Personalized Recommendation with Implicit Feedback via Learning - - PowerPoint PPT Presentation

Personalized Recommendation with Implicit Feedback via Learning Pairwise Preferences over Item-sets

Weike Pan1,2, Li Chen2∗ and Zhong Ming1∗

panweike@szu.edu.cn, lichen@comp.hkbu.edu.hk, mingz@szu.edu.cn 1College of Computer Science and Software Engineering

Shenzhen University, Shenzhen, China

2Department of Computer Science

Hong Kong Baptist University, Hong Kong, China This work is an extension of our previous work [Pan and Chen, 2013].

Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 1 / 34

Introduction

Problem Definition

Personalized Recommendation with Implicit Feedback Input: Observed feedback Rtr = {(u, i)} from n users and m items. Goal: Generate a personalized ranking list of items for each user u from the whole set of unobserved items Itr\Itr

u .

Notice that this problem is also called one-class collaborative filtering (OCCF) or collaborative filtering with implicit feedback.

Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 2 / 34

Introduction

Challenges/Limitations

For pointwise preference on an item:

Finding a good weighting strategy for each observed feedback is a very difficult task in real applications, since we usually have implicit feedback only. Treating all observed feedback as “like” and unobserved feedback as “dislike” may mislead the learning process.

For pairwise preferences over two items:

The pairwise assumption may not hold for each item pair.

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Introduction

Overall of Our Solution

Pairwise preferences over item-sets: a new and relaxed assumption that a user is likely to prefer a set of observed items to a set of unobserved items.

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Introduction

Advantage of Our Solution

Pairwise preferences over item-sets is likely to be more accurate and the corresponding pairwise relationship is more likely to be valid.

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Introduction

Notations (1/2)

Notation Description n number of users m number of items Utr = {u}n

u=1

training set of users Utr

i

training set of users w.r.t. item i Ute ⊆ Utr test set of users Itr = {i}m

i=1

training set of items Itr

u

training set of items w.r.t. user u Ite

u

test set of items w.r.t. user u P ⊆ Itr

u

set of items (presence of observation) A ⊆ Itr\Itr

u

set of items (absence of observation)

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Introduction

Notations (2/2)

u ∈ Utr user index i, j ∈ Itr item index Rtr = {(u, i)} training data Rte = {(u, i)} test data ˆ rui preference of user u on item i ˆ ruj preference of user u on item j ˆ ruP preference of user u on item-set P ˆ ruA preference of user u on item-set A ˆ ruij,ˆ ruiA,ˆ ruPA,ˆ ruPj pairwise preferences of user u Θ set of model parameters d number of latent dimensions Uu· ∈ R1×d user u’s latent feature vector Vi· ∈ R1×d item i’s latent feature vector bi ∈ R item i’s bias

Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 7 / 34

Method

Preference Assumption on Item-sets (1/2)

A user u’s preference on an item-set (a set of items) is defined as a function of user u’s preferences on items in the item-set. For example, a user u’s preference on an item-set P can be ˆ ruP =

i∈P ˆ

rui/|P|, or in

• ther forms.

A user u’s pairwise preferences over two item-sets is defined as the difference between user u’s preferences on two item-sets. For example, a user u’s pairwise preferences over item-sets P and A can be ˆ ruPA = ˆ ruP − ˆ ruA, or ˆ ruPA = ˆ ruP − ˆ ruj, j ∈ A, or in other forms.

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Method

Preference Assumption on Item-sets (2/2)

With the aforementioned two definitions, we further relax the assumption of pairwise preferences over items as made in [Rendle et al., 2009] and propose a new assumption called pairwise preferences over item-sets, represented in the following four forms, Set vs. Set (SS) : ˆ ruP > ˆ ruA, (1) Many “One vs. One” (MOO) : ˆ rui > ˆ ruj, i ∈ P, j ∈ A, (2) Many “One vs. Set” (MOS) : ˆ rui > ˆ ruA, i ∈ P, (3) Many “Set vs. One” (MSO) : ˆ ruP > ˆ ruj, j ∈ A, (4)

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Method

Optimization Problems

Assuming that a user u is likely to prefer an item-set P to an item-set A, we may introduce the aforementioned constraints in Eqs.(1-4). For a pair of item-sets P and A, we can have the following optimization problems, SS : min

Θu

R(u, P, A), s.t. ˆ ruP > ˆ ruA, (5) MOO : min

Θu

R(u, P, A), s.t. ˆ rui > ˆ ruj, i ∈ P, j ∈ A, (6) MOS : min

Θu

R(u, P, A), s.t. ˆ rui > ˆ ruA, i ∈ P, (7) MSO : min

Θu

R(u, P, A), s.t. ˆ ruP > ˆ ruj, j ∈ A, (8) where ˆ rui = bi + Uu·V T

i· is the predicted preference of user u on item i,

Θu = {Uu·, Vi·, bi, i ∈ Itr}, and R(u, P, A) is an L2 regularization term used to avoid overfitting during parameter learning [Koren, 2010].

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Method

Objective Functions (1/2)

We relax the constraints in Eqs.(1-4) and introduce a loss function in the objective function, min

Θu

L(u, P, A) + R(u, P, A), (9) where L(u, P, A) is the loss function w.r.t. user u’s preferences on item-sets P and A. For each user u, we have the following optimization problem, min

Θu

• P⊆Itr

u

• A⊆Itr\Itr

u

L(u, P, A) + R(u, P, A), (10) where P is a subset of items randomly sampled from Itr

u that denotes

a set of items with observed feedback from user u, and A is a subset

• f items randomly sampled from Itr\Itr

u that denotes a set of items

without observed feedback from user u.

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Method

Objective Functions (2/2)

Finally, we put all users together and reach the following optimization problem, min

Θ

• u∈Utr
• P⊆Itr

u

• A⊆Itr\Itr

u

L(u, P, A) + R(u, P, A), (11) where Θ = {Uu·, Vi·, bi, u ∈ Utr, i ∈ Itr} denotes the parameters to be

• learned. The loss function L(u, P, A) is defined on the user u’s

pairwise preferences over item-sets. The regularization term R(u, L, A) =

αu 2 Uu·2 + i∈P[αv 2 Vi·2 + βv 2 bi2] + j∈A[αv 2 Vj·2 + βv 2 bj2] is

used to avoid overfitting during parameter learning [Koren, 2010], where αu, αv, βv are hyper-parameters.

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Method

Loss Function

In order to directly compare our pairwise preferences over item-sets assumption with pairwise preferences over items as made in BPRMF [Rendle et al., 2009], we study four specific loss functions, SS : L(u, P, A) = − ln σ(ˆ ruPA), (12) MOO : L(u, P, A) = − 1 |P| 1 |A|

• i∈P
• j∈A

ln σ(ˆ ruij), (13) MOS : L(u, P, A) = − 1 |P|

• i∈P

ln σ(ˆ ruiA), (14) MSO : L(u, P, A) = − 1 |A|

• j∈A

ln σ(ˆ ruPj), (15) where ˆ ruPA = ˆ ruP − ˆ ruA, ˆ ruij = ˆ rui − ˆ ruj, ˆ ruiA = ˆ rui − ˆ ruA, ˆ ruPj = ˆ ruP − ˆ ruj, ˆ ruP =

i∈P ˆ

rui/|P|, ˆ ruA =

j∈A ˆ

ruj/|A|, and σ(x) =

1 1+exp(−x) is the

sigmoid function.

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Method

The Gradients in CoFiSet(SS)

For each (u, P, A) triple, we have ∇Uu· = ∂L(u, P, A) ∂ˆ ruPA ( ¯ VP· − ¯ VA·) + αuUu·, (16) ∇Vi· = ∂L(u, P, A) ∂ˆ ruPA Uu· |P| + αvVi·, i ∈ P, (17) ∇Vj· = ∂L(u, P, A) ∂ˆ ruPA −Uu· |A| + αvVj·, j ∈ A, (18) ∇bi = ∂L(u, P, A) ∂ˆ ruPA 1 |P| + βvbi, i ∈ P, (19) ∇bj = ∂L(u, P, A) ∂ˆ ruPA −1 |A| + βvbj, j ∈ A, (20) where ∂L(u,P,A)

∂ˆ ruPA

= ∂−ln σ(ˆ

ruPA) ∂ˆ ruPA

= −σ(−ˆ ruPA), ¯ VP· =

i∈P Vj·/|P|, and

¯ VA· =

j∈A Vj·/|A|.

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Method

The Gradients in CoFiSet(MOO)

For each (u, P, A) triple, we have ∇Uu· =

• i∈P
• j∈A

∂L(u, P, A) ∂ˆ ruij (Vi· − Vj·) + αuUu·, (21) ∇Vi· =

• j∈A

∂L(u, P, A) ∂ˆ ruij Uu· + αvVi·, i ∈ P, (22) ∇Vj· =

• i∈P

∂L(u, P, A) ∂ˆ ruij (−Uu·) + αvVj·, j ∈ A, (23) ∇bi =

• j∈A

∂L(u, P, A) ∂ˆ ruij 1 + βvbi, i ∈ P, (24) ∇bj =

• i∈P

∂L(u, P, A) ∂ˆ ruij (−1) + βvbj, j ∈ A, (25) where ∂L(u,P,A)

∂ˆ ruij

= − 1

|P| 1 |A|σ(−ˆ

ruij).

Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 15 / 34

Method

The Gradients in CoFiSet(MOS)

For each (u, P, A) triple, we have ∇Uu· =

• i∈P

∂L(u, P, A) ∂ˆ ruiA (Vi· − ¯ VA·) + αuUu·, (26) ∇Vi· = ∂L(u, P, A) ∂ˆ ruiA Uu· + αvVi·, i ∈ P, (27) ∇Vj· =

• i∈P

∂L(u, P, A) ∂ˆ ruiA −Uu· |A| + αvVj·, j ∈ A, (28) ∇bi = ∂L(u, P, A) ∂ˆ ruiA 1 + βvbi, i ∈ P, (29) ∇bj =

• i∈P

∂L(u, P, A) ∂ˆ ruiA −1 |A| + βvbj, j ∈ A, (30) where ∂L(u,P,A)

∂ˆ ruiA

= − 1

|P|σ(−ˆ

ruiA), and ¯ VA· =

j∈A Vj·/|A|.

Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 16 / 34

Method

The Gradients in CoFiSet(MSO)

For each (u, P, A) triple, we have ∇Uu· =

• j∈A

∂L(u, P, A) ∂ˆ ruPj ( ¯ VP· − Vj·) + αuUu·, (31) ∇Vi· =

• j∈A

∂L(u, P, A) ∂ˆ ruPj Uu· |P| + αvVi·, i ∈ P, (32) ∇Vj· = ∂L(u, P, A) ∂ˆ ruPj (−Uu·) + αvVj·, j ∈ A, (33) ∇bi =

• j∈A

∂L(u, P, A) ∂ˆ ruPj 1 |P| + βvbi, i ∈ P, (34) ∇bj = ∂L(u, P, A) ∂ˆ ruPj (−1) + βvbj, j ∈ A, (35) where ∂L(u,P,A)

∂ˆ ruPj

= − 1

|A|σ(−ˆ

ruPj), and ¯ VP· =

i∈P Vi·/|P|.

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Method

Update Rules

For each (u, P, A) triple, we have Uu· = Uu· − γ∇Uu· (36) Vi· = Vi· − γ∇Vi·, i ∈ P, (37) Vj· = Vj· − γ∇Vj·, j ∈ A, (38) bi = bi − γ∇bi, i ∈ P, (39) bj = bj − γ∇bj, j ∈ A, (40) where γ > 0 is the learning rate.

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Method

Learning the CoFiSet

Input: Rtr = {(u, i)} . Output: Θ = {Uu·, Vi·, bi·, u ∈ Utr, i ∈ Itr}. Initialization: Uuf , Vif , bi.

1: for t1 = 1, . . . , T do 2:

for t2 = 1, . . . , n do

3:

Randomly pick a user u ∈ Utr. // user-wise sampling

4:

Randomly pick an item-set P ⊆ Itr

u .

5:

Randomly pick an item-set A ⊆ Itr\Itr

u .

6:

Calculate euPA, euij, euiA and euPj for SS, MOO, MOS and MSO, respectively.

7:

Update Uu· via Eq.(36).

8:

Update Vi·, i ∈ P via Eq.(37) and the latest Uu·.

9:

Update Vj·, j ∈ A via Eq.(38) and the latest Uu·.

10:

Update bi, i ∈ P via Eq.(39).

11:

Update bj, j ∈ A via Eq.(40).

12:

end for

13: end for 14: return Θ.

Figure 1: The Algorithm of CoFiSet.

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Method

Complexity Analysis

For the time complexity of the four variants of our CoFiSet: CoFiSet(SS) : O(Tnd max(|P|, |A|)), CoFiSet(MOO) : O(Tnd|A||P|), CoFiSet(MOS) : O(Tnd|A||P|), CoFiSet(MSO) : O(Tnd|A||P|), where d is the number of latent features, T is the number of iterations and n is the number of users. For the memory requirement of CoFiSet and BPRMF, they are the same.

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Experiments

Datasets

We have 575281 observations from 6040 users and 3952 items in MovieLens1M, 155872 observations from 5000 users and 5000 items in Netflix, and 78294 observations from 5000 users and 5000 items in XING. The densities are 575281/6040/3952 = 2.41%, 155872/5000/5000 = 0.62% and 78294/5000/5000 = 0.31% for MovieLens1M, Netflix and XING, respectively. In our experiments, we randomly take 50% observed feedback as training data and the rest 50% as test data. We repeat this for 30 times to generate 30 copies of training data and test data, and report the average performance on those 30 copies of data. Note that we construct a validation data from training data via sampling

• ne (user, item) pair per user, which is used for parameter

searching.

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Experiments

Baselines

PopRank (popularity-based ranking) ARM (association rule mining) BPR (Bayesian personalized ranking) PMF (probabilistic matrix factorization)

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Experiments

Evaluation Metrics

Precision@5 Recall@5 F1@5 NDCG@5 1-call@5

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Experiments

Initialization

For fair comparison, we implement BPRMF and CoFiSet in the same code framework written in Java, and use the same initializations for the model variables [Pan et al., 2012], Uuf = (r − 0.5) × 0.01, f = 1, . . . , d, (41) Vif = (r − 0.5) × 0.01, f = 1, . . . , d, (42) bi =

• u∈Utr

i

1/n −

• (u,i)∈Rtr

1/n/m, (43) where r (0 ≤ r < 1) is a random value. The order of updating the variables in each iteration is also the same as that shown in Figure 1. Note that we can use the initialization of item bias, bi, to rank the items, which is actually PopRank [Shi et al., 2012].

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Experiments

Parameter Configurations

For the tradeoff parameters in all methods, we search the best values from αu = αv = βv ∈ {0.001, 0.01, 0.1} using the performance on NDCG@5 of the validation data of the first copy of each data, and then fix them in the rest 29 copies of each data. For the iteration number, we fix T = 105 in CoFiSet and BPRMF for sufficient training, and search it from T ∈ {100, 500, 1000} in PMF. For the number of latent features, we use d = 20 [Pan and Chen, 2013]. The learning rate is fixed as γ = 0.01 similar to that

• f [Koren, 2008].

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Experiments

Parameter Configurations (2/2)

For ARM, we include all possible rules. That is, we set the threshold of confidence as 0 and the threshold of the number of common users (i.e., support) as 1, because of the sparsity of the data. For PMF, we take the value of observed feedback as 1s and randomly sample 3|Itr| unobserved feedback as 0s in each iteration, and then apply the commonly used stochastic gradient descent algorithm to learn the model parameters. For CoFiSet, we first fix |P| = |A| = 3, and then try different values in {1, 2, 3, 4, 5}. In the case that there are not enough

• bserved feedback in Itr

u , we use P = Itr u .

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Experiments

Main Results (1/3)

Table 1: Recommendation performance of four variants of our CoFiSet and

• ther algorithms on MovieLens1M. The significantly best results in

comparison with the four baselines are marked in bold (p-value < 0.01).

Algorithm Trad. Pre@5 Rec@5 F1@5 NDCG@5 1-call@5 para. PopRank 0.2809±0.0023 0.0406±0.0006 0.0633±0.0008 0.2916±0.0021 0.6691±0.0061 ARM 0.3571±0.0054 0.0551±0.0010 0.0855±0.0015 0.3756±0.0069 0.7593±0.0065 PMF 0.01 0.4177±0.0035 0.0716±0.0010 0.1096±0.0014 0.4302±0.0034 0.8461±0.0036 BPRMF 0.01 0.4410±0.0025 0.0753±0.0007 0.1146±0.0010 0.4544±0.0028 0.8539±0.0042 CoFiSet(SS) 0.001 0.4466±0.0021 0.0756±0.0006 0.1154±0.0008 0.4624±0.0023 0.8537±0.0041 CoFiSet(MOO) 0.01 0.4562±0.0026 0.0782±0.0009 0.1190±0.0011 0.4707±0.0029 0.8636±0.0043 CoFiSet(MOS) 0.01 0.4114±0.0031 0.0675±0.0009 0.1036±0.0012 0.4257±0.0035 0.8237±0.0043 CoFiSet(MSO) 0.01 0.4789±0.0023 0.0830±0.0007 0.1261±0.0009 0.4977±0.0021 0.8810±0.0035 Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 27 / 34

Experiments

Main Results (2/3)

Table 2: Recommendation performance of four variants of our CoFiSet and

• ther algorithms on Netflix. The significantly best results in comparison with

the four baselines are marked in bold (p-value < 0.01).

Algorithm Trade Pre@5 Rec@5 F1@5 NDCG@5 1-call@5 para. PopRank 0.1703±0.0018 0.0562±0.0013 0.0679±0.0010 0.1779±0.0017 0.4455±0.0065 ARM 0.2004±0.0030 0.0738±0.0035 0.0853±0.0024 0.2171±0.0040 0.5161±0.0101 PMF 0.01 0.1960±0.0029 0.0930±0.0031 0.0985±0.0023 0.2123±0.0041 0.5566±0.0072 BPRMF 0.01 0.2347±0.0026 0.1033±0.0035 0.1107±0.0024 0.2570±0.0034 0.5857±0.0078 CoFiSet(SS) 0.001 0.2231±0.0037 0.0931±0.0037 0.1016±0.0028 0.2424±0.0049 0.5619±0.0090 CoFiSet(MOO) 0.01 0.2423±0.0022 0.1058±0.0033 0.1138±0.0023 0.2649±0.0031 0.5963±0.0075 CoFiSet(MOS) 0.001 0.1839±0.0035 0.0843±0.0027 0.0889±0.0022 0.1997±0.0046 0.5158±0.0068 CoFiSet(MSO) 0.01 0.2571±0.0024 0.1107±0.0039 0.1200±0.0027 0.2829±0.0040 0.6141±0.0088 Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 28 / 34

Experiments

Main Results (3/3)

Table 3: Recommendation performance of four variants of our CoFiSet and

• ther algorithms on XING. The significantly best results in comparison with

the four baselines are marked in bold (p-value < 0.01).

Algorithm Trad. Pre@5 Rec@5 F1@5 NDCG@5 1-call@5 para. PopRank 0.0253±0.0010 0.0123±0.0009 0.0138±0.0009 0.0282±0.0011 0.1094±0.0049 ARM 0.0767±0.0018 0.0337±0.0015 0.0379±0.0012 0.0842±0.0023 0.2339±0.0057 PMF 0.01 0.0673±0.0017 0.0299±0.0017 0.0334±0.0013 0.0723±0.0022 0.2130±0.0051 BPRMF 0.1 0.0796±0.0018 0.0393±0.0016 0.0422±0.0013 0.0879±0.0022 0.2549±0.0062 CoFiSet(SS) 0.01 0.0787±0.0014 0.0378±0.0016 0.0411±0.0010 0.0868±0.0019 0.2494±0.0047 CoFiSet(MOO) 0.1 0.0623±0.0030 0.0309±0.0013 0.0326±0.0011 0.0686±0.0028 0.2078±0.0047 CoFiSet(MOS) 0.01 0.0746±0.0017 0.0358±0.0018 0.0387±0.0013 0.0815±0.0022 0.2369±0.0056 CoFiSet(MSO) 0.01 0.0828±0.0020 0.0396±0.0017 0.0432±0.0015 0.0910±0.0026 0.2578±0.0060 Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 29 / 34

Experiments

Observations

For two of the three data sets, i.e., MovieLens1M and Netflix, our CoFiSet(MSO) achieves significantly better recommendation performance than all the four baselines regarding all the evaluation metrics; for XING, our CoFiSet(MOS) performs consistently better than the baselines. The result demonstrates the superior recommendation ability of CoFiSet(MSO), especially

• n the two relatively dense data sets MovieLens1M and Netflix.

Among the four variants of our CoFiSet, the overall performance

• rdering is CoFiSet(MSO) > CoFiSet(MOO), CoFiSet(SS) >

CoFiSet(MOS), which shows the effectiveness of different pairwise comparisons. . . .

Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 30 / 34

Related Work

Collaborative Recommendation

Preference type/assumption Algorithm Self-comp. i v.s. i′

• ne vs. one

CLiMF [Shi et al., 2012] Batch Pointwise i: like, j: dislike w/o competition iMF [Hu et al., 2008] Batch OCCF [Pan et al., 2008] Batch SLIM [Ning and Karypis, 2011] Batch FISMrmse [Kabbur et al., 2013] SGD i: like, j: learned ZaOV [Sindhwani et al., 2009] Batch Pairwise i − j = c

• ne vs. one

RankALS [Tak´ acs and Tikk, 2012] Batch SVD(ranking) [Jahrer and Toscher, 2011] SGD FISMauc [Kabbur et al., 2013] SGD i ≻ j

• ne vs. one

BPRMF [Rendle et al., 2009] SGD PLMF [Hong et al., 2012] SGD i ≻ j, j ∈ A many “one vs. one” CCF(SoftMax) [Yang et al., 2011] SGD i ≻ A

• ne vs. set

CCF(Hinge) [Yang et al., 2011] SGD P ≻ A set vs. set CoFiSet(SS) [Pan and Chen, 2013] SGD i ≻ j, i ∈ P, j ∈ A many “one vs. one” CoFiSet(MOO) SGD i ≻ A, i ∈ P many “one vs. set” CoFiSet(MOS) SGD P ≻ j, j ∈ A many “set vs. one” CoFiSet(MSO) SGD Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 31 / 34

Conclusions

Conclusions

We propose a novel algorithm, i.e., CoFiSet, for solving personalized recommendation with implicit feedback. Specifically, we propose a new assumption, pairwise preferences over item-sets, which is more relaxed than pairwise preferences over items [Rendle et al., 2009]. With this assumption, we develop a general algorithm with four variants, CoFiSet(SS), CoFiSet(MOO), CoFiSet(MOS) and CoFiSet(MSO). We study CoFiSet on three real-world data sets using five ranking-oriented evaluation metrics, and observe that CoFiSet(MSO) generates better recommendation results than the state-of-the-art methods.

Pan, Chen and Ming (SZU & HKBU) CoFiSet KAIS 2019 32 / 34

Conclusions

Future Work

We plan to study item-set selection strategies via incorporating the taxonomy information [Koenigstein et al., 2011] or the cluster structure [Zhu et al., 2016] because items’ relationships can help refine the item-set construction procedure. We plan to study different forms (e.g., maximum, minimum, medium and weighted linear combination) of users’ aggregated preferences on item-sets, and embed them in more preference handling algorithms such as factorization methods with learned similarities [Kabbur et al., 2013, Ning and Karypis, 2011].

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Thank you

Thank you!

We thank the support of Hong Kong RGC under the project RGC/HKBU12200415, Natural Science Foundation of China Nos. 61272365, 61502307 and 61672358.

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