The Discovery of Action Groups for Smart Home

Transcription

1 The Dscovery of Acton Groups for Smart Home Hsen-Chou Lao,* Bo-Yu La Sheng-Che Hsao Department of Computer Scence and Informaton Engneerng Chaoyang Unversty of Technology Wufong Townshp, Tachung County, Tawan Department of Informaton and Computer Educaton Natonal Tawan Normal Unversty Tape Cty 06, Tawan Receved August 006; Revsed 0 December 006 ; Accepted 8 January 007 Abstract: The concept of a smart home has been dscussed n recent years. Its prmary purpose s to make lfe more convenent, safe, and fun n varous areas, ncludng home automaton, securty, entertanment, and so on. In order to automate the nteractons between the nhabtants and devces n a home, the predcton of the nhabtant s actons s very mportant. Current predcton algorthms are usually based on the order of actons to be taken. However, the predcton accuracy of those algorthms s not satsfactory. Ths s because actons can be separated nto a set of groups, and actons n the same group are usually taken n an almost arbtrary order. The set of groups should be dscovered before the predcton of actons. In ths paper, an acton group dscovery (AGD) algorthm s proposed. The AGD algorthm s based on the -order Markov model and a reverse -order Markov model. Accordng to the combnaton of the two models, a set of group pars s generated. Then, the acton groups are generated by mergng these group pars. A group dscovery rate (GDRate) s defned to evaluate the effcency of the AGD algorthm. Expermental results show that the AGD algorthm can dscover most acton groups n varous stuatons. The AGD algorthm s thus helpful for predctng actons. Keywords: acton group dscovery, acton predcton, smart home, Markov model Introducton The evoluton of electronc hardware n sze and cost has made avalable the opportunty for equppng nexpensve devces n homes. Many next-generaton nformaton applances (IAs) are equpped wth processors for sophstcated communcaton and control capabltes among themselves and wth the outsde world. The prmary purpose of these devces and nterconnected IAs s to support smart servces. One of the mportant servces s home automaton,.e., the automaton of nteractons between nhabtants and devces. Home automaton manly reles on two knds of nformaton: an nhabtant s acton and locaton. The actons are those nteractons between an nhabtant and the home applances and devces. A seres of actons forms an acton sequence. Some researches have focused on the dscovery of sgnfcant patterns from an acton sequence for home automaton. For example, E. O. Heerman and D. J. Cook proposed a novel data-mnng algorthm, called Epsode Dscovery (ED), whch dscovers behavor patterns wthn an acton sequence n a smart home [- ]. The authors also proposed a Smart Home Inhabtant Predcton (SHIP) algorthm to predct the most lkely next acton [3]. SHIP matches the most recent actons wth a collected acton sequence. In expermental results, the greatest predcton accuraces for two data sets were 33.3 percent and 53.4 percent. Obvously, the predcton accuracy of SHIP s not hgh enough for use n a smart home. On the other hand, the Markov model s generally used n the predcton of Web page access [4-5]. In attemptng to utlze the Markov model to ncrease predcton accuracy, we dscover what s requred to predct actons accurately. Unlke Web page access, n whch a user must follow a specfc order to access desred Web pages, an nhabtant of a home may take a set of actons n dfferent orders. Assume that there are three actons to be taken: turnng on an ar condtoner (ArCondtonerOn), turnng on a desk lght (DeskLghtOn), and turnng on a computer (ComputerOn). The orders of the actons could be (DeskLghtOn, ComputerOn, ArCondtonerOn), (ArCondtonerOn, DeskLghtOn, ComputerOn), or (ComputerOn, ArCondtonerOn, DeskLghtOn). There are * Correspondence author

2 Journal of Computers Vol.8, No., July 007 sx possble orders,.e., permutatons, for three actons. Assume they have the same frequency to be taken. When the frst of the three actons s taken, the predcton accuracy of the most lkely next acton s only 50 percent. The more actons there are n a set, the smaller the predcton accuracy wll be. Beng able to correctly predct the order of actons determnes predcton accuracy n a smart home. Therefore, the most mportant thng before startng to predct actons s the dscovery of the actons that may be taken together. These actons that are taken together are defned as an acton group. In ths paper, we propose an Acton Group Dscovery (AGD) algorthm. The AGD algorthm s manly based on a postve and reverse -order Markov model constructed from an acton sequence. The two models are combned and a set of group pars s generated from the combned model. Acton groups are generated by mergng the group pars. In order to evaluate the effcency of the AGD algorthm, an acton sequence generator (ASG) s desgned and mplemented. A set of parameters, such as loss rate, nterlace count, and so on, are defned to generate possble sequences n the real world. A group dscovery rate (GDRate) s also defned to measure the effcency of the AGD algorthm. The expermental results show that the AGD algorthm can dscover most of the acton groups n varous stuatons. The rest of the paper s organzed as follows. Secton revews works related to smart homes. Secton 3 presents our methods, ncludng the postve and reverse -order Markov models, and the AGD algorthm. Secton 4 explans why and how the set of parameters of the ASG s defned and mplemented, such as loss rate, nterlace count, and so on. Secton 5 descrbes the experment desgn and results. Secton 6 gves the concluson of ths paper. Related works The researches related to smart homes can be classfed nto the followng categores. The frst category focuses on network communcaton and resource management. In a smart home, network communcaton s concerned wth communcaton among nformaton systems, ubqutous sensors, home applances, and so on. For example, Y. J. Ln et al. focused on power-lne communcaton and proposed a network nfrastructure for smart homes [6]. The network nfrastructure uses power-lne LANs for buldng ntegrated smart homes. All nformaton applances can be seamlessly nterconnected usng electrc wres. The nfrastructure can also guarantee QoS for realtme communcaton. On the other hand, the management of resources, such as power, storage, computng resources, and so on, s also an mportant concern. For example, A. Roy et al. proposed a locaton-awareness resource optmzaton scheme [7]. The asymptotc equpartton property (AEP) n nformaton theory s used to capture an nhabtant s typcal path segments. Reservng resources and actvatng devces are only along a typcal path n order to mnmze overall energy consumpton. The second category focuses on system archtecture and programmng envronments. Varous system archtectures have been proposed for smart homes. For example, R. Kango et al. proposed the ELIMA (Envronmental Lfe cycle Informaton Management and Analyss system) system [8]. ELIMA was proposed to promote smart servces based on the connected home applances. Therefore, a so-called ubqutous culture can be realzed n the future. D. Valtchev and I. Frankov proposed a servce gateway archtecture for smart homes [9]. Ths archtecture emphaszes the realzaton of an effectve and realstc gateway management system. It s based on the work of the Open Servce Gateway Intatve (OSG). Some researches focused on the programmng envronment to ncrease the abstracton level, thus ncreasng the effcency of systems development. For example, H. Jahnke and J. Ster focused on the key programmng challenges for smart homes, such as customzablty and extensblty. They proposed a vsual tool, called a mcrocommander, to rapdly program synergetc devces [0]. The thrd category focuses on smart servces and applcatons. One mportant servce and applcaton n ths category s the care of the elderly. For example, V. Stanford bult a pervasve computng envronment for the care of the elderly []. Three knds of data are gathered n the envronment: health vtals, nputs/outputs, and movement. The data offers effcent care allocaton for resdents. S. Helal et al. also bult a smart home nfrastructure for the elderly []. A precson n-door trackng system based on ultrasonc sensor technology was desgned nto the nfrastructure. Three applcatons, remote montorng, attenton capture, and ndoor blnd gudance, were mplemented to llustrate that many applcatons were enabled by the nfrastructure. The last category focuses on locaton detecton and acton predcton. They are essental for smart homes. If the most lkely next locaton and acton of nhabtants can be predcted precsely, the home can be automated and provde many smart servces. In addton to acton predcton of MavHome n [-3], S. P. Rao and D. J. Cook also proposed a smple Markov model [3]. Smple Markov model s an enhancement of Task-based Markov model (TMM). It categorzes actons nto abstract tasks and uses ths nformaton to make predcton. In the experment for real data, the predcton accuracy s smaller than 5 percent. The nterleaves of actons from dfferent tasks causes that the acton sequence s unable to dvde nto tasks exactly. It emphaszes the mportance on dscoverng of acton groups for ncreasng the predcton accuracy. Besdes, N. Noury, G. Vrone, and T. 08

3 Lao, La, and Hsao: The Dscovery of Acton Groups for Smart Home Creuzet proposed a rule-based system to nfer the best poston nsde the health-ntegrated smart home nformaton system (HIS ) [4]. The spaces n smart homes are classfed nto three categores: communcaton (e.g., entrance), exchange (e.g., corrdor), and destnaton (e.g., bedroom). Three types of sensors can be used to detect an nhabtant n a locaton. A set of rules based on the status of sensors s used to determne the nhabtant s poston. The set of rules are Boolean equatons that can easly be mplemented nto the memory of a low power mcro-controller. Many researches related to smart home are stll beng undertaken. People spend more tme n ther homes than n any other places. The ultmate goal of these works s to provde a safe, comfortable envronment for people to relax, communcate, or learn. 3 Methods 3. Postve and Reverse -order Markov Model Tradtonal Markov models are often employed to predct user access behavor. For the predcton of the next Web page a user would most lkely access, the tradtonal Markov model matches a user s current access sequence wth the user s hstorcal Web access sequences [4-5]. The order of the Markov model s defned as the length of suffxes of the user s current access sequence for matchng. The 0-order Markov model s uncondtonal probablty p ( xn) = Pr( X n ), whch s the page access probablty. The -order Markov model focuses on the trans- p x x = Pr X = x X =. ton probablty between pages: ( ) ( ) x The constructon of the -order Markov model s llustrated n Fg.. There are fve pages denoted {A, B, C, D, E}. A sample access sequence s lsted n Fg. (a). If the possble pages after page B are consdered, there are fve transtons, whch are marked by an underlne. Among these fve transtons, the transton probabltes of pages C, D, and E are 0.4,, and 0.4, respectvely. All the transton probabltes of the fve pages are computed separately. The constructed -order Markov model s represented n Fg. (b). An alternatve representaton of the constructed model s depcted n Fg. (c). In Fg. (c), the -order Markov model s represented n a tabular form. The frst column shows the current page, and the top row gves the next page. The transton probabltes n Fg. (b) are flled n the correspondng cells n Fg. (c). Therefore, the most lkely next page followed by a specfc page can be determned from ths table. For example, f the current page s D, the next page s most lkely C snce the correspondng transton probablty s hgher than that from D to B or D to E. The -order Markov model above s defned as postve snce the most lkely next page s predcted based on the current page. Here, a reverse -order Markov model s ntroduced. For the reverse -order Markov model, the most lkely prevous page of the current acton s computed based on the same prncple but n the reverse drecton. For the same example n Fg., the constructon of the reverse -order Markov model s llustrated n Fg.. {B, C, D, B, D, E, D, C, D, C, A, B, E, A, E, B, E, B, C, D} (a) A B C 5 E D 0.75 Next Current A B C D E A 0 (/) 0 0 (/) B (/5) (/5) 0.4(/5) C 5(/4) (3/4) 0 D 0 (/5) 0.4(/5) 0 (/5) E 5(/4) (/4) 0 5(/4) 0 (b) Fg.. (a) A sample access sequence (b) -order Markov model (c) Alternatve representaton of the model (c) 09

4 Journal of Computers Vol.8, No., July 007 {B, C, D, B, D, E, D, C, D, C, A, B, E, A, E, B, E, B, C, D} (a) A B C 5 E (b) 0.6 D Prevous Current A B C D E A 0 0 (/) 0 (/) B (/5) 0 0 (/5) 0.4(/5) C 0 (/4) 0 (/4) 0 D 0 (/5) 0.6(3/5) 0 (/5) E 5(/4) (/4) 0 5(/4) 0 (c) Fg.. (a) A sample access sequence (b) Reverse -order Markov model (c) Alternatve representaton of the model Accordng to the constructed reverse -order Markov model, the page n front of page B s most lkely page E. The postve and reverse -order Markov model can be used to predct the most lkely page before and after a specfc page. The access sequence of web pages s used as an example for llustratng the constructon of the reverse -order Markov model. However, the reverse model may be meanngless for the predcton of a web page snce web pages cannot be browsed n reverse order. On the other hand, the reverse model s manly used n the dscovery of acton groups. If the access sequence n Fg. and s the acton sequence n a smart home, the reverse model can be used to know the most lkely acton before a specfc acton. For a group of actons, an nhabtant usually takes these actons n dfferent orders. The reverse -order Markov model becomes useful for acton group dscovery. For example, n Fg. (c), the next acton of acton C s most lkely D. In Fg. (c), the prevous acton of acton D s most lkely C. By examnng the acton sequence,.e., access sequence, n Fg. (a), we found that the actons C and D are taken together but n a dfferent order. The basc prncple of AGD s based on the combnaton of the postve and reverse Markov models for dscoverng possble acton groups. The AGD algorthm s presented n the next secton. Acton sequence Construct postve -order Markov model Construct of reverse -order Markov model Combne postve and reverse -order Markov models Generate group pars Merge group pars Acton groups Fg. 3. The process of AGD 0

5 3. The Prncple of AGD Lao, La, and Hsao: The Dscovery of Acton Groups for Smart Home The process of AGD s shown n Fg. 3. The nput for AGD s an acton sequence. The postve and reserve - order Markov models are constructed separately accordng to the sequence. Then the two models are combned and group pars are generated from the combned model. Fnally, the acton groups are obtaned by mergng the group pars. The set of dstnct actons n the acton sequence s denoted as A={a, a, a 3,, a n }. For the postve -order Markov model, an acton a and each acton a j n A s assocated wth a transton probablty ( a j a ) order to dstngush the probablty n the reverse -order Markov model, Pr ( a j a ) s denoted as Ppos ( a j a ) acton a j and the assocated transton probablty ( ) a j a of a are collected nto a set denoted as Pos. Ppos are combned nto a par [ a, Ppos( a a) ] For the reverse -order Markov model, the par of an acton a s denoted as [ a, Prev( a a) ] are collected nto a set denoted as Rev. The equatons for Pos Rev = = Pos and {[ a, Ppos( a a) ],[ a, Ppos( a a) ],...,[ an, Ppos( an a) ]} {[ a, Prev( a a )], [ a, Prev( a a) ],...,[ a, Prev( a a) ]} n Rev are shown as follows: n j j j Pr [5]. In j. The. The n pars. The n pars of a The combnaton of the postve and reverse -order Markov models s the combnaton of Pos and Rev for each acton a ( n ). The probablty of Ppos ( a a j ) s equal to op j t, where op j s the number of tmes that a j follows a, and t s the total number of occurrences of a. Smlarly, the probablty of Prev ( a j a ) s equal to or t, where or j s the number of tmes that a j s n front of a. The equaton () s rewrtten as equaton (). j Pos Rev = = {( a, op t)(, a, op t),...,( an, opn t) } {( a, or t )(, a, or t ),...,( a, or t )} n Then the combnaton of Pos and Rev, denoted as Cmb, s equvalent to the combnaton of opj t and orj t for j n. Accordng to the prncple of condtonal probablty, the combnaton of opj t and or j t equals the sum of op j and or j dvded by two tmes t. The equaton s shown below: Cmb =..., [ a, ( op + or ) ( t) ], [ a,( op + or ) ( t )], [ ( ) ( )] an, opn+ orn t Cmb represents the condtonal probabltes that every acton a j occurs ether before or after acton a. After the postve and reverse models are combned, the next step s the dscovery of acton groups. It conssts of two substeps. The frst sub-step s the generaton of group pars; the second s the mergng of group pars. A group par ( ) a j a, s a par where the acton a j s assocated wth a value hgher than others n Cmb. The same example shown n Fg. and s used to llustrate the generaton of group pars. The access sequence of web pages s smlar to the acton sequence n a home. Assume the sequence n Fg. and s an acton sequence. The combnaton of two models n Fg. and s shown n Table (a). In Table (b), the pars of Pos 3 and Rev 3 come from the tables n Fg. (c) and (c). They are sorted accordng to the assocated probablty for the later process. The combnaton of Pos 3 and Rev 3,.e., Cmb 3, s sorted, too. The dfferences of assocated probablty between two successve pars are computed and lsted n the table. The smlar results of Cmb 4 are lsted n Table (c). When observng the sample acton sequence n Fg., t can be seen that the actons C (a 3 ) and D (a 4 ) are taken successvely but not n the same order. Therefore, the par wth acton D n Table (b) has the hgher value among the pars n Pos 3 and Rev 3, and the par wth acton C n Table (c) has the hghest value among the pars the postve and reverse models n Pos 4 and Rev 4. Ths means that the actons could be n the same group. The combnaton of the two models causes the par (D, 0.65) n Cmb 3 and (C, ) n Cmb 4 to have values hgher than the others. n () () (3)

6 Journal of Computers Vol.8, No., July 007 Table. (a) The combned example of Actons (a ) Cmb A (a ) {(A,0), (B,/4), (C,/4), (D,0), (E, /4)} B (a ) {(A,/0), (B,0), (C,/0), (D,/0), (E, 4/0)} C (a 3 ) {(A,/8), (B,/8), (C,0), (D,5/8), (E, 0)} D (a 4 ) {(A,0), (B,/0), (C,5/0), (D,0), (E, /0)} E (a 5 ) {(A,/8), (B,4/8), (C,0), (D,/8), (E, 0)} (b) The dfferences of pars n Cmb 3 Rank Pos 3 Rev 3 Cmb 3 Dff. (D, 0.75) (B, ) (D, 0.65) (A, 5) (D, ) (B, 5) (B, 0) (A, 0) (A, 0.5) (C, 0) (C, 0) (A, 0) 0 5 (E, 0) (E, 0) (D, 0) - (c) The dfferences of pars n Cmb 4 Rank Pos 4 Rev 4 Cmb 4 Dff. (C, 0.4) (C, 0.6) (C, ) 0.3 (B, ) (B, ) (B, ) 0 3 (E, ) (E, ) (E, ) 4 (A, 0) (A, 0) (A, 0) 0 5 (D, 0) (D, 0) (D, 0) - Although the combnaton causes those pars whose actons may be n the same group to be ranked n front of the sorted lst of Cmb, the next step s to determne how many pars could be ncluded n the group pars. Here, a threshold s defned for ths purpose. By observng the sorted lst of Cmb n Table (b) and (c), there s a large dfference between the assocated values of the pars that could be ncluded n the group pars and the others. Therefore, the threshold s defned as the largest value among the dfferences of two successve pars n Cmb. In Table (b) and (c), the threshold of Cmb 3 and Cmb 4 s and 0.3, respectvely. Those actons of the pars n front of the threshold are ncluded n the group pars. Thus, the group pars, (C, D) and (D, C), are generated from Cmb 3 and Cmb 4, respectvely. After group pars of all the Cmb are generated, the acton group can be dscovered accordng to the followng algorthm: Algorthm Merge_Group_Pars(GP) Input: GP (a set of generated group pars) 0Output: AG (a superset of acton groups) begn AG := ; repeat get one group par (a, a J ) from GP f a or a J an acton group ag n AG then end else ag := ag { } a j a, ; AG := AG { } a, ; a j remove (a, a J ) from GP untl GP = Fg. 4. The algorthm for dscoverng acton groups by mergng group pars

7 Lao, La, and Hsao: The Dscovery of Acton Groups for Smart Home Table 3. An example of dscoverng acton groups from group pars Iteraton GP AG 0 {(a, a 3 ), (a, a 4 ), (a 3, a ), (a 4, a ), (a 4, a 5 )} {(a, a 4 ), (a 3, a ), (a 4, a ), (a 4, a 5 )} {{a, a 3 }} {(a 3, a ), (a 4, a ), (a 4, a 5 )} {{a, a 3 },{a, a 4 }} 3 {(a 4, a ), (a 4, a 5 )} {{a, a 3 },{a, a 4 }} 4 {(a 4, a 5 )} {{a, a 3 },{a, a 4 }} 5 {{a, a 3 },{a, a 4, a 5 }} GP s a set of generated group pars. An acton group s a set of actons. AG s the superset of the entre acton group. It s ntally assgned to an empty set. For each group par n GP, the two actons makng up the par are checked to determne whether one of the actons s ncluded n any acton group n AG. If t s true, the other acton s added to the same acton group. Otherwse, a new acton group wth the two actons s added to AG. After all the group pars n GP are checked, the fnal AG contans the entre acton groups dscovered. Table 3 shows an example that llustrates the above algorthm. In the above example, although acton a does not have a group par to assocate wth a 5 drectly, a and a 5 are stll ncluded n the same acton group va another acton a 4. Ths means that AGD can dscover an acton group wthout any par of actons beng ncluded n the group par. A more complex example used to llustrate the process of AGD s shown n Fg. 5. Fg. 5 (a) shows a partal postve -order Markov model constructed from an acton sequence. Only op j of the transton probablty s marked on the lnk for better readablty. Fg. 5 (b) shows a partal reverse model. Smlarly, only or j s marked on the lnk. Fg. 5 (c) shows the combnaton of the two models. The labels on the lnks are the summaton of the labels on the correspondng lnks of the two models. The group pars are marked by bold lnks, and the dscovered acton group s marked by the gray area, as shown n Fg. 5 (d). 4 Fg. 5. An example of acton group dscovery (a) a partal postve -order Markov model (b) a partal reverse -order Markov model (c) a combnaton of the two models (d) the dscovered acton group s marked by the gray area 3

8 3 Acton Sequence Generator Journal of Computers Vol.8, No., July 007 In order to evaluate the performance of AGD, an acton sequence generator (ASG) s used. The purpose of an ASG s to provde parameters for generatng dverse acton sequences. The parameters come from the followng observatons of actons taken n real lfe. Frst, there are dfferent lengths of acton sequences, szes of acton groups, and szes of actons per group. Second, people may take the actons of a group n any order, and partal actons of a group may not be taken. Fnally, people may take the actons of another group before fnshng the actons of current group. Therefore, partal actons of two groups may be nterlaced on the boundary of two groups when people swtch from one group to another. Accordng to the above observatons, the parameters of ASG are lsted as follows: Group sze: the sze of possble acton groups Actons per group: the sze of actons n a group. Total actons: the total actons to be generated n an acton sequence. Loss rate: a value from zero to to ndcate the maxmum rato of actons that do not have to be taken,.e., loss n the actons taken. Interlace count: the maxmum number of actons to be nterlaced wth the actons of the next group. Table 4. The examples of loss rate and nterlace count (a) The possble results wth dfferent loss rate Acton group={a, a, a 3, a 4, a 5 } Acton orders Loss rate Results a 3, a, a 4, a, a 5 0 a 3, a, a 4, a, a 5 a 4, a 5, a 3, a, a a, a 4, a 5, a, a a 4, a 5, a 3, a, a a 4, a 5, a 3, a a, a 4, a 5, a, a 3 a, a 4, a 5, a a, a 4, a 5 (b) The possble results wth dfferent nterlace count Acton group A Acton group B Interlace count Results a 3, a, a 4, a, a 5 b, b 4, b, b 3 0 a 3, a, a 4, a, a 5, b, b 4, b, b 3 a 4, a 5, a 3, a, a b 3, b, b 4, b a, a 4, a 5, a, a 3 b 4, b 3, b, b a 3, a, a 4, a, a 5, b, b 4, b, b 3 a 4, a 5, a 3, a, b 3, a, b, b 4, b a 3, a, a 4, a, a 5, b, b 4, b, b 3 a 4, a 5, a 3, a, b 3, a, b, b 4, b a, a 4, a 5, b 4, a, b 3, a 3, b, b (c) The mxture of loss rate (0.4) and nterlace count () Possble results of acton group B Possble results of acton group A b 4, b 3, b, b b 4, b 3, b a, a 4, a 5, a, a 3 a, a 4, a 5, a a, a 4, a 5, a, a 3, b 4, b 3, b, b a, a 4, a 5, a, b 4, a 3, b 3, b, b a, a 4, a 5, b 4, a, b 3, a 3, b, b a, a 4, a 5, a, b 4, b 3, b, b a, a 4, a 5, b 4, a, b 3, b, b a, a 4, a 5, a, a 3, b 4, b 3, b a, a 4, a 5, a, b 4, a 3, b 3, b a, a 4, a 5, b 4, a, b 3, a 3, b a, a 4, a 5, a, b 4, b 3, b a, a 4, a 5, b 4, a, b 3, b a, a 4, a 5 a, a 4, a 5, b 4, b 3, b, b a, a 4, a 5, b 4, b 3, b 4

9 Lao, La, and Hsao: The Dscovery of Acton Groups for Smart Home Here, three examples are used to llustrate the loss rate and nterlace count. In Table 4 (a), the acton group conssts of fve actons. Three orders are assocated wth dfferent loss rates. When the loss rate equals, the maxmum number of actons that may not be taken s one (5 actons = ). Therefore, there are two possble results. Smlarly, there are three possble results when the loss rate s 0.4. In Table 4 (b), t s assumed that acton group A s followed by group B at a specfc tme. When the nterlace count equals zero, the result s the concatenaton of groups A and B wthout any nterlacng. When the nterlace count s one, t means that at most one acton can be nterlaced wth the actons of the next group. Thus, there are two possble results. In Table 4 (c), the loss rate and nterlace count equals 0.4 and, respectvely. The frst column and the frst row are the possble results of acton groups A and B wth the loss rate 0.4. The fnal results of the sx dfferent combnatons are shown n the correspondng column and row. If the number of group A s loss actons are greater than or equal to the nterlace count, there s no nterlacng n the fnal result. Such a stuaton can be found n the last row. The ASG algorthm for generatng an acton sequence, accordng to the above parameters, s shown n Fg. 6. In the ASG algorthm, some actons at the tal end of the current group must nterlace wth the actons of the next group. However, the next group s unknown n the current teraton. The sequence pre_a and a varable pre_c are used to store these actons n the next teraton. In the ASG algorthm, some actons at the tal end of the current group must nterlace wth the actons of the next group. However, the next group s unknown n the current teraton. The sequence pre_a and a varable pre_c are used to store these actons n the next teraton. Algorthm Generate_Acton_Sequence(gs, apg mn, apg max, ta, loss, c) Input: gs (group sze), apg mn, apg max (the mn and max values of actons per group), ta (total actons), loss (loss rate), and c (nterlace count) Output: AS (the acton sequence) begn AS := <>; {empty sequence} determne the number of actons for each group by choosng between apg mn and apg max randomly pre_c := 0 ; {the desgnated nterlace count of the prevous group} pre_a := <> ; {the actons sequence of the prevous group to be nterlaced} repeat choose a group g randomly p := a random permutaton of the actons n g ; n := loss number of actons n g ; choose a number n between 0 and n ; remove n actons from the tal of p f pre_c > 0 then p := merge pre_a and p by nterlacng actons n pre_a and the frst pre_c actons n p f (c n ) 0 then pre_c := 0 ; else pre_c := c n ; pre_a := pre_c actons from the tal of p remove pre_c actons from the tal of p AS := AS ^ p ; {concatenaton of AS and p} untl sze(as) ta end Fg. 6. The ASG s algorthm for generatng acton sequence 5

10 Journal of Computers Vol.8, No., July 007 Fg. 7. A screen shot of the acton sequence generator ASG s mplemented by usng VB.Net, accordng to the above algorthm. A screen shot s shown n Fg. 7. All the parameters are lsted on the left-hand sde. After ther values are entered, users can clck the Generate button to generate an acton sequence. The generated sequence s shown on the rght-hand sde. Users can clck the Save button for later analyss. A Clear button can be used to clear the current sequence for generatng a new one. Practcally, a behavor watcher or tracer must be nstalled to collect the real actons that are nvoked n a home envronment. The real acton may nclude the related nformaton, such as devce dentfer, locaton, state, happenng tme, etc. Although the happenng tme or locaton s helpful for the acton group dscovery, the ASG only focus on the devce dentfer. The AGD algorthm s manly desgned to dscover acton groups from the sequence of devce dentfer. 4 Expermental Study In order to evaluate the effectveness of the AGD algorthm on acton group dscovery, an experment was desgned. A group dscovery rate (GDRate) was defned to represent the effectveness of the AGD algorthm. The GDRate s the percentage of acton groups dscovered correctly. Its formula s shown below: number of acton groups dscovered correctly GDRate = 00% (4) total number of acton groups Fve experments were desgned to measure the GDRate of the AGD algorthm nfluenced by the followng parameters below: Total actons vs. GDRate Loss rate vs. GDRate Interlace count vs. GDRate Actons per group vs. GDRate Group sze vs. GDRate The parameter settngs of the fve experments are lsted n Table 5. These settngs were based on an nhabtant s possble behavor n a home. For example, the range of actons per group s from two to fve actons. These are reasonable values based on our observaton n real lfe. 6

11 Lao, La, and Hsao: The Dscovery of Acton Groups for Smart Home For each experment, ten dfferent acton sequences were generated for each combnaton of parameter values. The fnal GDRate was the average of the group dscovery rate of the ten sequences. The expermental results are shown n the followng fgures. The frst expermental result s shown n Fg. 8. The x-axs represents the total number of actons from 00 to,000. The y-axs represents the GDRate. Four dfferent curves represent the results wth the loss rates 0,, 0.4, and 0.6. Accordng to the fgure, the GDRate approaches 90% when the total number of actons s greater than or equal to 700. In addton, there s no obvous dfference wth the GDRates for four dfferent loss rates. Although partal actons of a group are lost n the acton sequence, the AGD algorthm can stll dscover most of the acton groups successfully. The second expermental result s shown n Fg. 9. The x-axs represents the loss rates from zero to 0.9. The y- axs represents the GDRate. Three dfferent curves represent the results wth the total number of actons of 300, 500, and 700. Theoretcally, the ncrease of loss rate should cause the GDRate to decrease. However, ths does not occur, accordng to the fgure. Ths means that the AGD algorthm does not suffer from an ncrease of loss rate. Table 5. The parameter settngs of fve experments Parameters Experments A. Total actons vs. GDRate B. Loss rate vs. GDRate C. Interlace count vs. GDRate D. Actons per group vs. GDRate E. Group sze vs. GDRate Total Actons Loss Rate Interlace Count Actons per Group Group Sze 00, 00,, 000 0,, 0.4, , 500, 700 0, 0.,, , 500, ,,, 3, 4, , 00,, , 3, 4, , 00,, , 0, 5, GDRate (%) Loss Rate Total Number of Actons Fg. 8. Total number of actons vs. GDRate 7

12 Journal of Computers Vol.8, No., July GDRate (%) Total Actons Loss Rate Fg. 9. Loss rate vs. GDRate GDRate (%) Total Actons Interlace Count Fg. 0. Interlace count vs. GDRate The thrd expermental result s shown n Fg. 0. The x-axs represents the nterlace count from zero to fve. The y-axs represents the GDRate. Three dfferent curves represent the results wth the total number of actons of 500, 000, and 500. The curves show that the GDRate decreases rapdly as the nterlace count ncreases. The settng of the nterlace count causes the pror and later actons to be nterlaced wth actons of other groups n the acton log. If the nterlace count equals two, four actons of a group are nterlaced wth other groups. Ths prevents the dscovery of acton groups. Therefore, the GDRate approaches zero when the nterlace count s greater than two. In real lfe, f the actons of groups are nterlaced less frequently, the AGD algorthm can stll dscover most of the acton groups. 8

13 Lao, La, and Hsao: The Dscovery of Acton Groups for Smart Home GDRate (%) Actons per Group Total Number of Actons Fg.. Actons per group vs. GDRate The fourth expermental result s shown n Fg.. The x-axs represents the total number of actons from 00 to,000. The y-axs represents the GDRate. Four dfferent curves represent the GDRate wth actons per group of two, three, four, and fve. When the actons per group equal two, three, and four, the GDRate can reach up to 80 percent when the total number of actons are approxmately 40, 380, and 700, respectvely. The curves show hat the more actons per group there are, the more total number of actons s needed for dscoverng all the acton groups correctly. The relatonshp between the actons per group and the total number of actons can be seen n Table 6. In Table 6, the data of the frst three rows were computed accordng to the curves n Fg.. The last row s a predcted result based on the frst three columns. The column of dstnct actons was computed by multplyng the actons per group by 0 groups. The approxmate total number of actons for the GDRate equalng 80 percent s lsted n the thrd column. The average number of tmes an acton appears n the approxmate total number of actons s shown n the fourth column. The ratos of the average numbers 6.3 and.6 to 3.5 are lsted n the last column. The rato for fve actons per group, accordng to the ncreasng trend of the ratos, was calculated usng lnear approxmaton. The predcted total actons were,733. Ths shows that when the actons per group are ncreased by one, the total number of actons must be ncreased by about.7 tmes to acheve the same GDRate. Table 6. The relatons between actons per group and total actons Actons per group Dstnct actons Approxmate total number of actons for GDRate=80% Average number of tmes Rato 40 ( actons 0 groups) (3 actons 0 groups) (4 actons 0 groups) (5 actons 0 groups) 733 (predcted)

14 Journal of Computers Vol.8, No., July GDRate (%) Group Sze Total Number of Actons Fg.. Group sze vs. GDRate The ffth expermental result s shown n Fg.. The x-axs represents the total number of actons from 00 to,000. The y-axs represents the GDRate. Four dfferent curves represent the GDRate wth the group szes 5, 0, 5, and 0. The curves show that the more group szes there are, the more total number of actons s needed for dscoverng most of the acton groups. The GDRate s over 90 percent for all the four dfferent group szes whle the total number of actons s larger than 700. If the acton sequence s ncreased by a rate of 50 actons per day, 4 days are needed to collect 700 actons. Ths s acceptable for nhabtants to allow the AGD algorthm to dscover ther acton groups. The effcency of the AGD algorthm, accordng to the above expermental results, s summarzed as follows: The GDRate of the AGD algorthm can reach 80 percent for 600 actons, accordng to the frst expermental result. The larger the actons per group or group szes there s, the longer the acton sequence s needed to reach a certan GDRate. The AGD algorthm can stll dscover acton groups wthout beng nfluenced by the loss rate. On the other hand, the alternaton of acton groups has a great mpact on the GDRate. Ths means that the dscovery of acton groups from an acton sequence wth ncomplete nformaton s much easer than that wth complete but faulty nformaton. In advance, a realstc evaluaton s also obtaned here. A real human acton sequence was recorded va a moble devce for three months. There were 9 dstnct actons and,59 actons collected n the sequence. After the process of AGD, three groups (total seven actons) were dscovered and verfed by the user successfully. However, these 9 actons are dstrbuted n a three-floor buldng. There are only seven actons average n a floor. It decreases the possble number of acton groups to be dscovered. Although the number of dscovered groups s small, t llustrates that AGD s work on dscoverng acton groups. 0

15 5 Concluson and Future Work Lao, La, and Hsao: The Dscovery of Acton Groups for Smart Home An nhabtant s nteractons wth devces n a smart home are usually n an arbtrary order. In fact, these actons form a set of acton groups. The set of groups should be dscovered before the acton predcton n order to ncrease the predcton accuracy. In ths paper, AGD algorthm s proposed to dscover the acton groups from the acton sequence. It s manly based on the postve and reverse -order Markov models. The expermental results show that the AGD algorthm can dscover most acton groups n varous stuatons. In the future, a group predcton approach based upon the acton groups wll be desgned. Current acton predcton technques focus on the predcton of next acton. A part of acton sequence s used for tranng the proposed model. The model s then used on acton predcton. The acton sequence s not nfluenced by the acton predcton. It s easly to compute the predcton accuracy. Oppostely, the acton groups dscovered by AGD can be used for the predcton of the next group. Those actons of the next group can be taken automatcally. The acton sequence may be nfluenced by the group predcton. For example, the actons from two groups are nterleavng n the acton sequence. The group predcton may cause the actons of the next group can be taken together. That s, the nterleavng of actons may be dsappeared and the fnal acton sequence s nfluenced by the group predcton. Consequently, the computaton of predcton accuracy has to be redefned. Ths s one of the problems on the desgn of group predcton approach. On the other hand, the ncorporaton of AGD and current acton predcton technques s also studed n order to mprove the predcton accuracy. References [] D. J. Cook, M. Youngblood, and E. O. Heerman, MavHome: An Agent-Based Smart Home, n Proceedngs of the Frst IEEE Int l Conf. on Pervasve Comp. and Comm. (PerCom 03), Vol.3, No.6, pp.5-54, March 003. [] E. O. Heerman and D. J. Cook, Improvng Home Automaton by Dscoverng Regularly Occurrng Devce Usage Patterns, n Proceedngs of the Thrd IEEE Int l Conf. on Data Mnng (ICDM 03), Vol.9, No., pp , Nov.003. [3] S. K. Das, D. J. Cook, et al., The Role of Predcton Algorthm n the MavHome Smart Home Archtecture, IEEE Wreless Communcaton, Vol.9, No.6, pp.77-84, 00. [4] V. N. Padmanabhan and J. C. Mogul, Usng Predctve Prefetchng to Improve World Wde Web Latency, Computer Comm. Rev., Vol.30, No.3, pp.-36, July 996. [5] P. Proll and J. Ptkow, Dstrbuton of Surfer s Paths through the World Wde Web: Emprcal Characterzaton, World Wde Web, Vol., No.-, pp.9-45, Jan [6] Y. J. Ln, H. A. Latchman, and M. Lee, A Power Lne Communcaton Network Infrastructure for the Smart Home, IEEE Wreless Communcaton, Vol.9, No.6, pp.04-, 00. [7] A. Roy, S. K. D. Bhaumk, A. Bhattacharya, et al., Locaton Aware Resource Management n Smart Homes, n Proceedngs of the Frst IEEE Int l Conf. on Pervasve Computng and Communcaton (PerCom 03), Vol.3, No.6, pp , March 003. [8] R. Kango, P. R. Moore, and J. Pu, Networked Smart Home Applances Enablng Real Ubqutous Culture, n Proceedngs of IEEE Ffth Internatonal Workshop on Networked Applance, Vol.30, No.3, pp.76-80, Oct. 00. [9] D. Valtchev and I. Frankov, Servce Gateway Archtecture for a Smart Home, IEEE Communcatons Magazne, Vol.40, No.4, pp.6-3, Aprl 00. [0] H. Jahnke and J. Ster, Facltatng the Programmng of the Smart Home, IEEE Wreless Communcatons, Vol.9, No.6, pp.70-76, Dec. 00. [] V. Stanford, Usng Pervasve Computng to Delver Elder Care, IEEE Pervasve Computng, Vol., No., pp. 0-3, 00.

16 Journal of Computers Vol.8, No., July 007 [] S. Helal, B. Wnkler, C. Lee, et al., Enablng Locaton-Aware Pervasve Computng Applcatons for the Elderly, n Proceedngs of the Frst IEEE Internatonal Conference on Pervasve Computng and Communcaton (PerCom 03), pp , March 003. [3] S. P. Rao and D. J. Cook, Predctng Inhabtant Acton Usng Acton and Task Models wth Applcaton to Smart Homes, Internatonal Journal on Artfcal Intellgence Tools, Vol.3, No., pp.8-99, 004. [4] N. Noury, G. Vrone, and T. Creuzet, The Health Integrated Smart Home Informaton System (HIS²): Rule Based System for the Localsaton of a Human, n Proceedngs of the Second Annual Internatonal IEEE-EMBS Specal Topc Conference on Mcrotechnologes n Medcne & Bology, pp.38-3, May 00. [5] A. P. Pons, Web-applcaton centrc object prefetchng, The Journal of Systems and Software, Vol.67, No.3, pp , 003.