1

A Unified Framework for

Recommendations Based on

Quaternary Semantic Analysis

Wei Chen*, Wynne Hsu*, Mong Li Lee*

*School of Computing, National University of Singapore

Introduction

The amount of information on the web is increasing

at a lightning pace. E.g products in Amazon, videos

in Youtube, movies in Netflix

Recommendation is necessary.

Introduction

Recommendation systems are typically classified

according to four types :

User recommendation

Item recommendation

Tag recommendation

Item rating prediction

Related Work

Most of the work in recommendation systems utilize only ternary relationships in generating recommendations.

The collaborative filtering-based recommendation systems use <user ,rating, items >

[B. Sarwar,WWW’01,SIGIR’09]

Tag-based recommendation systems utilize the <users, tags, items >.

Motivation

We argue that recommendations based on ternary

relationships are not accurate as they would have

missed out important associations

Motivation Example

Motivation Example

Beautiful Mind and Groundhog day will be recommended to U3

Motivation example

Motivation example

Groundhog Day and Toy story will be recommended to

U3

Motivation example

Motivation example

Groundhog day is recommended to U3

Motivation

The need of quaternary relationship is necessary. This is reinforced by the following observations:

Users may use the same tag for an item but have different ratings for it.

Items may have multiple tags indicating their different facets.

Some tags may carry implicit semantics that can reveal the users’ preferences.

Overview of the paper

We propose a model: using tensor to model the

quaternary relationship.

Higher-Order Singular Value Decomposition

(HOSVD) is applied in the 4-order tensor to reveal

the latent semantic associations among users,

items, tags and ratings.

BACKGROUND - Tensor

A tensor is a multidimensional array. An N-order

tensor is denoted as

BACKGROUND – Tensor unfolding

The matrix unfolding of an N-order tensor

along the dimension i are vectors

obtained by keeping the index fixed while varying

the other indices.

BACKGROUND – n-mode product

BACKGROUND – HOSVD

HOSVD is a generalization of Singular Value

Decomposition (SVD) to higher-order tensors and

can be written as n-mode product

Where U(n) contain the orthonormal vectors (n-

mode singular vector) spanning the column space

of the A (n) , is the core tensor

BACKGROUND – HOSVD

BACKGROUND – HOSVD

With this, the core tensor can be

constructed as described in [L. D.,SIAM 2000], that is

and we can get:

BACKGROUND- Rank, Low Rank

Approximation

BACKGROUND

Suppose we want to get the RANK-(2,3,3)

approximation, we first retain the first ci column of

matrix U(i) at mode i as follows:

BACKGROUND –Tensor

Approximation

We can now construct the approximate core tensor

using

BACKGROUND

Finally, we obtain the RANK-(2,3,3) approximation

QUATENARY SEMANTIC

ANALYSIS

The main idea is to capture the underlying

relationships among users-tags-items-ratings by

reducing the rank of the original tensor to minimize

the effect of noise on the underlying population

and reduce spareness.

QUATENARY SEMANTIC

ANALYSIS - Initialization

Input: list of quadruples < users, tags, rating, items>;

QUATENARY SEMANTIC

ANALYSIS - Initialization

constructed tensor

where |U|, |T|, |R| and |V| is the number of user, tags , ratings

and items respectively

QUATENARY SEMANTIC

ANALYSIS

Calculate the matrix unfolding A(1) , A(2) , A(3) and

A(4) from Tensor

Perform SVD on each matrix unfolding and get the

left singular matrix U(1) , U(2) , U(3) and U(4)

QUATENARY SEMANTIC

ANALYSIS Remove the least significant rows |U|-c1; |V |-c2; |T|-c3

and |R|-c4 from U(1);U(2);U(3); and U(4), respectively. We

choose c1= 4; c2 =4; c3 = 4; c4 = 2.

QUATENARY SEMANTIC

ANALYSIS

Calculate the approximate core tensor

Approximate the original tensor by:

QUATENARY SEMANTIC

ANALYSIS

QUATENARY SEMANTIC

ANALYSIS

Latent associations such as the newly added

quadruples in Table 6 may not be found if the

tensor data is sparse

We overcome this problem by applying a

smoothing technique to the tensor in Algorithm.

RECOMMENDATION

GENERATION

RECOMMENDATION

GENERATION

RECOMMENDATION

GENERATION

RECOMMENDATION

GENERATION

Experimental result – dataset

description

Datasets: Movielens Data

The first file contains users’ tags on different movies. The second file contains users’ ratings on different movies on a scale of 1 to 5.

By joining these two files over user and movie, we obtain the quadruples < user; movie; tag; rating >.

After preprocessing, the dataset has 11122 tuples with 201 users, 501 movies, and 404 tags.

Experimental result – Item

Recommendation

Compare method:

UPCC: User based recommendation

IPCC: Item based recommendation

Probabilistic Matrix Factorization (PMF)

Experimental result – Item

recommendation

Experimental result – Rating

Prediction

Experimental result – Tag

Recommendation

Compare method:

TSA [TKDE10]: Ternary Semantic Analysis

RTF [KDD.09]: Optimal ranking using tensor

factorization.

Experimental result – Tag

Recommendation

Experimental result – User

recommendation

Conclusion

We have shown that quaternary semantic analysis

can lead to more accurate recommendation.

We have proposed using a 4-order tensor to model

the four heterogeneous entities: users, items, tags

and ratings.

A unified framework is proposed that utilize

quaternary relation for user recommendation, item

recommendation, tag recommendation and rating

prediction.

Thank you very much!

Q/A

44