DSpace at VNU: HU-FCF: A hybrid user-based fuzzy collaborative filtering method in Recommender Systems tài liệu, giáo án...
Trang 15
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7Q1 Le Hoang Son⇑
8Q2 VNU University of Science, Vietnam National University, Viet Nam
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10
1 2
13 Keywords:
15 Football results prediction
16 Fuzzy Recommender Systems
17 Fuzzy similarity degrees
18 Hard user-based degrees
19 Hybrid fuzzy collaborative filtering
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2 1
a b s t r a c t
22 Recommender Systems (RS) have been being captured a great attraction of researchers by their
applica-23 tions in various interdisciplinary fields Fuzzy Recommender Systems (FRS) is an extension of RS with the
24 fuzzy similarity being calculated based on the users’ demographic data instead of the hard user-based
25 degree Based upon the observations that the FRS researches did not offer a mathematical definition of
26 FRS accompanied with its algebraic operations and properties, and the fuzzy similarity degree is not
27 enough to express accurately the analogousness between users, in this paper we will present a systematic
28 mathematical definition of FRS including theoretical analyses of algebraic operations and properties and
29 propose a novel hybrid user-based fuzzy collaborative filtering method that integrates the fuzzy
similar-30 ity degrees between users based on the demographic data with the hard user-based degrees calculated
31 from the rating histories into the final similarity degrees in order to obtain high accuracy of prediction
32 Experimental results on some benchmark datasets show that the proposed method obtains better
accu-33 racy than other relevant methods Lastly, an application for the football results prediction is given to
illus-34 trate the uses of the proposed method
35
Ó 2014 Published by Elsevier Ltd
36
37 38
39 1 Introduction
40 Recommender Systems (RS) have been being captured a great
41 attraction of researchers by their applications in various
interdisci-42 plinary fields RS, which are a subclass of decision support systems,
43 can give users information about predictive ‘‘rating’’ or
‘‘prefer-44 ence’’ that they would like to assess an item; thus helping them
45 to choose the appropriate item among numerous possibilities This
46 kind of expert systems is now commonly popularized in numerous
47 application fields such as books, documents, images, movie, music,
48Q3 shopping and TV programs personalized systems as stated byPark,
49 Kim, Choi, and Kim (2012)in a survey of 210 articles on
Recom-50 mender Systems from 46 journals published between 2001 and
51 2010 A large number of researches involving the uses of RS to
52 practical applications have been found in those journals especially
53 those focusing on expert and knowledge-based systems, for
exam-54 ple the work ofGhazanfar and Prügel-Bennett (2014)offering a
55 hybrid recommendation algorithm to make reliable
recommenda-56 tions for gray-sheep users that reduce the recommendation error
57 rate and maintain reasonable computational performance
58 Christidis and Mentzas (2013)handled the difficulty of processing
59
a large number of items bought and sold every day in auction
mar-60 ketplaces across the web by the mean of a RS system that exploits
61 the hidden topics of unstructured information The analysis of
stu-62 dent’s academic performance by a RS system determining the level
63
of learning productivity integrally through physiological,
psycho-64 logical and behavioral was studied by Kaklauskas (2013) Fang
65
et al (2012)developed a mobile RS to capture users’ preferences
66
in indoor shopping context through users’ positions and contextual
67 information Costa-Montenegro, Barragáns-Martínez, and
Rey-68 López (2012)addressed the issue of information overload when
69 downloading applications in markets by an integrated RS solution
70 Carrer-Neto, Hernández-Alcaraz, Valencia-García, and
García-71 Sánchez (2012) employed knowledge and social networks to a
72 hybrid RS for the cinematographic domain Shih, Yen, Lin, and
73 Shih (2011)implemented the most common three kinds of RS
tech-74 niques in order to recommend to customers which countries are
75 the best traveling locations.Borges and Lorena (2010)applied RS
76
to the domain of news and listed some typical examples such as
77 GroupLens, NewsWeeder, online newspaper P-Tango and Google
78 news personalization.Drachsler (2010)gave an application of RS
79 for technology enhanced learning Duan, Street, and Xu (2011)
80 studied nursing care plans in a healthcare RS Tag recommendation
81 for Social RS was investigated byDerntl (2011), Song, Zhang, and
82 Giles (2011) and Zheng and Li (2011) Industrial RS applications
http://dx.doi.org/10.1016/j.eswa.2014.05.001
0957-4174/Ó 2014 Published by Elsevier Ltd.
⇑ Address: 334 Nguyen Trai, Thanh Xuan, Hanoi, Viet Nam Tel.: +84 904171284;
fax: +84 0438623938.
E-mail address: sonlh@vnu.edu.vn
Contents lists available atScienceDirect
Expert Systems with Applications
j o u r n a l h o m e p a g e : w w w e l s e v i e r c o m / l o c a t e / e s w a
Trang 283 could be named but a few such as the personalized online store of
84 Amazon.com, music recommendation of YouTube, the hottest
85 news of Yahoo, Netflix, etc (Ricci, Rokach, & Shapira, 2011) Other
86 applications of RS could be referenced in Shapira (2011), Son,
87 Cuong, Lanzi, and Thong (2012), Son, Cuong, and Long (2013a),
88 Son, Minh, Cuong, and Canh (2013b), Son, Linh, and Long (2014),
89 Son (in press) and Son and Thong (submitted for publication)
90 These researches of RS applications clearly depict two remarks:
91 (i) RS is getting more and more important to practical applications;
92 (ii) the studies of RS and its computational intelligence techniques
93 such as the association rule, clustering algorithms, decision tree,
k-94 nearest neighbor, link analysis, neural network, regression and
95 other heuristic methods to enhance the accuracy of prediction
96 are significant to not only the community of expert and
knowl-97 edge-based systems researches but also the applied sciences
98 Our objective in this paper is to investigate an advanced
com-99 putational intelligence technique for RS to enhance the accuracy of
100 prediction We have already known that Collaborative Filtering (CF)
101 is one of the most popular, traditional hard user-based filtering
102 methods to predict the ratings of items based on the similarities
103 between users through the Pearson coefficient Rating of a user is
104 indeed approximated to the most frequent of those of other similar
105 users Nevertheless, the problem of CF can be recognized that the
106 calculation of similarities between users based on the rating
histo-107 ries is not accurate in many practical applications, and other
infor-108 mation such as users’ demographic data should be used instead
109 since those data reflect the correlation between users expressed
110 through various attributes of users more strictly than the rating
111 history An important issue in this observation is that the attributes
112 of users are not only continuous values but also discrete ones such
113 as ‘‘Gender’’, ‘‘Occupation’’, etc Thus, in order to calculate the
sim-114 ilarity between users based on the demographic data, it is
neces-115 sary to integrate fuzzy logic with RS, and this research
116 orientation belongs to the class of Fuzzy Recommender Systems
117 (FRS) Yager (2003) stated that the usefulness of information is
118 dependent upon its representation visualized by fuzzy sets so that
119 the final rating, calculated through the ordered weighted averaging
120 operator, bases solely on the preferences of the single individual
121 and makes no use of the preferences of other collaborators
122 Zenebe and Norcio (2009)presented a fuzzy set theoretic method
123 for RS including a representation method, similarity measures
124 and aggregation methods that handles the non-stochastic
uncer-125 tainty induced from subjectivity, vagueness and imprecision in
126 the data, and the domain knowledge and the task under
consider-127 ation.Cao and Li (2007)presented a fuzzy-based system for
con-128 sumer electronics that ranks customer needs by their importance
129 and sets up fuzzy rules between customer needs and product
fea-130 tures Porcel, López-Herrera, and Herrera-Viedma (2009) used
131 some filtering tools and a particular fuzzy linguistic modeling,
132 called multi-granular fuzzy linguistic modeling, which is useful
133 when different qualitative concepts have to be assessed for
134 research resources.Porcel and Herrera-Viedma (2010)investigated
135 the problem of incomplete information in a fuzzy linguistic RS and
136 presented a new system that facilitates the acquisition of the user
137 preferences to characterize the user profiles Palanivel and
138 Siavkumar (2010)adopted the fuzzy linguistic and fuzzy
multi-cri-139 teria decision making approaches to represent the user ratings and
140 accurately rank the relevant items.Romero, Ferreira-Satler, Olivas,
142 fuzzy linguistic model based on three dimensions such as
struc-143 tural, contextual and personal and applied it to learning object
144 repository.Serrano-Guerrero, Herrera-Viedma, Olivas, Cerezo, and
145 Romero (2011) introduced a novel fuzzy linguistic RS based on
146 the Google Wave capabilities for communicating researchers
inter-147 ested in common research lines.Boulkrinat, Hadjali, and Mokhtari
148 (2013)used linguistic terms for the rating of users’ preferences and
149 calculated the similarity between users on the basis of the
similar-150 ity of their preference relations which can better capture similar
151 users’ ratings patterns Some authors used soft computing method
152 for the calculation of similarities between users, for instancePark,
153 Yoo, and Cho (2006)applied Fuzzy Bayesian Networks to fuzzify
154 information obtained from sensors and Internet and to get suitable
155 contexts with the probability; thus determining the similarities
156 between users Al-Shamri and Bharadwaj (2008) presented a
157 hybrid fuzzy-genetic approach to fuzzify the user model and to
158 reflect more appropriately the fuzziness of each fuzzy feature
159 Terán and Meier (2010)designed a fuzzy interface for voters and
160 candidates to write their profiles, and used fuzzy clustering to
cal-161 culate the top-N recommendation in eElections Nadi, Saraee,
162 Bagheri, and Davarpanh Jazi (2011)focused on web users’
behav-163 iours problem and proposed a fuzzy-ant based RS based on
collab-164 orative behaviour of ants.Sevarac, Devedzic, and Jovanovic (2012)
165 proposed neuro-fuzzy pedagogical recommender, which is an
166 adaptive RS based on neuro-fuzzy inference, to create pedagogical
167 rules in technology enhanced learning.Lucas, Laurent, Moreno, and
168 Teisseire (2012) and Zhang et al (2013)proposed hybrid
method-169 ologies for RS, which use collaborative filtering and content-based
170 approaches in a joint method taking advantage from the strengths
171
of both approaches From the summary of relevant researches to
172 FRS, some important issues are drawn out as follows
173
Those relevant FRS researches solely used fuzzy sets to model
174 uncertain information existed in the users’ demographic data
175 but did not offer a mathematical definition of FRS accompanied
176 with its algebraic operations and properties
177
According to these researches, FRS is merely a small extension
178
of RS with the users’ demographic data being provided in
addi-179 tion to other datasets, and the calculation of the similarity
180 degrees between users is conducted on the demographic data
181 only Even though demographic data contain
multiple-dimen-182 sions comprehensive information of users, relying solely on this
183 type of data for the calculation of the similarity degrees without
184 the knowledge of rating histories may lead to erroneous and
185 inaccurate results Since previous ratings could somehow affect
186 the constitution of the considered one, it is better if the
similar-187 ities between users are evaluated both by the demographic data
188 and the rating histories
189 190 Motivated by the problems of the relevant FRS researches and
191 the work ofShih et al (2011)concluding that hybrid RS could
con-192 quer the shortcomings of the available filtering approaches, our
193 contributions in this article are expressed as follows
194
A systematic mathematical definition of FRS accompanied with
195 its algebraic operations and properties
196
A novel hybrid user-based fuzzy collaborative filtering method
197 so-called HU-FCF that integrates the fuzzy similarity degrees
198 between users based on the demographic data with the hard
199 user-based degrees calculated from the rating histories into
200 the final similarity degrees in order to obtain high accuracy of
201 prediction
202
An application of HU-FCF for the football results prediction
203 problem
204 205 The difference and the novel of the proposed approach in
compar-206 ison with the relevant FRS ones are expressed in the contributions
207 above Even though the idea of HU-FCF is quite simple, it could help
208 accelerating the accuracy of prediction since the final similarity is
209 evaluated more accurately through the integration of both the fuzzy
210 and hard user-based similarity degrees The relevant approaches
211 were based solely on either the hard similarities between users
212 (the CF method and its variants) or fuzzy similarities from the
Trang 3213 demographic data (the group of FRS methods) so that the group of
214 the most similar users to the considered one may admit irrelevant
215 users as a result of incorrect selection and computation Intuitively,
216 the proposed HU-FCF may result in better accuracy and flexibility
217 than other relevant approaches through the using of the hybrid
sim-218 ilarity degrees This may be verified and validated by experiments in
219 some benchmark RS datasets such as the MovieLens (GroupLens
220 research, 2014) and Book-Crossing (Ziegler, McNee, Konstan, &
221 Lausen, 2005) The advantage of the proposed method HU-FCF may
222 be not only the better accuracy than other relevant approaches but
223 also the capability to handle more numbers of cases than other
224 algorithms since when the coefficient or weight of the fuzzy (hard)
225 user-based similarity degree is set to zero, the HU-FCF algorithm
226 works similarly to the available relevant algorithms Additionally,
227 HU-FCF is constructed on the basis of a systematic mathematical
228 definition of FRS accompanied with its algebraic operations and
229 properties so that the theoretical foundation of the algorithm can
230 be guaranteed The disadvantage of HU-FCF is somehow the large
231 computational time since it has to compute more numbers of
simi-232 larity degrees than other algorithms However, this limitation could
233 be compromised if the priority of RS is dedicated to the accuracy of
234 prediction
235 The rest of the paper is structured as follows Section2presents
236 the main contributions of the paper including a mathematical
def-237 inition of FRS accompanied with its algebraic operations and
prop-238 erties and a novel hybrid user-based fuzzy collaborative filtering
239 method named HU-FCF Section 3 validated HU-FCF by
experi-240 ments on some benchmark datasets Section4introduces an
appli-241 cation of HU-FCF for the football results prediction Section5draws
242 the conclusions and delineates the future research directions
243 2 The proposed methodology
244 2.1 Definitions
245
246 Definition 1 (Recommender Systems – RSAdomavicius and Tuzhilin,
247 2005; Borges and Lorena, 2010; Ricci et al., 2011) Suppose U is a set
248 of all users and I is the set of items in the system The utility
249 function R is a mapping specified on U1 U and I1 I as follows
250
ðu1;i1Þ # Rðu1;i1Þ;
252
253 where Rðu1;i1Þ is a non-negative integer or a real number within a
254 certain range P is a set of available ratings in the system Thus,
255 RS is the system that provides two basic functions below
256 (a) Prediction: determine Rðu;iÞ for any ðu;iÞ 2 ðU; IÞ n ðU1;I1Þ
257 (b) Recommendation: choose i
2 I satisfying
258 i¼ arg maxi2IRðu; iÞ for all u 2 U
259
260
261
262 Definition 2 (Multi-criteria Recommender Systems – MCRSShapira,
263 2011) MCRS are the systems providing similar basic functions
264 with RS but following by multiple criteria In the other words,
265 the utility function is defined below
266
ðu1;i1Þ # ðR1;R2; ;RkÞ;
268
269 where Riði ¼ 1; kÞ is the rating of user u12 U1for item i12 I1
fol-270 lowing by criteria i In this case, the recommendation is performed
271 according to a given criteria
272 Example 1 Suppose that U = {John, David, Jenny, Marry} and
273
I = {Titanic, Hulk, Scallet} The set of criteria of a movie is
274
P = {Story, Visual effects} The ratings are assigned numerically
275 from 1 (bad) to 5 (excellent).Table 1describes the utility function Q4
276 From this table, it is clear that MCRS can help us to predict the
277 ratings of a user (Marry) to a movie that was not rated by her
278 beforehand (Titanic) This kind of systems also recommends her
279 favourite movie through available ratings In cases that there is
280 only an criterion in P, MCRS returns to the traditional RS Now,
281
we extend MCRS by the definition below
282 Definition 3 (Fuzzy Recommender Systems – FRS) Suppose U is a
283 set of all users, I is the set of items and C is the set of fuzzy contexts
284
in the system The utility function R is a mapping specified on
285
U1 U; I1 I and C1 C as follows
286
ðu1;i1;fc1;lcgÞ # ðfR1;l1g; fR2;l2g; ; fRk;lkgÞ; 288
289 wherelc2 ½0; 1 is the membership value of context c1 Riði ¼ 1; kÞ
290
is the rating of user u1to item i1in context c1by criteria Pi with
291 fuzzy membership li2 ½0; 1 FRS are the systems that provide
292 two basic functions below
293 (a) Prediction: the capability to determine Rðu;i;fc
1;lgÞ for
294 any ðu;i;fc
1;lgÞ 2 ðU; I; CÞ n ðU1;I1;C1Þ
295 (b) Recommendation: the capability to choose i2 I satisfying
296
i¼ arg maxi2IRðu; i; fc;lcgÞ for all u 2 U; fc;lcg 2 C and a
297 certain criterion
298 299
As we can recognize inDefinition 3, FRS is the generalized
def-300 inition of MCRS (Definition 2)and RS (Definition 1) since in cases
301 that C ¼ f/g andli¼ 1 ð8i ¼ 1; kÞ, FRS returns to MCRS If the
con-302 dition: k ¼ 1 is appended, FRS returns to the traditional RS Now,
303 let us consider the example below to illustrate the difference
304 between FRS and other types of RS
305 Example 2 Suppose that U = {John, David, Jenny, Marry},
306
I = {Titanic, Hulk, Scallet} and C = {Weather, Mood} The fuzzy
lin-307 guistic labels of ‘‘Weather’’ are {‘‘Fine’’, ‘‘Normal’’, ‘‘Bad’’}, and those
308
of ‘‘Mood’’ are {‘‘Happy’’, ‘‘Normal’’, ‘‘Angry’’} The set of criteria of a
309 movie is P = {Story, Visual effects} whose fuzzy linguistic labels are
310 {‘‘Very good’’, ‘‘Fair’’, ‘‘Boring’’} and {‘‘Amazing’’, ‘‘Thrill’’,
‘‘Mel-311 ody’’}, respectively.Table 2describes the utility function of FRS
312 313
It is obvious that the ratings for a movie of a user are expressed
314
by fuzzy linguistic labels in terms of criteria For example, when
315 the weather is ‘‘Normal’’ and the mood of user John is ‘‘Happy’’,
316
he would like to assess the story and visual effect of movie ‘‘Hulk’’
317 being ‘‘Fair’’ and ‘‘Amazing’’, respectively Contrary to the utility
318 function of MCRS in Table 1 where the rating is assigned by
319 numeric values, the rating for a criterion is expressed by the set
320
of fuzzy linguistic labels In the example above, the set of fuzzy
Table 1 Movies’s rating.
Trang 4321 linguistic labels for criterion ‘‘Story’’ accompanied with fuzzy
322 memberships as stated in Eq (3)is {(‘‘Very good’’, 0.2); (‘‘Fair’’,
323 0.7); (‘‘Boring’’, 0.1)} Since the fuzzy membership of label ‘‘Fair’’
324 is the maximum among all, the rating value for criterion ‘‘Story’’
325 is ‘‘Fair’’ as shown inTable 2 By using the fuzzy linguistic labels,
326 FRS has tackled the problem of vague, incomplete and uncertainty
327 that exist in RS and MCRS
328 The aims of FRS consist of the prediction and the
recommenda-329 tion of a user for a movie in a specific context For example, we
330 would like to know the ratings of user Marry in terms of {‘‘Story’’,
331 ‘‘Visual effects’’} for the movie ‘‘Titanic’’ in the contexts of weather
332 and mood being ‘‘Normal’’ and ‘‘Normal’’, respectively
Further-333 more, the best movie in term of a specific criterion that Marry
334 has ever seen should be recommended
335 2.2 Some algebraic operations of FRS
337 FRS ¼ fU; I; C; fPig j i ¼ 1; ng below
338
FRS1¼ U1;I1;C1; P1
ii
n oi ¼ 1; n
FRS2¼ U2;I2;C2; P2
i
n oi ¼ 1; n
FRS3¼ Un 3;I3;C3;n oP3i i ¼ 1; no
340
341 where,
342
C1¼ c1;j;lc
1;j
lc
1;j ¼ cg1;j;lg
1;j
P1
i ¼ R1i;l1
i
i;q;l1 i;q
C2¼ c2;j;lc
2;j
lc
2;l¼ cg
2;j;lg
2;j
P2i ¼ R2i;l2
i
¼ R2i;q;l2
i;q
C3¼ c3;j;lc
3;j
lc3;j ¼ cg3;j;lg
3;j
P3
i ¼ R3i;l3
i
i;q;l3 i;q
C ¼ncj;lcjj ¼ 1; lo
lc
j¼ cg
j;lg
j
Pi¼ R i;li
¼nRi;q;li;qq ¼ 1; ro
344
345 Some algebraic operations of FRS are defined below
346 (a) Union:
347
349
351
FRS12¼ U12;I12;C12; P12
l
C12¼ c12;j;lc
12;j
lc12;j¼ cg12;j;lg
12;j
lg
12;j¼ maxflg
1;j;lg
P12 i
¼ R12i ;l12 i
;l12
l12
i;q;l2 i;q
354 (b) Intersection:
355
358 where
359
FRS12¼ Un 12;I12;C12;nP12l o
C12¼ c12;j;lc
12;j
lc 12;j¼ cg 12;j;lg
12;j
lg
12;j¼ min lg
1;j;lg
2;j
P12i
¼ R12i ;l12 i
¼nR12i;q;l12q ¼ 1;r;l 2 N;k 2 No
l12¼ min l1
i;q;l2 i;q
362 (c) Complement:
363
FRSC
¼ UC;IC
;CC
; P1 C
i
366 where
367
UC
CC1¼ c1C ;j;lc
1C ;j
lc 12;j¼ cg
1 C ;j;lg
1C ;j
lg
1C ;j¼ 1 lg
P1iC
¼ R1iC;l1 C
i
¼ R1i;qC;l1 C
i;q
l1C i;q¼ 1 l1C
370
371 2.3 Properties
372 (a) Commutative:
374
377 (b) Associative:
378
382
We prove the first commutative property in Eq (45) Other
383 properties are proven analogously
384
FRS12¼ Un 12;I12;C12;nP12l o
Table 2
The utility function of FRS
Weather Mood Story Visual effects
John Scallet Bad Normal Very good Melody
David Titanic Fine Happy Very good Amazing
David Scallet Normal Normal Boring Amazing
Jenny Titanic Fine Normal Very good Melody
Trang 5387 where
388
C12¼ c12;j;lc
12;j
lc
12;j¼ cg
12;j;lg
12;j
lg
12;j¼ maxflg
1;j;lg
P12i
¼ R12i ;l12
i
¼nR12i;q;l12q ¼ 1; r; l 2 N; k 2 No
i;q;l2 i;q
390
391 Similarly, we have
392
FRS21¼ Un 21;I21;C21;nP21l o
394
395 where
396
C21¼ c21;j;lc
21;j
lc21;j¼ cg21;j;lg
21;j
lg
21;j¼ max lg
2;j;lg
1;j
P21
i
¼ R21i ;l21
i
¼nR21;l21q ¼ 1; r; l 2 N; k 2 No
i;q;l1 i;q
398
399 Thus,
400
402
403 2.4 The HU-FCF algorithm
404 In this section, we present a novel hybrid user-based fuzzy
col-405 laborative filtering method so-called the Hybrid User-based Fuzzy
406 Collaborative Filtering (HU-FCF) Since most of the available RS
407 datasets are designed in the forms of {User, Item, Criterion} and a
408 fuzzy filtering method could be developed either on the set of
409 {User, Item, Context} or the set of {Criteria} or both of them, we
410 consider the reduction of the definition of FRS (Definition 3) to that
411 of RS (Definition 1) and perform the fuzzy filtering method on the
412 user dataset Most of the relevant FRS approaches were also
413 designed by this way, and the proposed HU-FCF would be an
414 extension of them in order to achieve the objective of better
accu-415 racy of prediction To be frank, the HU-FCF method is designed for
416 the original RS but not truly for the FRS as stated inDefinition 3
417 Nonetheless, by providing an appendage of fuzzy similarity
418 degrees, this method could be considered as one of the fuzzy
filter-419 ing methods for FRS The basic idea of HU-FCF method is to
inte-420 grate the fuzzy similarity degrees between users based on the
421 demographic data with the hard user-based degrees calculated
422 from the rating histories into the final similarity degrees As such,
423 those degrees would reflect more exactly the correlation between
424 users in terms of the internal (attributes of users) and external
425 information (interactions between users) Each similarity degree
426 (fuzzy/hard) is accompanied by weights automatically calculated
427 according to the numbers of analogous users Once the final
simi-428 larity degrees are calculated, the final rating will be constructed
429 based on the rating values of neighbors of the considered user
430 Depending on the domain of a specific problem, the final rating will
431 be approximated to its nearest value in that domain accompanied
432 by an error threshold, which is normally smaller than 5% A list of
433 nearest values with equivalent error thresholds is also given as the
434 prediction ratings of a user for an item The following pseudo-code
435 will describe the ideas more details
Input: – The users’ demographic data: U ¼ fU1; ;UNg
where each Ui¼ Un 1i; ;Ulo
ði ¼ 1; NÞ; N is the number of users and l is the number of demographic attributes;
– The items set: I ¼ fI1; ;IMg where M is the number of items;
– The rating histories: R ¼ fRðUi;IjÞ j Ui2 U; Ij2 Ig; – The similarity threshold: h 2 ½0; 1;
– The weights of the demographic attributes: wi
ði ¼ 1; lÞ;
Output: – Rða; iÞ or ra;i for any ða; iÞ 2 ðU; IÞ HU-FCF:
1: Set the number of similarity degrees in the users’
demographic data: c ¼ 0;
2: Determine the membership functions for demographic attributes and calculate the membership values of all users according to the demographic attributes The most frequent used function for various type of data is the standard normal Gaussian as recommended bySubasi (2006); 3: For each demographic attribute i:
4: Based upon the membership function, calculate the fuzzy distances between the considered user and other ones by the formula below:
where ai; bi are the membership values according to the demographic attribute i of the considered user a and another user b
6: End for 7: Calculate the global fuzzy distances between the considered user and other ones by the formula:
GFDða; bÞ ¼Xl
i¼1
where wi2 ½0; 1 is the weight of the demographic attribute i showing the influence to the global results and satisfying the condition,
Xl i¼1
8: Calculate the fuzzy similarity degrees between the considered user and other ones by the formula:
9: Determine the hard (user-based) similarity degrees between the considered user and other ones from the rating histories by the Pearson coefficient below:
HSDða; bÞ ¼
i¼1ðra;i raÞ ðrb;i rbÞ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
i¼1ðra;i raÞ2
q
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
i¼1ðrb;i rbÞ2
where ra;iis the rating value of the considered user a for item
i 2 I;
rb;iis the rating value of user b for item i 2 I;
rais the average rating value of the considered user
a by all items;
rbis the average rating value of user b by all items; 10: Calculate the final similarity degrees between the considered user and other ones from Eqs.(71), (72)as follows
(continued on next page)
Trang 6SIMða; bÞ ¼a FSDða; bÞ þ b HSDða; bÞ; ð73Þ
where a ðbÞ is the weight of the fuzzy (hard) similarity
degree, and is calculated through the equations below
11: Calculate the final rating by the equation below
Rða; i
Þ ¼ raþ
P
b2UnfagSIMða; bÞ ðrb;i rbÞ P
b2Unfagj SIMða; bÞ j : ð76Þ
12: Determine the nearest value of Rða; iÞ in the domain D of
the problem as the final result, and calculate the error
threshold as follows
Þ d j
where d 2 D is the nearest value of Rða; i
Þ
529
530 In Step 7 of the HU-FCF algorithm, the weights of the
demo-531 graphic attributes are normally taken from the experience of
532 experts according to a given context Nevertheless, the formula
533 below could be used to estimate those weights in a general case.\
534
i
Pl
i¼1Ui
Ui
¼ median U $i
j ¼ 1; N
536537
538 where U$i is the normalized value of Ui
ði ¼ 1; l; j ¼ 1; NÞ Eqs ((78)
539 and (79)) determine the values of weights according to their
contri-540 butions in all demographic attributes Let us consider the example
541 below to illustrate the calculation of weights
542 Example 3 Suppose that we have a demographic dataset of 15
543 users inTable 3
544 Normalize the demographic dataset we obtain the results in
545 Table 4 Take the median values by demographic attributes in Eq
546 (79)we haveTable 5 Use Eq (78)we get the values of weights
547 548 inTable 6
549
3 Evaluation
550 3.1 Experimental design
551
In this part, we describe the experimental environments such
552 as,
553
Experimental tools: We have implemented the proposed
algo-554 rithm – HU-FCF in addition to the fuzzy collaborative filtering
555 algorithms of Lucas et al (2012) and Zenebe and Norcio
556 (2009) in C programming language and executed them on a
557
PC Intel Pentium Dual Core 1.80 GHz, 1 GB RAM
558
Experimental dataset: the benchmark RS datasets such as the
559 MovieLens (GroupLens research, 2014) and Book-Crossing
560 (Ziegler et al., 2005) MovieLens datasets consist of 2 types:
561 100k and 1M and show the rating values from 1 (Bad) to 5
562 (Excellent) of users for a collection of movies in the system
563 The data were collected through the MovieLens web site
564 (movielens.umn.edu) during the seven-month period from
Sep-565 tember 19th, 1997 through April 22nd, 1998 The Book-Crossing
566 dataset was collected by Cai-Nicolas Ziegler in a 4-week crawl
567 (August/September 2004) from the Book-Crossing community
568 and showed the rating values from 1 to 10 of users for a set
569
of books Besides these data, there are other benchmark RS
570 datasets such as Jester (
http://goldberg.berkeley.edu/jester-571 data), Sushi (http://www.kamishima.net/sushi), HetRec2011
572 (http://grouplens.org/datasets/hetrec-2011), WikiLens (http://
573 grouplens.org/datasets/wikilens), etc However, they do not
574 contain the demographic information so that for the best of
575 comparison we adopt the MovieLens and Book-Crossing for
Table 3
The demographic dataset.
User Age Education No children Living standard
Table 4 The normalized demographic dataset.
User Age Education No children Living standard
1 0.04411765 0.058823529 0.046153846 0.066666667
2 0.08272059 0.029411765 0.153846154 0.088888889
3 0.07904412 0.058823529 0.107692308 0.088888889
4 0.07720588 0.088235294 0.138461538 0.066666667
5 0.06617647 0.088235294 0.123076923 0.044444444
6 0.03492647 0.117647059 0 0.066666667
7 0.06985294 0.058823529 0.092307692 0.044444444
8 0.03860294 0.088235294 0.015384615 0.044444444
9 0.04963235 0.058823529 0.046153846 0.088888889
10 0.08272059 0.029411765 0.123076923 0.044444444
11 0.06985294 0.029411765 0.030769231 0.066666667
12 0.07720588 0.029411765 0.061538462 0.066666667
13 0.08088235 0.117647059 0.015384615 0.088888889
14 0.07720588 0.058823529 0.015384615 0.066666667
15 0.06985294 0.088235294 0.030769231 0.066666667
Table 5 The median values of demographic dataset.
Age Education No children Living standard 0.069852941 0.058823529 0.046153846 0.066666667
Table 6 The weights.
Table 7 The descriptions of datasets.
Dataset No users No attributes No items No Ratings
Book-Crossing 278,858 2 271,379 1,149,780
Trang 7576 experiments The cross-validation method used to get the
train-577 ing and testing datasets is 3-fold.Table 7gives an overview of
578 those datasets
579 The validity indices: we use the Mean Accuracy (MA) and the
580 computational time
581 Parameters setting: the similarity threshold is set as h ¼ 0:2
582 Objective:
583 To compare the accuracy of HU-FCF with those of relevant
585 To evaluate the computational time of algorithms
586
587
588 3.2 Experimental results
589 In this section, we present the experimental results expressed
590 inTable 8 In this table, we compare the proposed algorithm
HU-591 FCF with the algorithms of Lucas et al (a.k.a Lucas) and Zenebe
592 and Norcio (a.k.a ZN) in terms of accuracy and computational time
593 The experimental datasets are denoted as 100k (MovieLens 100k),
594 1M (MovieLens 1M) and BC (Book-Crossing) In order to validate
595 the efficiency of the method to determine the weights of
demo-596 graphic attributes in Eqs.(78) and (79), we made the experiments
597 by various cases of weights such as,
598 Weight 1: the values of weights wið8i ¼ 1; lÞ are calculated by
599 Eqs.(78) and (79);
600 Weight 2: the values of weights wið8i ¼ 1; lÞ are set up equally:
601 wi¼ 1=l;
602 Weight 3: the values of weights wið8i ¼ 1; lÞ are randomly set
603 up in (0,1) satisfying constraint(70)
604
605 According to the results inTable 8, we clearly recognize that the
606 accuracy of HU-FCF is better than those of Lucas and ZN For
exam-607 ple, in cases of Weight 1 and the 1M dataset, the MA value of
HU-608 FCF is 82.2% which is larger than those of Lucas and ZN with the
609 numbers being 78.4% and 62.1% In cases of Weight 2 and the BC
610 dataset, we also recognize that the MA value of HU-FCF is still
bet-611 ter than those of Lucas and ZN with the numbers being 79.4%,
612 79.4% and 63.4%, respectively Lastly, the MA values of all
algo-613 rithms in cases of Weight 3 and the 100k dataset also show that
614 HU-FCF is better than the algorithms of Lucas and ZN with the
615 numbers being 82.1%, 81.4% and 55%, respectively Those examples
616 clearly affirm that the accuracy of the HU-FCF algorithm is better
617 than those of Lucas and ZN
618 Nevertheless, there are some cases that the accuracy of
HU-619 FCF is worse than those of Lucas and ZN For example, in cases
620 of Weight 1 and the 100k dataset, the MA value of HU-FCF is
621 76.7% which is smaller than that of Lucas with the number being
622 81.4% Similarly, in cases of Weight 3 and the BC dataset, the MA
623 values of HU-FCF, Lucas and ZN algorithms are 77.4%, 79.4% and
624 63.4%, respectively However, the numbers of such bad cases are
625 small in comparison with the rests, and most of time the accuracy
626 of HU-FCF is still better than those of other algorithms Taking the
627 comparison of algorithms by various cases of weights, we clearly
628 recognize that the case of Weight 1 often results in better
accu-629 racy of the HU-FCF algorithm than the cases of Weight 2 and
630 Weight 3 Even though there exists a bad case of the accuracy
631 of HU-FCF in comparison with other algorithms in each case of
632 weight, the average MA value of HU-FCF by various datasets in
633 the case of Weight 1 is 80.7% whilst those in cases of Weight 2
634 and Weight 3 are 80.1% and 79.3%, respectively This clearly
635 affirms the fact that using the generation method in Eqs (78)
636 and (79)to create the values of weights wið8i ¼ 1; lÞ is more
effi-637 cient than other methods of weights As we have early predict the
638 drawback of the computational time of HU-FCF over other
rele-639 vant methods, the results inTable 8re-confirm that the
compu-640 tational time of HU-FCF is longer than those of other
641 algorithms For example, in case of the 100k dataset, it takes
642 the HU-FCF algorithm approximately 26.1 s on average by various
643 cases of weights This number is larger than those of Lucas and
644
ZN with the numbers being 15.3 and 18.4 s, respectively In case
645
of the 1M dataset, the values of computational time of HU-FCF,
646 Lucas and ZN are 123, 78 and 93 s, respectively Lastly, the values
647
of computational time of HU-FCF, Lucas and ZN in case of the BC
648 dataset are 145, 96 and 115 s, respectively Even though the
com-649 putational time of HU-FCF is larger than those of other
algo-650 rithms, it is obvious that the difference is unremarkable and
651 can be acceptable
652 3.3 Concluding remarks
653 Throughout the experimental results, we have extracted the
fol-654 lowing concluding remarks
655
The accuracy of HU-FCF is better than those of other relevant
656 algorithms;
657
The generation method of weights of demographic attributes in
658 Eqs (78) and (79) of Section 2.4 is the most effective ones
659 among other methods of weights;
660
The drawback of the computational time of HU-FCF can be
661 acceptable
662
663
4 An application of HU-FCF for football results prediction
664
In this section, we illustrate an application of HU-FCF for the
665 football results prediction problem The experimental datasets
666 were taken from the Barclays English Premier League (BEPL)
667 including 20 teams and 38 rounds (Statto organisation, 2014)
668 From the datasets, we have summarized some characteristics of a
669 team byTable 9
Table 8 The comparison of algorithms.
Weight 1
Weight 2
Weight 3
Table 9 Statistical information of a football team in BEPL.
Psychological/non-psychological information The number of games that failed to score The average age of players The number of goals scored (in home
team)
Injury per game
The number of goals against (home team) The number of red (yellow)
cards The number of clean sheets (home team) The number of penalties
(against) The average number of shots per game
Trang 8670 Now, we describe how the HU-FCF algorithm can be applied to
671 predict the football results Let us take a look at the statistics of
672 BEPL season 2012–2013 visualized byFig 1 From this figure, we
673 split the scoring results into 2 subsets: the training and testing
674 by the hold-out method, and use the training as the rating
histo-675 ries The users and items sets in this case are identical and consist
676 of 20 football teams whose demographic data are shown inTable 9
677 Next, we use the HU-FCF algorithm to predict the result of the
678 match between Manchester United (Home team) and Arsenal
679 (Away team) The similarity threshold is set as h ¼ 0:2, and the
680 weights of the demographic attributes are wi¼ 1=9 ði ¼ 1; 9Þ From
681 the rating histories, we encode a result ‘‘x—y’’ to the form of
682
‘‘x 10 þ y’’ for easy calculation so that the domain of the problem
683
is now transformed to D ¼ ½0; ; 99
684 According to Eq.(67), the fuzzy distances matrix is calculated
685 as,
Fig 1 Results of BEPL season 2012–2013.
FDT
¼
0
B
B
B
B
B
B
B
B
@
1 C C C C C C C C A
;
ð80Þ
Trang 9686 From Eq.(80), we calculate the number of similarity degrees as
687 c ¼ 65 Thus,a¼ 0:77 and b ¼ 0:23 The fuzzy similarity degrees
688 matrix is then expressed in Eq.(81) From the rating histories we
689 calculate the hard similarity degrees and the final similarity
690 degrees matrices in Eqs.(82) and (83), respectively
691 Thus, the final rating is Rða; i
Þ ¼ 21:248 From the domain, we
692 determine the nearest value of Rða; i
Þ is ‘‘21’’ that means ‘‘2–1’’
693 with the error threshold beingD¼ 1:16% This result is identical
694 to that inFig 1 If we use the existing fuzzy collaborative filtering
695 methods such as the work ofLucas et al (2012) and Zenebe and
696 Norcio (2009), the predictive results are ‘‘0–1’’ and ‘‘1–1’’,
respec-697 tively Eventually, we have made the comparative experiments
698 for the remaining matches in the testing data of the season
699 2012–2013 and the matches of other seasons and received the
700 results inTable 10
701 If domain D returns to {‘‘Win’’, ’’Draw’’, ‘‘Lose’’} then we receive
702 the results inTable 11
703 5 Conclusions
704 In this paper, we aimed to enhance the accuracy of prediction of
705 the available filtering method in Fuzzy Recommender Systems
706 From the scanning literature, we have pointed out the limitations
707 of the relevant researches that are the lack of a well-defined
math-708 ematical definition of Fuzzy Recommender Systems accompanied
709 with its algebraic operations and properties and the fuzzy
similar-710 ity degree is not enough to express accurately the analogousness
711 between users Thus, we have made the following contributions:
712 (i) a systematic mathematical definition of Fuzzy Recommender
713 Systems that is a generalization of the existing definitions of
Rec-714 ommender Systems and Multi-Criteria Recommender Systems
715 with an illustrated example from the MovieLens dataset was
pro-716 posed; (ii) some basic algebraic operations in Fuzzy Recommender
717 Systems such as the union, the intersection and the complement
718 accompanied with their properties were presented; (iii) a novel
719 hybrid user-based fuzzy collaborative filtering method for Fuzzy
720 Recommender Systems so-called HU-FCF that utilizes both fuzzy
721 and hard user-based similarity degrees and automatically
calcu-722 lates the weights of attributes and degrees was described
Experi-723 mental results conducted on some benchmark RS datasets such as
724 MovieLens and Book-Crossing showed that HU-FCF obtains better
725 accuracy than other relevant fuzzy filtering methods
726 The proposed methodology has good impacts and practical
727 implications to the community researches of Recommender
Sys-728 tems and expert & knowledge-based systems Firstly, it enriches
729 the knowledge of modeling and formulation of Fuzzy
Recom-730 mender Systems Secondly, some basic algebraic operations of
731 Fuzzy Recommender Systems could be used for further studies
732 involving the mathematical foundations of Recommender Systems
733 Thirdly, an application of the fuzzy filtering method HU-FCF for the
734 football results prediction in Section4has shown the capability of
735 the proposed method to be applied to various practical problems
736 Last but not least, general readers could have a great benefit from
737 taking the know-how of system modeling and algorithmic
formu-738 lation; thus utilizing them for cross interdisciplinary researches
739
As being mentioned in Section2.4, the HU-FCF algorithm was
740 designed on the basis of Recommender Systems so that one of
fur-741 ther research directions is to extend this algorithm to work with
742 truly Fuzzy Recommender Systems expressed inDefinition 3 by
743 considering the fuzzification both in the left and right sides of
744
Eq.(3) Furthermore, some other algebraic operations of Fuzzy
Rec-745 ommender Systems should be developed for the completeness of
746 the system Finally, a combination of the HU-FCF algorithm with
747
a neuro-fuzzy network for some forecast problems to accelerate
748 the accuracy is also our target
749 Acknowledgments
750 The authors are greatly indebted to the editor-in-chief Prof B
751 Lin and anonymous reviewers for their comments and suggestions
Table 10
The comparison of accuracy (%).
Table 11
The comparison of accuracy (%) with the new domain.
BEPL season HU-FCF Lucas et al Zenebe and Norcio
ð81Þ
HSDT
¼ 0:42 0:42 0 0:32 0:43 0:14 0:33 0:28 0:06 0:09 0:02 0:12 0:14 0:64 0:21 0:71 0:31 0:28 0:44ð Þ;
ð82Þ
SIMT
¼ 0:49 0:48 0:61 0:43 0:48 0:57 0:64 0:64 0:59 0:58 0:63 0:53 0:58 0:46 0:64 0:47 0:69 0:52 0:44ð Þ: ð83Þ
Trang 10752 that improve the clarity and quality of the paper Other thanks are
753 sent to Mr Khuat Manh Cuong, VNU for the calculation works This
754 work is sponsored by the NAFOSTED under contract No
102.05-755 2014.01
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