ9F+hqSmmJFx0UsVSRAeoB7pGMpRTJSfTc8YwxOjhDAS0hTXcKr+nshQrNQoDkxnjHRfzXsT8T+vk+roys8oT1JNOJ59FKUMagEnmcCQSoI1GxmCsKRmV4j7SCKsTXJFE4I7f/IiaVYr7nmlentRqtXzOArgEByDMnDBJaiBG1AHDYDBA3gCL+DVerSerTfrfda6ZOUzB+APrI9vpWyX/A==</latexit>
A 
(fixed)
W
(trainable)

2. Neighborhood
A
B
NEIGHBORS

Neighborhood
vertices share similar connections are treated as similar pairs
commonly purchasedcommon interests

item2vec RecSys’16, MLSP’16
Oren Barkan, Noam Koenigstein: Item2vec: Neural Item Embedding for
Collaborative Filtering. RecSys Posters 2016 
Oren Barkan, Noam Koenigstein: ITEM2VEC: Neural item embedding for
collaborative filtering. MLSP 2016: 1-6
ter that
s to be
d iw is
d to the
und to
ibution,
rare and
edure is
each pair of items that share the same set as
example. This implies a window size that is d
from the set size. Specifically, for a given se
the objective from Eq. (1) is modified as follo
1
1
log ( | )
K K
j i
i j i
p w w
K = ≠
∑∑
Another option is to keep the objective in Eq
and shuffle each set of items during runtim
experiments we observed that both options p
the given K items
purchasing logs

To Model Neighborhood
context 
space
vertex 
space
purchasing logs
shared 
neighbor
userA
userB
space for shared neighbor
w2v

SamplerGraph
user-item graph
item2vec in SMORe
( , )
(itemA, itemB)
A B
A
B

SamplerGraph
Mapper
user-item graph
item2vec in SMORe
vertex 
embedding lookup
A
~vv
<latexit sha1_base64="n/DRd03R+fmi3AovMrJcYZKlFBM=">AAAB+3icbZBNS8NAEIY39avWr1iPXoJF8FSSKuix4MVjBdsKTSyb7aRduvlgd1JaQv6KFw+KePWPePPfuG1z0NYXFh7emWFmXz8RXKFtfxuljc2t7Z3ybmVv/+DwyDyudlScSgZtFotYPvpUgeARtJGjgMdEAg19AV1/fDuvdycgFY+jB5wl4IV0GPGAM4ra6ptVdwIsm+RPmYswRU1536zZdXshax2cAmqkUKtvfrmDmKUhRMgEVarn2Al6GZXImYC84qYKEsrGdAg9jRENQXnZ4vbcOtfOwApiqV+E1sL9PZHRUKlZ6OvOkOJIrdbm5n+1XorBjZfxKEkRIrZcFKTCwtiaB2ENuASGYqaBMsn1rRYbUUkZ6rgqOgRn9cvr0GnUnct64/6q1mwVcZTJKTkjF8Qh16RJ7kiLtAkjU/JMXsmbkRsvxrvxsWwtGcXMCfkj4/MHZ5qVXg==</latexit>
context 
embedding lookup
B ~vc
<latexit sha1_base64="HJbdihIJmLvMuY2eQ/2t7MTPmYg=">AAAB+3icbVBNS8NAEN3Ur1q/Yj16CRbBU0mqoMeCF48VbCs0sWy2k3bp5oPdSWkJ+StePCji1T/izX/jts1BWx8MPN6bYWaenwiu0La/jdLG5tb2Tnm3srd/cHhkHlc7Kk4lgzaLRSwffapA8AjayFHAYyKBhr6Arj++nfvdCUjF4+gBZwl4IR1GPOCMopb6ZtWdAMsm+VPmIkwxY3neN2t23V7AWidOQWqkQKtvfrmDmKUhRMgEVarn2Al6GZXImYC84qYKEsrGdAg9TSMagvKyxe25da6VgRXEUleE1kL9PZHRUKlZ6OvOkOJIrXpz8T+vl2Jw42U8SlKEiC0XBamwMLbmQVgDLoGhmGlCmeT6VouNqKQMdVwVHYKz+vI66TTqzmW9cX9Va7aKOMrklJyRC+KQa9Ikd6RF2oSRKXkmr+TNyI0X4934WLaWjGLmhPyB8fkDSqiVSw==</latexit>
( , )
A B
A
B
(itemA, itemB)

Mapper
user-item graph
item2vec in SMORe
vertex 
embedding lookup
A
~vv
context 
embedding lookup
B ~vc
( , )
A B
Log Likelihood
A B
log (~vv
· ~vc
)<latexit sha1_base64="+ijKtwEXuygdqvbeIqq2UeNudQM=">AAACIHicbZBNS8NAEIY3flu/oh69LBZBLyVRoR4FLx4r2FZoatlspu3STTbsTool9Kd48a948aCI3vTXuK05aPWFhZdnZpidN0ylMOh5H87c/MLi0vLKamltfWNzy93eaRiVaQ51rqTSNyEzIEUCdRQo4SbVwOJQQjMcXEzqzSFoI1RyjaMU2jHrJaIrOEOLOm41kKoXGNGL2WEwBJ4Px7d5gHCH1o0DHimcwdxietRxy17Fm4r+NX5hyqRQreO+B5HiWQwJcsmMafleiu2caRRcwrgUZAZSxgesBy1rExaDaefTA8f0wJKIdpW2L0E6pT8nchYbM4pD2xkz7JvZ2gT+V2tl2D1r5yJJM4SEfy/qZpKiopO0aCQ0cJQjaxjXwv6V8j7TjKPNtGRD8GdP/msaxxX/pHJ8dVo+rxVxrJA9sk8OiU+q5JxckhqpE07uySN5Ji/Og/PkvDpv361zTjGzS37J+fwCQLeliA==</latexit>
A
B
(itemA, itemB)

3. Community
A
B
COMMUNITY

Community
vertices share similar communities are treated as similar pairs
connected to the same group
not connected

Heterogeneous Preference Embedding (HPE) RecSys’16
Chih-Ming Chen, Ming-Feng Tsai, Yu-Ching Lin, Yi-Hsuan Yang: Query-based
Music Recommendations via Preference Embedding. RecSys 2016: 79-82
aper includes:
dation is proposed
arch work of infor-
mender system.
ommendation as a
propose a method
between users and
ms.
onducted to verify
ethod.
ENDATIONS
the task of query-
User
Track
Album
Artist
U1
T1
T2
T3
T4
T5
Ar1
U2
U3
Ar2
Ar3
Al1
Al2
Al3
Al4T6
U4
Figure 1: The user preference network. Suppose there are
totally four kinds of data attributes in the music listening
dataset. In the ﬁgure, the user U4 may frequently listen to

Heterogeneous Preference Embedding (HPE) RecSys’16
Chih-Ming Chen, Ming-Feng Tsai, Yu-Ching Lin, Yi-Hsuan Yang: Query-based
Music Recommendations via Preference Embedding. RecSys 2016: 79-82
T5 Al4U3 U4
target 
vertexT5 U3
U3 U4 Al4U3
Edge Sampling from
whole network
Weighted Random Walks from 
preceding vertex
Walk Direction
T5U3
…
( , )
( , )
( , ) ( , )
context 
vertex
( , )
the training pairs
ure 2: Edge sampling via weighted random walks for
ning pairs. In our sampling scheme, the ﬁrst sampling
is derived from the edge sampling over the whole network.
Algorithm 1: Heterogeneous Prefer
Input: User Preference Network:
Walk Steps: w, Sampling Times: n
1 for v 2 V do
2 Initialize the representation: (
3 for i 2 {1, ..., n} do
4 (v1, v2) = EdgeSampling(G)
5 Update (v1), context v2 by mi
6 Update (v2), context v1 by mi
7 for v0
2 RandomWalk(v2, w
8 Update (v1), context v0
by
Output: Vertex representations
Table 1: Dataset
Pr(vj| (vi)) =
0 otherwise
Maximizing the above posterior probabi
to minimizing the negative log likelihood,
function of the second-order proximity can
follows:
O =
X
(i,j)2S
wi,j log p(vj| (vi)) +
X
i
where S is a set of sampling pairs and w ind
of the edge. In practice, the observed ed
tive information and thus falls into the one
problem. We adopt the widely-used solutio
sampling to sample the additional user-to-o
weight embedding

SamplerGraph
user-item graph
HPE in SMORe
( , )V C ( , )V C ( , )V C

Mapper
user-item graph
HPE in SMORe
( , )V C ( , )V C ( , )V C
vertex 
embedding lookup
~vv
V
V
context 
embedding lookup
~vc
C
C
Log Likelihood
V C
log (~vv
· ~vc

4. Centrality (Degree)
92
A
B
DEGREE 4
DEGREE 4

Centrality
vertices share similar properties are treated as similar pairs
hub item hub item

struc2vec KDD’17
Leonardo Filipe Rodrigues Ribeiro, Pedro H. P. Saverese, Daniel R.
Figueiredo: struc2vec: Learning Node Representations from Structural
Identity. KDD 2017: 385-394

struc2vec KDD’17

struc2vec KDD’17
user-user graph
fn1( ) = structure1_A
fn1( ) = structure1_B
A
B
A
B
fn2( ) = structure2_C
C
C
1-step:
2-steps:

SamplerGraph
user-user graph
struc2vec in SMORe
( , )V
fn1()
S ( , )V
fn2()
S

Mapper
user-user graph
struc2vec in SMORe
~vv
V
V
~vc
S
S
Log Likelihood
V S
log (~vv
· ~vc
( , )V
fn1()
S ( , )V
fn2()
S
note. original work adopts hierarchal softmax for learning
vertex 
embedding lookup
context 
embedding lookup

Recap
Sampler Mapper Optimizer
MF Adjacency Vertex Embedding
Dot product
RMSE
SLIM Adjacency Vertex Embedding
Dot product
RMSE
item2vec Neighborhood
Vertex Embedding
Context Embedding
Sigmoid Dot Product
Log Likelihood
HPE Community
Vertex Embedding
Context Embedding
Sigmoid Dot Product
Log Likelihood
struc2vec Centrality
Vertex Embedding
Context Embedding
Sigmoid Dot Product
Log Likelihood

Edge Information
• Weight 
- reflects strength of interaction
• Closeness 
- reflects order of interaction
• Semantics 
- sample with grammar
• Inductiveness 
- information diffuses through edges

1. Weight
B
C
A
12
1

node2vec
edge weight guides the walk
BFS Walk DFS Walk
Aditya Grover, Jure Leskovec: node2vec: Scalable Feature Learning for Networks.
KDD 2016: 855-864
KDD’16
v
α=1
α=1/q
α=1/q
α=1/p
x2
x3t
x1
2: Illustration of the random walk procedure in node2vec.
alk just transitioned from t to v and is now evaluating its next
t of node v. Edge labels indicate search biases ↵.
x denotes the shortest path distance between nodes t and x.
hat dtx must be one of {0, 1, 2}, and hence, the two parame-

node2vec in SMORe
v
α=1
α=1/q
α=1/q
α=1/p
x2
x3t
x1
2: Illustration of the random walk procedure in node2vec.
alk just transitioned from t to v and is now evaluating its next
t of node v. Edge labels indicate search biases ↵.
x denotes the shortest path distance between nodes t and x.
hat dtx must be one of {0, 1, 2}, and hence, the two parame-
Sampler
customized 
random walk

2. Closeness
A
strong weak

High-order Proximity for Recommendations (HOP-Rec)
RecSys’18
w
Chih-Ming Chen
National Chengchi University
Taipei, Taiwan
104761501@nccu.edu.tw
w
Ming-Feng Tsai
National Chengchi University
Taipei, Taiwan
mftsai@nccu.edu.tw
many e-commerce
pular approaches
els; the former ap-
he observed direct
r extracts indirect
item interactions.
ecient method
posed method in-
order information
d of factorizing a
dence weighting
n simultaneously,
action matrix and
lks. Experimental
performs the state
tasets.
andom walks; bi-
back
and Ming-Feng Tsai.
ecommendation. In
i1
i2
i3
i4
u1
1st 1st
u2
1st 1st
u3
1st 1st
i1 i2 i3 i4
u1
1st 1st 2nd 3rd
u2
2nd 1st 1st 2nd
u3
3rd 2nd 1st 1st
(c) (d)
(a) (b)
i1
u1
i2 i3 i4 i1
u1 u2
i2 i3
u3
i4
u2 u3
Figure 1: High-order proximity between users and items
within observed interactions
Collaborative ltering (CF) is commonly used to leverage this
Jheng-Hong Yang, Chih-Ming Chen, Chuan-Ju Wang, Ming-Feng Tsai: HOP-rec: high-
order proximity for implicit recommendation. RecSys 2018: 140-144
these factorization and graph models, we build HOP-Re
framework that (1) captures high-order preference info
a given user-item interaction matrix, and (2) scales to l
real-world datasets by using random surng on the corr
interaction graph. The objective of HOP-Rec is dened
LHOP =
X
1k K
u,(i,i0)
graph model
z }| {
C(k) E i⇠Pk
u
i0⇠PN
factorization model
z }| {f
F
⇣ |
u i0,
|
u i
⌘g
+ k
where Pk
u (·) denotes the k-order probability distribut
item sampled from the walk sequence Su (see Denit
denotes a uniform distribution by which an item is sam
the set of all items, and K denotes the maximum orde
in our method. The main idea behind the proposed met
approximation of high-order probabilistic matrix factor
conducting random walk (RW) with a decay factor for c
cit Recommendation RecSys ’18, October 2–7, 2018, Vancouver, BC, Cana
uild HOP-Rec, a united
eference information in
2) scales to large-scale
g on the corresponding
ec is dened as
model
{
|
u i
⌘g
+ k k2
2 , (3)
Finally, the ranking objective function is composed with an in
cator function and a pairwise logistic loss, and we thus dene F
Eq. (3) as
F (
|
u i0,
|
u i ) = 1{
|
u i0
|
u i k } log
f ⇣ |
u i0
|
u i
⌘g
,
where 1B denotes the indicator function for condition B and k
an order-aware margin set to /k. Note that item i0 is uniform
sampled from the set of all items as we assume a simplied u
form distribution PN for less preferred items; this assumption
order-aware interaction

HOP-Rec in SMORe
SamplerGraph
user-item graph
( , )
1(~v · ~v ~v · ~v margin)latexit sha1_base64=iBNmKDj8/YuJu40Ok7W0yOl30QA=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
R
greater 
margin
smaller 
margin

HOP-Rec in SMORe
Mapper
user-item graph
embedding lookup
BPRLoss
( , )
~vlatexit sha1_base64=m1L29Cxyzv4kq0gD0isZHiqvweE=AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lqQY8FLx4r2A9oQ9lsJ+3SzSbsbgol9Ed48aCIV3+PN/+N2zYHbX0w8Hhvhpl5QSK4Nq777RS2tnd294r7pYPDo+OT8ulZW8epYthisYhVN6AaBZfYMtwI7CYKaRQI7AST+4XfmaLSPJZPZpagH9GR5CFn1Fip058iy6bzQbniVt0lyCbxclKBHM1B+as/jFkaoTRMUK17npsYP6PKcCZwXuqnGhPKJnSEPUsljVD72fLcObmyypCEsbIlDVmqvycyGmk9iwLbGVEz1uveQvzP66UmvPMzLpPUoGSrRWEqiInJ4ncy5AqZETNLKFPc3krYmCrKjE2oZEPw1l/eJO1a1bup1h7rlUYzj6MIF3AJ1+DBLTTgAZrQAgYTeIZXeHMS58V5dz5WrQUnnzmHP3A+fwC0XY/a/latexit
~vlatexit sha1_base64=m1L29Cxyzv4kq0gD0isZHiqvweE=AAAB7nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lqQY8FLx4r2A9oQ9lsJ+3SzSbsbgol9Ed48aCIV3+PN/+N2zYHbX0w8Hhvhpl5QSK4Nq777RS2tnd294r7pYPDo+OT8ulZW8epYthisYhVN6AaBZfYMtwI7CYKaRQI7AST+4XfmaLSPJZPZpagH9GR5CFn1Fip058iy6bzQbniVt0lyCbxclKBHM1B+as/jFkaoTRMUK17npsYP6PKcCZwXuqnGhPKJnSEPUsljVD72fLcObmyypCEsbIlDVmqvycyGmk9iwLbGVEz1uveQvzP66UmvPMzLpPUoGSrRWEqiInJ4ncy5AqZETNLKFPc3krYmCrKjE2oZEPw1l/eJO1a1bup1h7rlUYzj6MIF3AJ1+DBLTTgAZrQAgYTeIZXeHMS58V5dz5WrQUnnzmHP3A+fwC0XY/a/latexit
log (~v · ~v ~v · ~v )latexit sha1_base64=O9uo0NROxizRILxvgLgJbQT9HME=AAACIXicbZDLSsNAFIYn9VbrLerSzWAR6sKSVMEui25cVrAXaEKZTCbp0EkmzEwKJfRV3Pgqblwo0p34Mk7bCNr2h4GP/5zDmfN7CaNSWdaXUdjY3NreKe6W9vYPDo/M45O25KnApIU546LrIUkYjUlLUcVINxEERR4jHW94P6t3RkRIyuMnNU6IG6EwpgHFSGmrb9YdxkNH0jBCFWdEcDaaONjn6pfhFVxrX/bNslW15oKrYOdQBrmafXPq+BynEYkVZkjKnm0lys2QUBQzMik5qSQJwkMUkp7GGEVEutn8wgm80I4PAy70ixWcu38nMhRJOY483RkhNZDLtZm5rtZLVVB3MxonqSIxXiwKUgYVh7O4oE8FwYqNNSAsqP4rxAMkEFY61JIOwV4+eRXatap9Xa093pQbd3kcRXAGzkEF2OAWNMADaIIWwOAZvIJ38GG8GG/GpzFdtBaMfOYU/JPx/QMUnaSs/latexit
1. Steffen Rendle, Christoph
Freudenthaler, Zeno Gantner, Lars
Schmidt-Thieme: BPR: Bayesian
Personalized Ranking from Implicit
Feedback. UAI 2009: 452-461
1(~v · ~v ~v · ~v margin)latexit sha1_base64=iBNmKDj8/YuJu40Ok7W0yOl30QA=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
R
R
greater 
margin
smaller 
margin

3. Semantics
A
USER
VENUE

metapath2vec KDD’17
Org Author Paper Venue
a1
a2
a3
a4
a5
MIT
CMU
ACL
KDD
p1
p2
p3
APVPA
OAPVPAO
APA
meta paths
(a) An academic network
KDD 0
0
0
0
0
1
0
0
0
0
0
0
ACL
MIT
CMU
a1
a2
a3
a4
a5
p1
p2
p3
input layer hidden
layer
|V|-dim
(b) Skip-gram in metapa
a heteroge-
erogeneous
ion Learn-
learn the d-
V | that are
ong them.
trix X, with
ding to the
re dierent
ed into the
the heterogeneous network structures into skip-gram, we propose
meta-path-based random walks in heterogeneous networks.
Heterogeneous Skip-Gram. In metapath2vec, we enable skip-
gram to learn eective node representations for a heterogeneous
network G = (V, E,T ) with |TV | 1 by maximizing the probability
of having the heterogeneous context Nt ( ),t 2 TV given a node :
arg max
X
2V
X
t 2TV
X
ct 2Nt ( )
logp(ct | ; ) (2)
where Nt ( ) denotes ’s neighborhood with the tth type of nodes
and p(ct | ; ) is commonly dened as a somax function [3, 7, 18,
KDD’17, August 13–17, 2017, Halifax, NS, Canada
different types neighbors in given typeYuxiao Dong, Nitesh V. Chawla, Ananthram Swami:
metapath2vec: Scalable Representation Learning for
Heterogeneous Networks. KDD 2017: 135-144
metapath carries semantics

RecSys'19 SMORe

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