A Collaborative Context Prediction Technique

A Collaborative Context Prediction Technique Christian Voigtmann, Sian Lun Lau, Klaus David Department of Computer Science University of Kassel, Germany {voigtmann, slau, david}@uni-kassel.de Abstract—The prediction of contexts plays an important part in the field of context aware systems and environments for adapting services proactively to users’ needs. To the best of our knowledge, most research literature on context prediction focused on forecasting a user’s contexts only using his available context history. In the case of a user suddenly changing his behaviour in an unexpected way, the context history of the user does not provide future context information for the observed pattern. Hence context prediction algorithms will fail to forecast the appropriate future context. To overcome the gap of missing context information in the user’s context history, we propose the Collaborative Context Prediction (CCP) approach. Our results show that the proposed CCP approach is able to give accurate predictions in the absence of needed context information and outperforms the Active LeZi method. Index Terms—context prediction, context awareness, tensor decomposition, hosvd, collaborative. recommendation systems [1], [2]. With regard to the abovementioned scenario, the teacher’s future context - giving a biology class - which is based on movement patterns unknown to the system, could be predicted by utilising the context histories of his colleagues. In Section II existing state of the art to context prediction is presented. A brief introduction to the Collaboration-based Context Prediction algorithm and to the underlying HOSVD technique is given in Section III. Furthermore, a proof of concept, by comparing the CCP approach to the state of the art context predictor Active Lezi [3] is outlined in Section IV. Both methods have been applied to a real-world context data set, consisting of movement patterns of multiple users, and compared to each other with regard to the obtained accuracy. II. R ELATED W ORK I. I NTRODCTION With the help of predicted context information, users in ubiquitous environments can be assisted additionally. This can be illustrated by taking, for example, a teacher of history and maths, who gives lessons in the same classroom daily. Before he enters the classroom, a context aware prediction system spanning the whole school automatically pre-initialises the whiteboard and the students’ tablet pcs. Therefore, the latest updates are installed on the tablet pcs and the needed teaching materials are automatically transferred from a server to the pcs. The teacher’s movement patterns recorded in the past are possible context information useful for the prediction ”giving a history lesson”. However, if the teacher has to fill in for a colleague who teaches biology in a classroom he has not given a lecture in before, his current movement patterns are unknown to the context prediction system. Current context prediction approaches that rely on the context history of a single user would fail to forecast the user’s next context - teaching biology -. Therefore, the pre-initialisation of the whiteboard and the tablet pcs would not take place. Instead of using only the context history of the user whose next context has to be predicted, we propose using a collaborative approach. This approach enriches the context history of the user with additional context information of other users whose histories show similarities to the concerned user. This method called Collaboration-based Context Prediction (CCP) uses Higher Order Singular Value Decomposition (HOSVD) technique. The idea of finding latent information between users using HOSVD already has been successfully applied to tag- In this section two existing works of research on context prediction that utilises collaborative mechanisms are introduced first. Then some works of research related to predicting future contexts are presented briefly. The first research work on context prediction that considered collaborative aspects in a process of context prediction has been introduced in [4]. The authors suggest a method to predict a user’s next location by using and interpreting his or her GPS data. In this approach the gained GPS data is clustered to meaningful locations and a Markov model is used for the prediction process. Thereby the paper presents ideas for singleand multi-user/collaborative applications based on location data. One outlined scenario for a collaborative application indicates serendipitous meetings between friends similar to Google Latitude1 , e.g. if the prediction model of Bob knows that Alice will be at a particular place at a certain time he could be notified if he happens to be in the vicinity at the same time. A second research work that is trying to combine context prediction and collaborative aspects is the SenseCast2 project at the University of Braunschweig. One of the goals of the SenseCast project is to develop new methods for context prediction in wireless-sensor networks by employing collaborative strategies. A broad overview of existing approaches to context prediction is given next. The Active LeZi [3] context predictor that is being compared to our CCP approach in this work has been developed in the course of the MavHome [5] project 1 http://www.google.com/latitude/ 2 http://www.ibr.cs.tu-bs.de/projects/senseCast/ 978-1-4244-8331-0/11/$26.00 ©2011 IEEE conducted by Diana J. Cook. Active LeZi has been taken to forecast devices the inhabitants of the MavHome will interact next with, for example. A context time-series prediction algorithm that is based on local-alignment techniques is introduced in [6], [7]. The approach is inspired by algorithms taken from computational biology. On the one hand, the author evaluated his proposed context prediction method by applying Alignment to a windpower data set to predict the wind power required in the future. On the other hand, a data set consisting of the information on a mobile user’s location was used to predict his location trajectory. In [8] a Structured Context Prediction algorithm is presented. The approach tries to overcome the trade-off for context prediction methods needing to be generic and efficient at the same time. Therefore, additional knowledge about the application domain given by the developer at design time is used. The used evaluation approach focuses on the availability prediction of two services. Another interesting approach to context prediction is outlined in [9]. The authors propose a probabilistic method to forecast future contexts of mobile users. Instead of using well-known machine learning paradigms, they introduce a novel graphical structure with time-based edge weights called time-inferred multiple pattern network (TIMPN). The proof of concept was given by the authors by applying the proposed method to real-world context data of a mobile user. In contrast to the collaborative approaches presented in this section the CCP approach introduced and evaluated next focuses on collaboration to overcome missing context information in the user’s context history to gain more reliable prediction results. III. I NTRODUCTION T O C OLLABORATIVE -BASED C ONTEXT P REDICTION We propose the Collaborative-based Context Prediction (CCP) approach that increases the possibility for making a currently unknown context pattern of a user available to forecast the next future context. The Collaborative Ubiquitous Environment presented in figure 1 forms the foundation of the CCP approach. The environment consists of three different entities. The first entity is represented by the set of users U ∈ U of the Collaborative Ubiquitous Environment, the second by the set of possible context patterns Cp ∈ CP and the third by the set of predictable future contexts Fc ∈ FC. Therefore the history of a user Ui is described by Hi ⊆ CP × FC. HOSVD is used to enrich the context history of the user with additional latent information by using existing relations (equal context parts) between the context histories of the users in the Collaborative Ubiquitous Environment (see figure 1). Latent information comprises new context parts in the context history of the user that were formerly unknown and can be used to infer the next future context. The basic idea of HOSVD is to restrict the dimensionality of each entity of a Collaborative Ubiquitous Environment to a specific size Collaborative Ubiquitous Environment User Context History U1 Cp2|Fc1 Cpm-1|Fci Cp5|Fc9 Cpm-1|Fci U2 Cp5|Fc9 Cp7|Fc5 Cp8|Fcj Cp3|Fc2 U3 Cp1|Fcn Cpm|Fc1 Cpm-1|Fci Cp8|Fcj Un Cp8|Fcj Cpm-1|Fci Cp2|Fc1 Cpm|Fc1 Fig. 1. Presents n users of a Collaborative Ubiquitous Environment with n different context histories. Equal context parts are marked in the same colour. Every context part in the context history Hi of the user Ui consists of two elements. Cp ∈ CP indicates the context pattern and Fc ∈ F C indicates the future context that follows the previous context pattern. Altogether the Collaborative Ubiquitous Environment consists of n different users, m different context patterns and j different future contexts. Cp1Cp2Cp3 U1 Cpm 1 1 1 U2 1 U3 Un 1 1 Fcj Fc2 Fc1 Fig. 2. 3-order tensor to store data of a Collaborative Ubiquitous Environment. The first dimension characterises all users U of the Collaborative Ubiquitous Environment that provide information in the form of context data. The second dimension represents all context patterns CP that are available in the context histories of the users. F C symbolises the third dimension, the future contexts, that can be inferred as the next possible context of a user U ∈ U for a given context pattern. where each entity contains relevant, less noisy information by using the n-mode product outlined in equation 1. Afterwards, the downsized information space is used to recalculate the Collaborative Ubiquitous Environment based on the most relevant information using the n-mode product again. For a more profound introduction to HOSVD we refer to [10], [11]. A ×n U (1) To demonstrate the practical use of HOSVD this technique is applied to the presented Collaborative Ubiquitous Environment. For the storage of the data we use a 3-order tensor A ∈ ℜ|U |×|CP|×|F C| , compare with Figure 2. The existing relations between the entities U, CP, FC are stored in the tensor structure A as a one. All relations that do not exist are treated as values of zero. To minimise the number of unknown context patterns in the user’s history the dimensionality sizes of the 3-order tensor structure A are downsized. As a result a 3-order tensor Σ ∈ ℜc1 ×c2 ×c3 is received, whose three dimensions are c2 c1 c3 Fig. 3. Downsized 3-order tensor structure that contains only the most relevant data of every dimension. ... reduced to the information that spans the space that contains the most relevant information. The size of the dimension U is reduced to c1 , the size of the dimension CP is reduced to c2 and the third dimension FC is collapsed to the size of c3 . Figure 3 shows the tensor - marked in red - with reduced dimensionality size. Σ symbolises the approximation of the tensor A. Afterwards HOSVD is used to retransform the tensor Σ into the initial dimension size of the tensor A by reusing the n-mode product as described above. The resulting tensor A′ ∈ ℜ|U |×|CP|×|F C| finally concludes with new information in terms of new relations between the three dimensions that can be used to forecast the user’s next contexts. IV. E XPERIMENTAL R ESULTS In this section the CCP approach is compared with the Active LeZi method concerning their accuracy in a realworld context data set. The data set used for the evaluation process contains acceleration data that was recorded using the accelerometer in a smartphone annotated with the movements performed by test users, such as going upstairs, going downstairs, sitting, walking and standing. This was carried out similarly to the experiments performed in our previous work [12]. Smartphones used for the recording of acceleration included a Nokia N95, a 5730 Xpressmusic and a N900. For the purpose of this work, the Symbolic Aggregate approXimation (SAX) representation of the time series proposed by Lin et. al [13] is used to transform the magnitude of the raw acceleration data into a series of alphabetical symbols. Each time series was normalised and split into windows of 4 seconds characterising the movement patterns of a user. The Symbolic Aggregate approXimation represents every movement pattern as a string with a length of 32 and a total of six different symbols {a, b, c, d, e, f}. Furthermore, we divided every different set of recorded movement patterns into a maximum of three sub-clusters. Sub-clusters of ”going upstairs” are represented by the labels {C0, C1, C2}. Henceforth the subcluster labels represent the context information in the history of the users. Figure 4 illustrates an exemplary time series with a window size of 4 seconds that characterises the movement pattern ”going upstairs” and its transformation using SAX. The data snippet below shows the label, the SAX transformation of the accelerator data and the respective sub-cluster label of a user’s recorded movement pattern. For this evaluation four context histories of four users were utilised. Every context history contains approximately GoDownStairs - baecdbbbeedfebceeaceebabfeaceeda - B1 GoDownStairs - cdcccccccbcdfaacddefbbcefacdcddb - B0 ... GoDownStairs - bacbfbabddebabbfdabdfdcabbfabcfe - B2 GoUpStairs - ebebbcefadebbdfeafebdfcaeccccddb - C1 GoUpStairs - ccdcdccbcefdcabfccbcfddaafdccbfd - C1 GoUpStairs - eafbbbceccbbfddbcdeabfcbfaaedccb - C2 ... ... Fig. 4. Illustration of acceleration data and their SAX representation. 1000 time ordered sub-cluster labels. The labels represent the context information resulted from the recorded movement behaviours of the users. To gain a representative number of different evaluation sets (context histories), the data sets were split using different sizes {3, 5, 7} for the length of the context parts. A context part with a size of three for example, consists of two sub-cluster labels representing the context pattern and one sub-cluster label representing the future context. Moreover, additional evaluation sets were generated by removing context parts that occurred successively. Data sets without successive context parts are called single-mode data sets, data sets with successive context parts are called all-mode data sets. For the evaluation of the prediction accuracy of the Collaborative Context Predictor and the Active LeZi predictor these approaches were applied to different test data sets. A test data set consisted of intersections of exactly two users’ context histories. Intersections are context parts that occur in both histories. The test data sets were used to simulate missing context information in the context history of the respective users. For every test data set there are three training data sets that are used to construct the prediction models for the applied context prediction approaches. The first training data set contains the information on the context histories of the two users the test data set has been generated from. The second training data set extends the information of the first training data set by adding the context history of a third user. The third data set extends the second by adding the history of a fourth user. For the prediction process we use the ”leave-one-out” strategy for both context prediction approaches. In doing so, each single context part of the test data set is removed temporally one after the other from the context history of the corresponding user in the current training data set. Every time a single context part is removed temporally, the prediction model is constructed anew with the reduced training data set and is used to forecast the next context of the context pattern given by the current context part of the test data set. Finally, the predicted context is compared to the future context also given by the current context part afterwards. Altogether 24 different test data sets were generated. The test data sets resulted from different combinations of usercontext history pairs. We combined the context histories of user one and two, user two and three, user one and three and user two and four. In addition, each combination was combined with the aforementioned three lengths of the context parts and the two data set modes. The results in gained accuracy for the both context prediction approaches are presented in the Figures 5 to 8. The number of instances in each test data set can be found in the subtitles of the figures. The subfigures on the left side show the results for the single-mode data set and the subfigures on the right the achieved results for the all-mode data set. In each case only the user dimension of the tensors has been reduced to the size of one to construct the models of the CCP approach based on the training data sets. The size of the two other dimensions containing the context patterns and the future contexts remains unchanged. If the size of the second or the third dimension is reduced in addition to the first dimension, the accuracy of the context prediction process worsens. The results presented on the eight different charts indicate that the CCP approach outperforms Active LeZi for predicting the future context of a user based on unknown context patterns. The division of the context histories into context parts of different sizes shows that the prediction results for smaller sizes mostly achieve less accuracy than for larger sizes. That is because, among other things, the smaller the chosen size of the context parts, the higher the number of entries in the test data set. In the comparison of the single-mode data sets and the allmode data sets, it can be recognized that in most cases the prediction for the all-mode data sets achieved better results for context parts of size three. For the test data sets with a context part of size five and seven respectively, the achieved prediction results are quite similar in regard to the two modes. Furthermore, it becomes evident that the prediction results can be improved for any given test data set by increasing the number of user histories used to build the respective prediction model. V. C ONCLUSIONS In this paper the approach of Collaborative-based Context Prediction was presented briefly and compared with the wellknown Active LeZi predictor. Both prediction methods have been applied to several test data sets. Test data sets consist of equal context parts found in the context histories of different pairs of users. These context parts have been used to simulate missing information in the user’s context history. Therefore, we used the leave-one-out strategy by first removing the context part from the context history of the respective user. Subsequently, we have predicted the future context of the respective context pattern by enriching the context history of the user with extra information which was obtained from the additional context histories of other users. The results show that the CCP method received mostly better results respective accuracy than the Active LeZi approach on the test data sets. For future work fuzziness is intended to add to a CCP approach for which context patterns in the histories of the users do not have to match exactly to be considered as existing relations. ACKNOWLEDGMENTS The authors are involved in the VENUS research project. VENUS is a research cluster at the interdisciplinary Research Center for Information System Design (ITeG) at Kassel University. We thank Hesse’s Ministry of Higher Education, Research, and the Arts for funding the project as part of the research funding program ”LOEWE - Landes-Offensive zur Entwicklung Wissenschaftlich-ökonomischer Exzellenz”. For further information, please visit: http://www.iteg.unikassel.de/venus. The authors would like to acknowledge the German Federal Ministry of Education and Research (BMBF) for funding the project MATRIX (Forderkennzeichen 01BS0802). The authors are responsible for the content of the publication. R EFERENCES [1] P. Symeonidis, A. Nanopoulos, and Y. Manolopoulos, “Tag recommendations based on tensor dimensionality reduction,” in RecSys ’08: Proceedings of the 2008 ACM conference on Recommender systems. New York, NY, USA: ACM, 2008, pp. 43–50. [2] S. Rendle and L. Schmidt-Thieme, “Pairwise interaction tensor factorization for personalized tag recommendation,” in WSDM ’10: Proceedings of the third ACM international conference on Web search and data mining. New York, NY, USA: ACM, 2010, pp. 81–90. [3] K. Gopalratnam and D. J. 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Available: http://dx.doi.org/10.1007/s10618-007-0064-z Based on test dataset of user 1 and user 2 (single data) Based on test dataset of user 1 and user 2 (all data) 100 100 2User(CCP) 2User(AL) 3User(CCP) 3User(AL) 4User(CCP) 4User(AL) 80 Accuracy in % Accuracy in % 80 60 40 20 60 40 20 0 0 CP=3 CP=5 CP=7 Size of Context Parts CP=3 (a) Size of test data sets are 54, 34 and 18 Fig. 5. Test data sets generated from the intersections of user 1 and user 2. Used with different context part sizes and data modes. Based on test dataset of user 2 and user 3 (single data) Based on test dataset of user 2 and user 3 (all data) 100 2User(CCP) 2User(AL) 3User(CCP) 3User(AL) 4User(CCP) 4User(AL) 60 40 2User(CCP) 2User(AL) 3User(CCP) 3User(AL) 4User(CCP) 4User(AL) 80 Accuracy in % Accuracy in % 80 20 60 40 20 0 0 CP=3 CP=5 CP=7 Size of Context Parts CP=3 (a) Size of test data sets are 32, 48 and 12 Fig. 6. CP=5 CP=7 Size of Context Parts (b) Size of test data sets are 32, 48 and 12 Test data sets generated from the intersections of user 2 and user 3. Used with different context part sizes and data modes. Based on test dataset of user 1 and user 3 (single data) Based on test dataset of user 1 and user 3 (all data) 100 100 2User(CCP) 2User(AL) 3User(CCP) 3User(AL) 4User(CCP) 4User(AL) 60 40 2User(CCP) 2User(AL) 3User(CCP) 3User(AL) 4User(CCP) 4User(AL) 80 Accuracy in % 80 Accuracy in % CP=5 CP=7 Size of Context Parts (b) Size of test data sets are 54, 34 and 18 100 20 60 40 20 0 0 CP=3 CP=5 CP=7 Size of Context Parts CP=3 (a) Size of test data sets are 28, 44 and 10 Fig. 7. CP=5 CP=7 Size of Context Parts (b) Size of test data sets are 28, 44 and 10 Test data sets generated from the intersections of user 1 and user 3. Used with different context part sizes and data modes. Based on test dataset of user 2 and user 4 (single data) Based on test dataset of user 2 and user 4 (all data) 100 100 2User(CCP) 2User(AL) 3User(CCP) 3User(AL) 4User(CCP) 4User(AL) 60 40 20 2User(CCP) 2User(AL) 3User(CCP) 3User(AL) 4User(CCP) 4User(AL) 80 Accuracy in % 80 Accuracy in % 2User(CCP) 2User(AL) 3User(CCP) 3User(AL) 4User(CCP) 4User(AL) 60 40 20 0 0 CP=3 CP=5 CP=7 Size of Context Parts (a) Size of test data sets are 38, 68 and 16 Fig. 8. CP=3 CP=5 CP=7 Size of Context Parts (b) Size of test data sets are 38, 68 and 16 Test data sets generated from the intersections of user 2 and user 4. Used with different context part sizes and data modes.