Recommender System based on Higherorder Logic Data Representation

Size: px

Start display at page:

Download "Recommender System based on Higherorder Logic Data Representation"

Darrell Marshall
5 years ago
Views:

1 Recommender System based on Hgherorder Logc Data Representaton Lnna L Bngru Yang Zhuo Chen School of Informaton Engneerng, Unversty Of Scence and Technology Bejng Abstract Collaboratve Flterng help users to deal wth nformaton overload and gude them n a personalzed way to nterestng or useful objects n a large space of possble optons. In ths paper, we present a novel and elegant hybrd recommender system called HOLCF, whch use hgherorder logc as data representaton and ntegrate content and demographc nformaton nto a collaboratve flterng framework by usng hgher-order logc dstance computaton approaches wthout the effort of feature constructon. Our experments suggest that the effectve combnaton of varous knds of nformaton based on hgher-order logc dstance computaton approaches provdes mproved accurate recommendatons. Keywords: Collaboratve Flterng; Hgher-order logc data representaton; hgher-order logc dstance 1. Introducton Recommender systems have been wdely used n e-commerce. Some companes such as Amazon.com can provde nterestng and powerful recommendaton servces. One of the most dffcult challenges for these systems s predctng a ratng, whch ndcates how a partcular user lked a partcular object. Recommender systems are usually classfed nto the followng three categores accordng to the sources of data on whch recommendaton s based. In collaboratve flterng systems, the typcal sources of data consst of a vector of tems and ther ratngs, contnuously augmented as the user nteracts wth the system over tme. In content-based recommender systems, the objects of nterest are defned by ther assocated features and the user wll be recommended objects smlar to the ones the user preferred n the past. In demographc recommender systems, the systems am to categorze the user based on personal attrbutes and make recommendatons based on demographc classes. In fact, every approach has ts own advantages and dsadvantages to makng recommendaton and the strengths of them are complementary [1]. To avod certan shortcomngs of each pure category recommender systems, many researchers have explored hybrd recommender systems [, 3]. These hybrd recommender systems can be classfed as propostonal systems and frstorder logc systems accordng to data representaton formalsm adopted by them. Propostonal hybrd recommender systems employ attrbute-value language to descrbe data. As attrbute-value language use a fxed number of features to represent data, the addtonal effort of data form transformaton and feature constructon s needed n most of the category hy- 1

2 brd recommender systems. At the same tme, t makes t dffcult to apply these systems to domans where data s rch n structure because the smplcty of attrbute-value language. Frst-order logc hybrd recommender systems are proposed wth the emergng of research to multrelatonal data mnng n recent years. The category systems manly employ relatonal database to store data and relatonal dstance to compute smlarty between objects. However, the scalablty and effcency of these systems are questonable because of large number of database scans when computng smlarty between objects. In ths paper, we present a novel and elegant hybrd recommender system called HOLCF, whch use hgherorder logc as data representaton and ntegrate content and demographc nformaton nto a collaboratve flterng framework by usng hgher-order logc dstance computaton approaches. Our experments suggest that HOLCF has mproved accurate recommendatons than propostonal hybrd recommender systems and better scalablty and effcency than frstorder logc hybrd recommender systems. The remander of the paper s organzed as follows. Secton ntroduces the general recommender approaches. The hgher-order logc recommender system HOLCF are dscussed n secton 3. In secton 4, we conduct experments to compare HOLCF to other hybrd recommender systems. Secton 5 concludes our work.. Recommender approaches In ths secton, the fundamental deas behnd three categores recommender systems are dscussed. In a recommender system scenaro, there s a lst of m users U={u 1, u,, u m } and a lst of n tems I={ 1,,, n }. Each user has a ratng vector V, where v,k represents that user s ratng for tem k. (The user s opnon and preference are gven by the ratng score.) The task of recommender system s for a gven actve user (or called target user) u a, (1) to predct the ratng score for an unrated tem k (called the target tem) or () to recommend some tems that may be nterestng to user u a. In ths paper, we wll concentrate on task 1, snce f we can acheve task1, task can be easly acheved wth some subjectve recommendaton strategy..1. Collaboratve flterng There are two types of collaboratve flterng (CF) algorthms, user-based and tem-based. User-based CF algorthms use some statstcal technques to fnd a set of users, called user neghbors for the target user. Then dfferent methods can be adopted to combne the user neghbors ratngs to produce a predcton ratng for the target user. We dscuss n detal tem-based CF algorthms n the followng. Item-based collaboratve flterng algorthms consst of two processes, fndng smlar tems and generatng ratng predcton based on smlar tems ratngs. Many measures can be used to compute the smlarty between tems, for example, cosne smlarty, correlaton-based smlarty and adjusted cosne smlarty. The adjusted cosne smlarty between tem p and q can be computed as follows. m (v u,p v ) ( u vu,q v ) u u 1 sm(, p ) q m (v v ) (v v ) u 1 u,p u u,q Here, s the average ratng of user u. vk After computng the smlarty between tems, a set of most smlar tems to the target tem can be obtaned. Suppose the set s S k. the predcton v a,k, on target tem k for user u a can be computed by adoptng these smlarty and ratngs of u

3 each tem n S K gven by user u a. We use a weghted sum as follows. ( v sm(, )) a,p k p p Sk va,k sm(, ) k p p Sk.. Content-based Recommendatons Content-based methods make recommendatons by analyzng the descrpton of the tems that have been rated by the user and the descrpton of tems to be recommended. A varety of algorthms have been proposed. Many approaches are specalzed versons of classfcaton learners, n whch the goal s to learn a functon that predcts whch class an tem belongs to (.e. ether lked or not-lked). Other algorthms would treat ths as a regresson problem n whch the goal s to learn a functon that predcts a numerc value. There are two mportant sub problems n desgnng a content-based flterng system. The frst s fndng a representaton of tems. The second s to create a profle that allows for target tems to be recommended..3. Demographc-based Recommendatons Demographc nformaton can be used to dentfy the types of users that lke a certan tem, for example, the nformaton on the age, gender, educaton, etc. of users that rated an tem together wth ther ratng of the tem. One mght expect to learn the types of user that lke a certan tem. A demographc-based recommender system attempts to dentfy one of preexstng clusters to whch a user belongs to talor recommendatons to users based upon nformaton about others n ths cluster. 3. Recommender system based on Hgher-order Logc Data Representaton The recommender system HOLCF actually s tem-based collaboratve flterng. One crtcal step n the tem-based collaboratve flterng algorthm s to compute the smlarty between tems. Here, we want to calculate smlarty between tems by adoptng not only ratngs on these tems but also some semantc nformaton about tems. We employ Escher [4, 5], a hgher-order logc declaratve programmng language, to represent tem ndvduals whch nclude all above mentoned nformaton. Furthermore, we use dstance measure over the representaton wth Escher to address exactly the problem of calculate smlarty usng all these nformaton Escher Escher s a strongly typed declaratve programmng language whch ntegrated the best features of both functonal and logc programmng language. It has types and modules, hgher-order and metaprogrammng facltes, concurrency, and declaratve nput/ouput. It combnes the best deas of exstng functonal and logc languages, such as Haskell and Gödel n a practcal and comprehensve way [4]. As the knowledge representaton formalsm, ts basc prncple s that an ndvdual should be represented by a term. In order to descrbe knowledge, t needs the followng syntax: Integers, natural numbers, floats, characters, strngs, and Booleans. Data constructors. Tuples. Sets. Multsets. Lsts. Trees. Graphs. The frst group, called the base types, s the basc buldng blocks for knowledge representaton. The type of ntegers s denoted by Int, the type of natural 3

4 numbers by Nat, the type of floats by Float, the type of characters by Char, the type of strngs by Strng, and the type of Booleans by. Also needed are data constructors for user-defned types. For example, see the data constructors Sunny, Overcast, Ran for the type Outlook n example 1. These data constructors have arty 0 and are usually called constants. Data constructors for more complcated types are also needed and wll be dscussed n the followng. Example 1. Consder the classcal dataset used n machne learnng: playng tenns accordng to the weather. Type weather can be defned as follows. Outlook = Sunny Overcast Ran; Temperature=Hot Mld Cool; Humdty=Hgh Normal Low; Wnd=Strong Medum Weak; Weather=Outlook Temperature Humdt y Wnd Here, Outlook, Temperature, Humdty, Wnd and Weather all are types, each of them s composed wth ts own data constructors. Weather s also a user-defned type whch s composed by types Outlook, Temperature, Humdty and Wnd. Tuples are essentally the bass of the attrbute-value representaton of ndvduals. It s constructed by data constructor. If μ 1,, μ n are types, then μ 1 μ n s a tuple. Set s constructed by data constructor {}. If μ s a type, then {μ} s a set whose elements have type μ. Multsets are a useful generalzaton of sets. A straghtforward approach to multsets s to regard a multset as a functon of type μ Nat, where μ s the type of elements n the multsets and the value of the multset on some tem s ts multplcty, that s, the number of tmes t occurs n the multsets. Lsts are represented usng the followng data constructors. []: Lst μ (:):μ Lst μ Lst μ A lst has a type Lst μ, where μ s the type of the tems n the lst. Lsts are constructed as usual from the empty lst [] and the cons functon (:). The standard representaton of a tree (where the subtrees have an order) uses the data constructor Node, where Node: μ Lst(Tree μ)tree μ Here Tree μ s the type of a tree and Node s a data constructor whose frst argument s the root node and second argument s the lst of subtrees. Graphs are dvded nto undrected Graphs and drected Graphs. The type of an undrected graph s Graph v ε, where v s the type of nformaton n the vertces and ε s the type of nformaton n the edges. Label=Nat Graph v ε={label v} {(Label Nat) ε} The type of an undrected graph s Dgraph v ε, where v s the type of nformaton n the vertces and ε s the type of nformaton n the edges. Dgraph v ε={label v} {(Label label) ε} 3.. Hgher-order logc dstance As each ndvdual s expressed by a term, the dstance on two terms can be defned as follows. Dstance functon d s: d: ß ß R, R denotes the set of real numbers. Here, ß represents a basc term whch s represented wth Escher [6]. Defnton 1. The functon d: ß ß R, s defned nductvely on the structure n ß as follows, let s, t ß, (1) If s, t ß,where =T 1 n, for some T, 1,, n, then If CD, d(s, t)=1, n 1 otherwse, dst (,) (, ) 1 dst where s, s C s 1 s n and t s Dt 1 t m (n m), s 1, s,, s n, t 1, t,, t m all are type, C and D are type constructor. C s 1 s n 4

5 represents a type whch s constructed by s 1 s n under type constructor C. Dt 1 t m have the smlar meanng. ß={t ß t has type more general than }. The ntutve meanng of ß s that t s the set of terms representng ndvduals of type. () If s, t ß, where =, for some,,then B dv ( ( sr), Vtr ( )) dst (,) where, f 1 B dv ( ( sr), Vtr ( )), typed, then represents a multset, each element of whch s type, usually s type Nat. V(t, r) s the value returned when t s appled to r. (3) If s, t ß, where = 1 n, for some 1,, n, then n 1 dst (,) d(, ) n s t where s s (s 1,, s n ) 1 and t s (t 1,, t n ). (4) If there does not exst such that s, tß, then d(s, t)=1. In Part 1 of the defnton, f n=0, then =0. The factor of 1/ means that n 1 d (, ) 1 s t the greater the depth to whch s and t agree, the smaller wll be ther dstance apart. So for lsts, for example, the longer the prefxes on whch two lsts agree, the smaller wll be ther dstance apart. Ths part s the case for complex type s composed by several basc types or userdefned types. It also can be the condton that several complex types compose more complex type. The defnton means that dstance between complex types s determned by dstance between ther subtypes. Also n Part of the defnton, the sum dv ( ( sr), Vtr ( )) s fnte snce s and t r B dffer on at most fntely many r n ß. In the case of sets and multset, dv ( ( sr), Vtr ( )) s the cardnalty of rb the symmetrc dfference of the sets s and t. The part manly s for the case of set and multset. Part 3 s the case for tuple type. Part 4 means that f the types of two ndvduals do not match, the dstance s 1. It should be clear that the defnton of d does not depend on the choce of such that s, t ß. There may be more than one such. What s mportant s only whether has the form T 1 n,, or 1 n. The defnton gven above for d s a general framework. As for specfc applcaton, there are some possbltes. For example, n part 1, a weght w can be set for d(s, t ), d(s, t) can be n (, ) 1w d n s t ( 1 1w ). d(s, t) can be a functon about d( V ( sr), V ( tr)) and satsfy (x)[0. B 1] and (x+y) (x)+(y) n part. It can be proofed that the dstance measure takes values n the range [0, 1] and trangle nequalty holds for t. The smlarty between two ndvduals s 1-d. 4. Experments 4.1. Datasets and Evaluaton Measure Two well-known datasets of move ratng are used n our experments: MoveLens [7] and Book-Crossng [8]. For MoveLens dataset, we extracted a subset of 500 users wth more than 40 ratngs. For Book-Crossng dataset, we extracted a subset of 10,000 users wth more than 40 ratngs. Recommender systems research has used several types of measures for evaluatng the qualty of a recommender system. We use MAE as our choce because t s most commonly used and easest to nterpret drectly. MAE s a measure of the devaton of recommendatons from ther true user-specfed values. For each ratngs-predcton par <p, q > ths metrc treats the absolute error between them, 5

6 .e., p -q equals. The MAE s computed by frst summng these absolute errors of the N correspondng ratng-predcton pars and then computng the average. Formally, N 1 p MAE q N The lower the MAE, the more accuracy the recommendaton system predcts user ratngs. 4.. Experments Results We compared HOLCF to standard collaboratve flterng approaches, ncludng user-based Pearson Correlaton Coeffcent (User-Based), tem-based approach (Item-Based) whch only use collaboratve nformaton [9] and nductve learnng approach (IL) whch use collaboratve and content nformaton [].The results of our experments are shown n Fg. 1. Our experments suggest that the effectve combnaton of varous knds of nformaton based on relatonal dstance approaches provdes mproved accurate recommendatons than other approaches. MoveLens Book-Crossng User-Based Item-Based IL HOLCF Fg. 1: Expermental result. 5. References [1] Pazzan, M. J. A Framework for Collaboratve, Content-Based and Demographc Flterng. Artf. Intell. Rev. 13, [] C.Basu, H.Hrsh and W.Cohen. Recommendaton as classfcaton: usng socal and content-based nformaton n recommendaton. In Proceedngs of the Ffteenth Natonal/Tenth Conference on Artfcal ntellgence/nnovatve Applcatons of Artfcal ntellgence, Menlo Park, CA, [3] Toward the Next Generaton of Recommender Systems: A Survey of the State-of-the-Art and Possble Extensons. IEEE Trans. on Knowl. and Data Eng. 17, [4] J.W.Lloyd. Declaratve Programmng n Escher. Techncal Report CSTR , Department of Computer Scence. Unversty of Brstol, [5] P.A.Flach, C.Graud-Carrer and J.W.Lloyd. Strongly Typed Inductve Concept Learnng. In Proceedngs of the Eghth Internatonal Conference on Inductve Logc Programmng. LNAI 1446, Sprnger-Verlag, pp [6] J.W.Lloyd. Logc for Learnng: Knowledge Representaton, Computaton and Learnng n Hgher-order Logc. Sprnger-Verlag Berln and Hedelberg GmbH & Co. KG, 00. [7] MoveLens dataset : GroupLens/ [8] Book-Crossng dataset: [9] Sarwar B., Karyps G., Konstan J., and Redl J Item-based collaboratve flterng recommendaton algorthms. In Proceedngs of the 10th nternatonal Conference on World Wde Web (Hong Kong, Hong Kong, May 01-05, 001). WWW '01. ACM, New York, NY, DOI= [10] x.asp. 6

For instance, ; the five basic number-sets are increasingly more n A B & B A A = B (1)

For instance, ; the five basic number-sets are increasingly more n A B & B A A = B (1) Secton 1.2 Subsets and the Boolean operatons on sets If every element of the set A s an element of the set B, we say that A s a subset of B, or that A s contaned n B, or that B contans A, and we wrte A