Matrix Factorizations for Recommender Systems on Implicit Data

Matrix Factorizations for
Recommender Systems on Implicit
Data
Li-Yen Kuo and Ming-Syan Chen
National Taiwan University.

郭立言 Kuo, Li-Yen
NetDB, EE Dept, National Taiwan University
Python, JuliaLang, Matlab
Unsupervised Learning, Recommender Systems,
Bayesian Graphs, GANs, Adversarial Training

5
The Internet changes business model and user behaviors.
Clayton Christensen, a Harvard professor, said that Blockbuster’s ignorance and
laziness was its own undoing. Netflix began serving a ‘niche market’ and slowly
began to take over Blockbuster’s entire market [1].
THE INTERNET CHANGES OUR LIFE
[1] https://medium.com/@ScAshwin/the-rise-of-netflix-and-the-fall-of- 3blockbuster-29e5457339b7
Source: https://www.dailymail.co.uk/sciencetech/article-
5301869/Website-Flixable-makes-easier-browse-Netflix.html
Source: https://techcrunch.com/2018/07/13/theres-now-just-
one-blockbuster-remaining-in-the-u-s/

6
Recommender systems are widely used in many popular commercial on-line systems.
HOW TO PROVIDE RECOMMENDATION?
Editorial Systems
hand-curated
Global RecSys
simple statistics popularity
Personalized RecSys
tailored to Individuals, e.g., Amazon and Netflix

7
小編很辛苦...QQ
Editorial Systems
hand-curated
Global RecSys
Personalized RecSys

8
Editorial Systems
hand-curated
Global RecSys
Personalized RecSys
Popular / latest items may attract most of people.
But NOT EVERYONE! (80/20 rule)

9
Editorial Systems
hand-curated
Global RecSys
Personalized RecSys
It can explore the tastes of the rest 20%. But it difficult.

10
Over 75% of what people watch comes from a recommendation.
EVERYTHING IS PERSONALIZED
Ranking
Row: category

11
Ariana Grande
Lady Gaga
Coldplay
Miles Davis
User 1
User 2
User 3
User 4
Item 1
Item 2
Item 3
Item 4
L. Beethoven
Item 5
Item 1 Item 2 Item 3 Item 4 Item 5
User 1
User 2
User 3
User 4
User-item relationship can be represented by a utility matrix.
The meaning of an entry depends on the scenario.
DEFINITION OF UTILITY MATRIX

12TWO TYPES OF UTILITY MATRIX
utility matrix
explicit
implicit
binary
count
rating

13
In rating systems, such as MovieLens [1] and Allmusic [2], the value of an entry
denotes the rating of the item given by the user.
UTILITY MATRIX ON EXPLICIT RATINGS
Ariana Grande
Lady Gaga
Coldplay
Miles Davis
User 1
User 2
User 3
User 4
Item 1
Item 2
Item 3
Item 4
L. Beethoven
Item 5
3
4
5
4
3
4
1
3
5
User 1 3 4 ? ? ?
User 2 ? 5 4 ? 3
User 3 ? ? 4 1 ?
User 4 ? ? ? 3 5
[1] https://movielens.org/
[2] https://www.allmusic.com/

14
Considering personal offset is important. Ratings can explicitly reflect the preference of
an individual.
Users always give ratings on what they are familiar with.
UTILITY MATRIX ON EXPLICIT RATINGS
Ariana Grande
Lady Gaga
Coldplay
Miles Davis
User 1
User 2
User 3
User 4
Item 1
Item 2
Item 3
Item 4
L. Beethoven
Item 5
3
4
5
4
3
4
1
3
5
User 1 3 4 ? ? ?
User 2 ? 5 4 ? 3
User 3 ? ? 4 1 ?
User 4 ? ? ? 3 5
[1] https://movielens.org/
[2] https://www.allmusic.com/

15
Ariana Grande
Lady Gaga
Coldplay
Miles Davis
User 1
User 2
User 3
User 4
Item 1
Item 2
Item 3
Item 4
L. Beethoven
Item 5
User 1 1 1 ? ? ?
User 2 ? 1 1 ? 1
User 3 ? ? 1 1 ?
User 4 ? ? ? 1 1
For instance, in a music podcast service, the value of an entry may denote the
subscription.
UTILITY MATRIX ON IMPLICIT BINARY DATA

16UTILITY MATRIX ON IMPLICIT COUNT DATA
Ariana Grande
Lady Gaga
Coldplay
Miles Davis
User 1
User 2
User 3
User 4
Item 1
Item 2
Item 3
Item 4
L. Beethoven
Item 5
User 1 120 242 ? ? ?
User 2 ? 33 17 ? 10
User 3 ? ? 5116 72 ?
User 4 ? ? ? 6 3942
Or it may denote the play count.
120
242
33
17
10
5116
72
6
3942

17EXPLICIT OR IMPLICIT?
Lady Gaga
Coldplay
User 2
Item 2
Item 3
L. Beethoven
Item 5
Explicit Feedback
Has negative feedback.
Neglect noise.
Reflect preference.
5
4
3
Lady Gaga
Coldplay
User 2
Item 2
Item 3
L. Beethoven
Item 5
33
17
10
543
neutral
desirableundesirable
Implicit Feedback
No negative feedback.
Comes with noise.
Reflect confidence rather than preference.
0
positive & incremental

18GOAL OF RECSYS
Ariana Grande
Lady Gaga
Coldplay
Miles Davis
User 1
User 2
User 3
User 4
Item 1
Item 2
Item 3
Item 4
L. Beethoven
Item 5
User 1 120 242 0 0 0
User 2 0 33 17 0 10
User 3 0 0 5116 72 ?
User 4 0 0 0 6 3942
A principal goal in recommender systems is to retrieve unconsumed items that the
target user would likely consume in the future.

20MATRIX FACTORIZATION FOR RECSYS
The most well-known method for recommendation is matrix factorization (MF).
MF is a class of collaborative filtering (CF) algorithms.
Rec
Sys CF MF

21
Why do we need MF? Let’s see an example below.
Ariana Grande
Lady Gaga
Sheeran Ed
Coldplay
User 1
User 2
User 3
User 4
Item 1
Item 2
Item 3
Item 4
Linkin Park
Item 5
The 1975
Item 6
MATRIX FACTORIZATION FOR RECSYS
Item 1 Item 2 Item 3 Item 4 Item 5 Item 6
User 1
User 2
User 3
User 4

22
Rock
Pop Music
The fact that similar users consume similar items can be represented by a latent
factor.
Ariana Grande
Lady Gaga
Sheeran Ed
Coldplay
User 1
User 2
User 3
User 4
Item 1
Item 2
Item 3
Item 4
Linkin Park
Item 5
The 1975
Item 6
User 1
User 2
User 3
User 4

23
Rock
Pop Music
A user would likely consume an item involving the same latent factor with her.
Ariana Grande
Lady Gaga
Sheeran Ed
Coldplay
User 1
User 2
User 3
User 4
Item 1
Item 2
Item 3
Item 4
Linkin Park
Item 5
The 1975
Item 6
User 1
User 2
User 3
User 4

24
When using two low-rank matrices 𝜽 and 𝜷 to regenerate utility matrix 𝐗, the
optimizer will preserve the information embedded in 𝐗 as much as possible.
Hence, MF factorizes a utility matrix to acquire latent factors.
≈ ×
𝐗 𝜽
𝜷

25
≈ ×
𝐗 𝜽
𝜷
𝑥'' ≈ 𝜽'
(
𝜷' ⇒ 𝑝 𝑥'' 𝜽'
(
𝜷'

26
≈ ×
𝐗 𝜽
𝜷
𝑥'+ ≈ 𝜽'
(
𝜷+ ⇒ 𝑝 𝑥'+ 𝜽'
(
𝜷+

27
≈ ×
𝐗 𝜽
𝜷
𝑥+' ≈ 𝜽+
(
𝜷' ⇒ 𝑝 𝑥+' 𝜽+
(
𝜷'

28
≈ ×
𝐗 𝜽
𝜷
∀ 𝑢, 𝑖 , 𝑥01 ≈ 𝜽0
(
𝜷1 ⇒ 2 𝑝 𝑥01 𝜽0
(
𝜷1
0,1
⇒ 4 log 𝑝 𝑥01 𝜽0
(
𝜷1
0,1

User 1
User 2
User 3
User 4
Item
1
Item
2
Item
3
Item
4
Item
5
Item
6
× =
User 1
User 2
User 3
User 4
User 1
User 2
User 3
User 4
represent
approximate
Rock
Pop Music
Ariana Grande
Lady Gaga
Sheeran Ed
Coldplay
User 1
User 2
User 3
User 4
Item 1
Item 2
Item 3
Item 4
Linkin Park
Item 5
The 1975
Item 6

32
MFUnsupervisedSupervised
MODELING IMPLICIT COUNT DATA
A machine learning method can somehow represented by the 3-tiers structure.
Objective
function
Model
Data
𝑝 𝑦 𝑓 𝑥
𝑓 ;
𝑥, 𝑦
𝑝 𝑥 𝑓
𝑓
𝑥
𝑝 𝑋 𝜽𝜷(
𝜽𝜷(
𝑋
LTR
𝑝 ≻ 𝑓 𝑖, 𝑗
𝑖 ≻ 𝑗
𝑓 ;

33MODELING IMPLICIT COUNT DATA
Unlike ratings, user preference is extracted implicitly from these count data.
Accordingly, we have 4 assumptions as the prior knowledge.
Based on some of these assumptions, various objectives are proposed.
1 Most of unconsumed items are undesirable for a target user.
2 Items consumed frequently are more desirable than those which
consumed occasionally.
3 The value of an entry is assumed to be over a Poisson.
4 The value of an entry is assumed to be over a negative binomial.
5 Items are exposed to the target user before she/he consumes them.

Assumption 1.1
Assuming that most of unconsumed items are undesirable for a target user, we set
these unobserved entries to zero, namely, consuming 0 times.
User 1 120 242 0 0 0
User 2 0 33 17 0 10
User 3 0 0 5116 72 0
User 4 0 0 0 6 3942
User 1 120 242 ? ? ?
User 2 ? 33 17 ? 10
User 3 ? ? 5116 72 ?
User 4 ? ? ? 6 3942

Assumption 1.2
Assuming that most of unconsumed items are undesirable for a target user, we rank
consumed items higher than unconsumed ones.
User 1
{Item 1, Item 2} ≻ {Item 3, Item 4, Item 5}
User 2
{Item 2, Item 3, Item5} ≻ {Item 1, Item 4}
User 3
{Item 3, Item 4} ≻ {Item 1, Item 2, Item 5}
User 4
{Item 4, Item5} ≻ {Item 1, Item 2, Item 5}
User 1 120 242 ? ? ?
User 2 ? 33 17 ? 10
User 3 ? ? 5116 72 ?
User 4 ? ? ? 6 3942

36BAYESIAN PERSONALIZED RANKING (BPR)
By using assumption 1.2, in BPR (Rendel et al., 2009), the consumed-or-not problem
is considered as a pairwise learning to rank.
[Rendel et al.] Rendle, Steffen, et al. BPR: Bayesian personalized ranking from implicit feedback. AUAI Press, 2009.
Objective
function
Model
Data
MF or K-NN
𝑖 ≻0 𝑗

37
Model MF:
Objective
function
BAYESIAN PERSONALIZED RANKING (BPR)

Assumption 2
Items consumed frequently are more desirable than those which consumed occasionally.
This can lead to regression-based and LTR objective.
User 1
{Item 2} ≻ {Item 1}
User 2
{Item 2} ≻ {Item 3} ≻ {Item 5}
User 3
User 4
{Item5} ≻ {Item 4}
User 1 120 242 ? ? ?
User 2 ? 33 17 ? 10
User 3 ? ? 5116 122 ?
User 4 ? ? ? 6 3942

39
User 1 120 242 0 0 0
User 2 0 33 17 0 10
User 3 0 0 5116 122 0
User 4 0 0 0 6 3942
Assumption 3
Exploiting the nature of count data, one can assume the value of each entry to be over
a Poisson distribution independently.

40HIERARCHICAL POISSON FACTORIZATION (HPF)
HPF (Gopalan et al., 2015), where each entry is assumed to be a Poisson, is a
widely-used MF method for recommendation on implicit count data.
Objective
function
Model
Data
2 𝑝 𝑥01 𝜽0
?
𝜷1
0,1
, where 𝑝 𝑥01 𝜽0
?
𝜷1 ~Poi 𝑥01; 𝜽0
?
𝜷1
𝑋
MF with Gamma latent factors

41HIERARCHICAL POISSON FACTORIZATION (HPF)
HPF (Gopalan et al., 2015), where each entry is assumed to be a Poisson, is a
widely-used MF method for recommendation on implicit count data.

42
Since PF can down-weight the effect of zero entries and updates with the
computational cost linear to the number of nonzero entries, PF widely used for large
sparse utility matrices.
HIERARCHICAL POISSON FACTORIZATION (HPF)
log 0! = log 1 = 0

43PERSONALIZED RANKING ON PF (PRPF)
In PRPF (Kuo et al., 2018), a pairwise LTR model is proposed to permute consumed
items for each user according to assumption 2.
[Kuo et al., 2018] Kuo, Li-Yen, et al. Personalized Ranking on Poisson Factorization. In SDM, 2018.
Objective
function
Model
Data 𝑖 ≻0 𝑗
MF with Gamma latent factors
User 1
User 2
{Item 2} ≻ {Item 3} ≻ {Item 5}
User 3
User 4
{Item5} ≻ {Item 4}
User 1 120 242 ? ? ?
User 2 ? 33 17 ? 10
User 3 ? ? 5116 72 ?
User 4 ? ? ? 6 3942

44CHALLENGES OF IMPLICIT COUNT DATA
Challenge 1: data overdispersion
Real-life user consuming behaviors follow power-law distributions approximately.
Data are often overdispersed.

Some songs are played quite frequently since one may always listen to the songs by the artists
who she likes.
User 1 120 242 0 0 0
User 2 0 33 17 0 10
User 3 0 0 5116 122 0
User 4 0 0 0 6 3942

In fact, the problem can be addressed that the Poisson distribution cannot model the data
owning to its limited variance. As long as the variance the model assumes is larger than the
variance of data, the effect of outliers will be reduced.
0 5116
0 5116
0 5116

Challenge 2: failure exposure estimation
An outlier entry in a utility matrix can be explained that the user always plays the songs on
her/his own initiative, which means that almost no failure exposures might exist.
Accordingly, the number of failure exposures vary with users and items since user behaviors are
different.
Nevertheless, most previous works only consider successful events but omit failure exposure.
The failure exposure is hard to model and can merely be regarded as an implicit information
estimated from the relationship between observations and the corresponding model inference.
Ariana Grande
User 1 Item 1
120 Ariana Grande
User 1 Item 1
120
???
Success exposure count
Failure exposure count

48SCENARIO OF USER CONSUMPTION
Scenario
Success
exposure
Failure
exposure
Observed event (nonzero entry)
User 𝑢 plays 𝑖 on her/his own initiative. High Very Low
User 𝑢 is exposed to 𝑖 and 𝑢 plays 𝑖.
Medium/
Low
Medium/
Low
Unobserved event (zero entry)
User 𝑢 is exposed to 𝑖 and 𝑢 does not play 𝑖. 0
Medium/
Low
User 𝑢 has not been exposed to 𝑖 yet. 0 ?

49
User 1 120 242 0 0 0
User 2 0 33 17 0 10
User 3 0 0 5116 122 0
User 4 0 0 0 6 3942
Assumption 4
To alleviate the data dispersion problem, the value of each entry is assumed to be a
negative binomial distribution independently.

50NEGATIVE BINOMIAL OR POISSON?
Negative Binomial Poisson
Notation 𝑥01~NB 𝑟01,
𝜽0
( 𝜷1
𝑟01 + 𝜽0
( 𝜷1
𝑥01~Poi 𝜽0
( 𝜷1
Success Event Count 𝜽0
( 𝜷1 𝜽0
( 𝜷1
Failure Event Count 𝑟01 ∞
Expectation 𝜽0
( 𝜷1 𝜽0
( 𝜷1
Variance 𝜽0
( 𝜷1 1 +
𝜽0
( 𝜷1
𝑟01
𝜽0
( 𝜷1

51NEGATIVE BINOMIAL OR POISSON?
Negative Binomial Poisson
Notation 𝑥01~NB 𝑟01,
𝜽0
( 𝜷1
𝑟01 + 𝜽0
( 𝜷1
𝑥01~Poi 𝜽0
( 𝜷1
Success Event Count 𝜽0
( 𝜷1 𝜽0
( 𝜷1
Failure Event Count 𝑟01 ∞
Expectation 𝜽0
( 𝜷1 𝜽0
( 𝜷1
Variance 𝜽0
( 𝜷1 1 +
𝜽0
( 𝜷1
𝑟01
𝜽0
( 𝜷1

Assumption 5
Items are exposed to the target user before she/he consumes them.
Ariana Grande
User 1 Item 1
120
???
Ariana Grande
User 1 Item 1Exposure

53EXPOMF
In ExpoMF (Liang et al., 2016), a probabilistic approach directly incorporates user
exposure to items into collaborative filtering.
[Liang et al., 2016] Liang, Dawen, et al. Modeling User Exposure in Recommendation. In WWW, 2016.
Objective
function
Model
Data 𝑌
MF incorporating Bernoulli exposure

54EXPOMF
In ExpoMF (Liang et al., 2016), a probabilistic approach directly incorporates user
exposure to items into collaborative filtering.
[Liang et al., 2016] Liang, Dawen, et al. Modeling User Exposure in Recommendation. In WWW, 2016.

HIERARCHICAL NEGATIVE
BINOMIAL FACTORIZATION

56
PRELIMINARY:
NEGATIVE BINOMIAL DISTRIBUTION
As such, in NBF, entry 𝑥 𝑢𝑖 can be sampled from the generative process
Compared with Poisson distribution, where the mean equals the variance, NB is more
feasible to data with larger variance. The mean and the variance of NB in Eq. (1) are
Ariana Grande
User 1 Item 1
𝜽0
(
𝜷1
𝑟01
Success probability =
𝜽0
(
𝜷1
𝑟01 + 𝜽0
(
𝜷1

57
PRELIMINARY:
POISSON-GAMMA MIXTURE
The NB can also be viewed as a Poisson-gamma mixture (Lawless, 1987; Gardner et
al., 1995), which is defined as
where the latent variables 𝑑01 denotes the dispersion of variable 𝑥 𝑢𝑖.
𝑥01
𝑑01
𝑟01
𝜽0 𝜷1𝑥01
𝑟01
𝜽0 𝜷1
Poisson
Gamma
Equivalent
NB

58
PRELIMINARY:
Poisson-gamma mixture
Since the variance of 𝑑 𝑢𝑖 is 𝑟𝑢𝑖
−1
, the less 𝑟𝑢𝑖 can be, the larger the variance of 𝑑 𝑢𝑖 is.
When 𝑟01 is fixed as a constant, the variety of 𝑑01 is limited.
𝑥01
𝑑01
𝑟01
𝜽0 𝜷1
Poisson
Gamma

59
PROPOSED: HIERARCHICAL
Poisson-gamma mixture
Since the variance of 𝑑 𝑢𝑖 is 𝑟𝑢𝑖
−1
, the less 𝑟𝑢𝑖 can be, the larger the variance of 𝑑 𝑢𝑖 is.
When 𝑟01 is fixed as a constant, the variety of 𝑑01 is limited.
To tackle this, we let 𝑟01 be a gamma variable according to the conjugate prior
relationship.
𝑥01
𝑑01
𝑟01
𝜽0 𝜷1
Poisson
Gamma
𝑥01
𝑑01
𝜽0 𝜷1
Poisson
Gamma
𝑟01 Gamma
𝑔 ℎ

060
Hierarchical Negative
Binomial Factorization (HNBF)
! ∈ ℐ$ ∈ %
&' )'*+
,-
.'*
/'*
0'
1
2
/
3* 4*
5 ℎ

061
! ∈ ℐ$ ∈ %
&' )'*+
,-
.'*
/'*
0'
1
2
/
3* 4*
5 ℎ

062
! ∈ ℐ$ ∈ %
&' )'*+
,-
.'*
/'*
0'
1
2
/
3* 4*
5 ℎ

063
too slow!
! ∈ ℐ$ ∈ %
&' )'*+
,-
.'*
/'*
0'
1
2
/
3* 4*
5 ℎ

064
FastHNBF
(",$) ∈ '(
$ ∈ ℐ" ∈ *
+, .,/
0, 1/
2
3
ℎ5
ℎ6
7
8, 9/
:5
:6
;,/: ℎ
<,/
.,/
(",$) ∈ '=
>,
?<
@/ A/ B

065
FastHNBF
(",$) ∈ '(
$ ∈ ℐ" ∈ *
+, .,/
0, 1/
2
3
ℎ5
ℎ6
7
8, 9/
:5
:6
;,/: ℎ
<,/
.,/
(",$) ∈ '=
>,
?<
@/ A/ B

66UPDATING: VARIATIONAL INFERENCE
Since the variables are tangled, we use variational inference to optimize the posteriori.
Variational inference (VI) is a method for approximating posterior distributions, indexed by free
variational parameters, by maximizing the evidence lower bound (ELBO), a lower bound on
the logarithm of the marginal probability of the observations log 𝑝(𝑥). (Jordan et al., 1999;
Hoffman et al., 2013).

67UPDATING: VARIATIONAL INFERENCE
The simplest variational family of distributions is the mean field family, where each latent
variable is independent and governed by its own variational parameter. Thus, the traditional
coordinate ascent algorithm for fitting the variational parameters is used.
The variational family of the proposed framework is

69DATASETS AND COMPETING METHODS
HPF Hierarchical Poisson Factorization
(Gopalan et al., 2015)
PRPF Personalized Ranking on Poisson Factorization
(Kuo et al., 2018)
CCPF Coupled Compound Poisson Factorization
(Basbug & Engelhardt, 2017)
NBF Negative Binomial Factorization
(Gouvert et al., 2018)
BPR Bayesian Personalized Ranking
(Rendle et al., 2009)
ExpoMF Exposure Matrix Factorization
(Liang et al., 2016)

70CONVERGENCE
HPF converges fast since it does not consider data dispersion.
NBF converges slightly slower than HPF because of the augmented variables for data
dispersion.
Since HNBF comprises a Bayesian structures for data dispersion, the latent variables for
dispersion vary freely. Thus, HNBF converges slower than NBF. Even so, HNBF still converges
efficiently owing to the low updating cost per epoch.

71COMPUTING TIME
Since HPF only considers nonzero entries during the updating of latent variables, the updating
cost is the least. HNBF has augmented variables for estimating data dispersion, so that the
updating is slightly slower. Notice that HNBF runs much faster than NBF even though HNBF is
more sophisticated than NBF.

72RESULTS ON IMPLICIT COUNT DATA
Last.fm1K Prec@5 Prec@10 Rec@5 Rec@10
HPF
34.8% 32.2% 1.41% 2.54%
1.16% 0.74% 0.04% 0.07%
PRPF
44.1% 39.6% 1.79% 3.11%
1.2% 0.9% 0.1% 0.1%
CCPF-HPF
33.54% 30.91% 1.35% 2.41%
1.38% 0.84% 0.06% 0.05%
NBF
37.29% 34.08% 1.51% 2.71%
1.55% 0.93% 0.08% 0.08%
FastHNBF
47.9% 42.9% 1.81% 3.12%
0.50% 0.43% 0.03% 0.04%
BPR
31.3% 28.6% 1.21% 2.12%
1.42% 1.17% 0.04% 0.05%
ExpoMF
55.1% 50.3% 2.20% 3.87%
0.28% 0.18% 0.03% 0.04%

HPF
14.8% 11.7% 6.85% 10.72%
0.65% 0.41% 0.30% 0.37%
PRPF
19.9% 15.0% 9.24% 13.76%
0.45% 0.29% 0.20% 0.26%
CCPF-HPF
14.5% 11.5% 6.70% 10.60%
0.69% 0.45% 0.33% 0.44%
NBF
16.06% 12.42% 7.43% 11.45%
0.51% 0.23% 0.24% 0.21%
FastHNBF
20.8% 15.5% 9.63% 14.25%
0.34% 0.18% 0.17% 0.17%
BPR
19.5% 14.2% 9.04% 13.11%
1.42% 1.17% 0.04% 0.05%
ExpoMF
24.0% 17.7% 11.14% 16.20%
0.28% 0.18% 0.03% 0.04%

HPF
9.20% 7.58% 4.29% 7.05%
0.24% 0.17% 0.11% 0.16%
PRPF
9.77% 7.93% 4.52% 7.33%
0.17% 0.15% 0.11% 0.15%
CCPF-HPF
9.25% 7.64% 4.31% 7.11%
0.14% 0.10% 0.07% 0.09%
NBF
n/a n/a n/a n/a
n/a n/a n/a n/a
FastHNBF
10.08% 8.21% 4.70% 7.64%
0.15% 0.10% 0.07% 0.10%
BPR
n/a n/a n/a n/a
n/a n/a n/a n/a
ExpoMF
n/a n/a n/a n/a
n/a n/a n/a n/a

MovieLens100K Prec@5 Prec@10 Rec@5 Rec@10
HPF
40.14% 34.48% 12.28% 20.27%
0.78% 0.43% 0.39% 0.33%
PRPF
39.18% 33.24% 12.26% 19.67%
1.15% 1.26% 0.34% 0.64%
CCPF-HPF
39.91% 34.23% 12.00% 19.91%
0.58% 0.50% 0.30% 0.47%
NBF
40.31% 34.58% 12.24% 20.45%
0.51% 0.37% 0.21% 0.37%
FastHNBF
40.93% 34.84% 12.46% 20.41%
0.34% 0.26% 0.20% 0.28%
BPR
34.28% 29.45% 11.47% 18.81%
0.82% 0.67% 0.28% 0.46%
ExpoMF
44.05% 37.13% 14.02% 22.67%
0.15% 0.14% 0.05% 0.18%

MovieLens1M Prec@5 Prec@10 Rec@5 Rec@10
HPF
36.14% 31.43% 7.56% 12.64%
0.57% 0.42% 0.26% 0.38%
PRPF
35.56% 30.93% 7.35% 12.28%
0.43% 0.36% 0.17% 0.27%
CCPF-HPF
35.48% 30.98% 7.33% 12.35%
0.37% 0.34% 0.20% 0.33%
NBF
35.72% 31.04% 7.53% 12.60%
0.40% 0.35% 0.17% 0.24%
FastHNBF
36.19% 31.52% 7.58% 12.67%
0.20% 0.20% 0.08% 0.18%
BPR
26.85% 23.02% 5.86% 9.78%
0.47% 0.41% 0.13% 0.22%
ExpoMF
40.50% 35.13% 9.06% 14.90%
0.05% 0.05% 0.03% 0.03%

77EFFICIENT OR EFFECTIVE?
The methods for recommendation are categorized into two types: efficient models and effective
models. The two types of models should be concerned respectively.
0.21
0.34
0.97
5.54
0.30
44.04
0.1
1
10
100
HPF HNBF NBF PRPF CCPF ExpoMF
Time (Seconds)

78THE ARCHITECTURE OF RECSYS
ExpoMF
Source: https://medium.com/netflix-techblog/system-architectures-for-
personalization-and-recommendation-e081aa94b5d8
FastHNBF

THANK YOUhttps://github.com/iankuoli/Test_Julia

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