An Approach to Collaborative Context Prediction

Christian Voigtmann, Sian Lun Lau, Klaus David

Department of Computer Science

University of Kassel, Germany

{voigtmann, slau, david}@uni-kassel.de

Abstract—Context prediction approaches forecast future con-texts based on known context patterns to adapt e.g., services inadvance. In the case of the user’s context history not providingsuitable context information for the observed context pattern, tothe best of our knowledge context prediction algorithms will failto forecast the appropriate future context. To overcome the gapof missing context information in the user’s context history, wepropose the Collaborative Context Prediction (CCP) approach.CCP utilises the collaborative characteristics of existing recom-mendation systems of social networks. To evaluate the CCPmethod an experimental comparison of the proposed methodagainst the local Alignment context predictor is carried out.

Index Terms—context prediction, context awareness, tensordecomposition, hosvd, collaborative.

I. INTRODCTION

One interesting research issue in the field of context-aware

systems and environments is context prediction. Based on the

available context data, such systems and environments predict

future context of the user. With the help of this predicted

information, users in ubiquitous environments can be assisted

to a greater extend in different ways. Taking for example, a

research assistant who presents the progress of his work in

the same room every week. Before he enters the room for

his next presentation, the context-aware system automatically

adapts the designated services in the room to be ready for

his presentation using a prediction system spanning the whole

university. Possible context information useful for the predic-

tion are his movement patterns or devices he has used in the

past. A common approach to enable the prediction of future

context is to make use of the gathered and stored contexts

related to the user’s actions or to the user’s environment. The

information is needed by a context prediction algorithm to

forecast contexts for a given context pattern. However, if the

research assistant gives his presentation in a room he has not

been 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

fail to forecast the user’s next context - doing a presentation.

Therefore, the adaptations would not take place.

To overcome the problem of missing context information in

a single user’s context history, we utilise a collaboration-based

technique. We propose including and utilising the context

histories from other users to solve the problem of missing

context patterns in a user’s context history. We call this idea

Collaboration-based Context Prediction (CCP). To enrich the

context history of the user, we use the Higher Order Singular

Value Decomposition (HOSVD) method that has been applied

successfully in the field of tag recommendation [1]. With

regard to the above-mentioned scenario, the future context of

the research student - giving a presentation - which is based on

unknown movement patterns could be predicted using CCP, if

the context is provided by context histories of his colleagues

and if these histories show sufficient similarities to the research

student’s history.

Existing state of the art to context prediction is outlined in

the next Section. An introduction to the Collaboration-based

Context Predictor and to the underlying HOSVD technique is

outlined in Section III. Section IV gives a detailed example

to illustrate how the approach works. A proof of concept

regarding accuracy is given in Section V, by comparing the

CCP approach to an Alignment predictor which is based on the

Smith-Waterman-Algorithm. Section VI concludes the paper.

II. RELATED WORK

In this section we present existing state of the art context

prediction approaches briefly. One of the first projects that in-

cludes a mechanism to forecast future contexts is the Neuronal

Network House project directed by Michael C. Mozer [2]. In

this project, lifestyle information of occupants was gathered

to predict their next actions. Another smart home project

conducted by Diana J. Cook is called MavHome [3]. In the

case of this project the Active LeZi approach [4], a sequence-

matching algorithm, and the Episode Discovery algorithm [5]

have been developed to forecast, among others, devices the

inhabitants will be interacting next with. The authors in [6]

suggest a method to predict a user’s next location by using

and interpreting his or her GPS data. The introduced approach

clusters the gained GPS data to meaningful locations and uses

a Markov model for the prediction process.

A context time series prediction algorithm that is based on

local alignment techniques is introduced in [7]. This approach

is inspired by algorithms with a focus on computational

biology. On the one hand, the author evaluated his proposed

context prediction method by applying Alignment to a wind

power dataset to predict the wind power required in the future.

On the other hand, a dataset consisting of the information on

the location of a user’s mobile phone has been used to predict

the user’s location trajectory.

In [8] a Structured Context Prediction algorithm is pre-

sented. This approach tries to overcome the trade-off for

context prediction methods needing to be generic with being

efficient by using additional knowledge about the application

domain given by the developer at the time of design. The used

8th IEEE Workshop on Context Modeling and Reasoning

978-1-61284-937-9/11/$26.00 ©2011 IEEE 438

evaluation approach focuses on the availability prediction of

two services. The mentioned approaches only use the context

history of the user whose future context should be predicted

and do not explicitly make use of existing relations of users

context histories. Thus, the fact to use context histories of other

users to gain extra information for the forecasting process has

not been considered so far. In the next section our proposed

approach is described in more detail.

III. COLLABORATIVE-BASED CONTEXT PREDICTION

We propose the Collaborative-based Context Prediction

(CCP) approach that increases the possibility to make a

currently unknown context pattern of a user available for fore-

casting the next future context. The Collaborative Ubiquitous

Environment presented in Figure 1 forms the foundation for

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.

U1

U2

U3

Un

Cp |Fc2 1 Cp |Fc5 9

Cp |Fc7 5 Cp |Fc8 j Cp |Fc3 2

Cp |Fc1 n Cp |Fcm-1 i

Cp |Fcm 1

Context HistoryUser

Collaborative Ubiquitous Environment

Cp |Fc2 1

Cp |Fcm 1

Cp |Fcm-1 i

Cp |Fc5 9

Cp |Fc8 j

Cp |Fc8 j

Cp |Fcm-1 iCp |Fcm-1 i

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 twoelements. Cp ∈ CP indicates the context pattern and Fc ∈ FC indicates thefuture context that follows the previous context pattern.

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 formally 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 where each entity

only contains relevant, less noisy information by using the

n-mode product [9]. 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.

U1

U2

U3

Un

Cp1Cp2Cp3 Cpm

Fc1

Fc2

Fcj

11

1

1

1

1

Fig. 2. 3-order tensor to store data of a Collaborative Ubiquitous Envi-ronment. The first dimension characterises all users U of the CollaborativeUbiquitous Environment that provide information in the form of context data.The second dimension represents all context patterns CP that are availablein the context histories of the users. FC symbolises the third dimension, thefuture contexts, that can be inferred as the next possible context of a userU ∈ U for a given context pattern.

c1

c2

c3

Fig. 3. Downsized 3-order tensor structure that contains only the mostrelevant data of every dimension.

To demonstrate the practical use of HOSVD we apply this

technique to the presented Ubiquitous Collaborative Environ-

ment. For the storage of the data we use a 3-order tensor

A ∈ ℜ|U|×|CP|×|FC|, compare Figure 2. The existing relations

between the entities U , CP, FC are stored in the tensor

structure A with a one. All relations that do not exist are

treated as values of zero.

To minimize the number of unknown context pattern in

the user’s history we downsize the dimensionality sizes of

the 3-order tensor structure A. As a result, we receive a

3-order tensor Σ ∈ ℜc1×c2×c3 whose three dimensions are

reduced to the information that spans the space that contains

the most relevant information. The size of the dimension Uis 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 its

reduced dimensionality size. Σ symbolises the approximation

of the tensor A. Afterwards HOSVD is used to retransform the

tensor Σ to the initial size of the dimension of the tensor A by

reusing the n-mode product as described above. The resulting

tensor A′ ∈ ℜ|U|×|CP|×|FC| finally concludes new information

in terms of new relations between the three dimensions that

can be used to forecast the user’s next contexts.

IV. ILLUSTRATIVE EXAMPLE

In order to show how our approach works, the Collaborative

Context Predictor is applied to an illustrative example. This

example presupposes three users of a Collaborative Ubiquitous

Environment. Figure 4 presents the three context histories of

the users. Equal context parts are marked with the same color.

In contrast to the used datasets in our experimental section,

439

in this example context patterns are not mapped to multiple

future contexts. The size of the context parts is determined

to an equal window size of four. Therefore every context part

consists of three contexts and one future context marked in

bold. All in all there are five different context parts composing

of ten different contexts.

U1

U2

U3 BBCY BBDZ BCCY BBDZ EFGZ BBDZ EFGZ EFGZ

FFXY FFXY BBDZ BBDZ

ABCX ABCX BCCY ABCX BCCY EFGZ EFGZ

User

1 2 3 4 5 6 7 8

EFGZ

BBDZ BBDZ FFXY FFXY

ContextParts

Fig. 4. Sample dataset consisting of context histories of three users.

As we can see, the context history of U1 does not provide

information for the context pattern {FFX, BBD}, the history

of U2 does not provide information for the context pattern

{ABC, BCC, EFG} and in the history of U3 the patterns

{ABC, FFX} haven’t been stored yet. Hence it is not possible,

for example, to provide a prediction for the next sensed

context pattern for U1, if this context pattern is either FFX

or BBD. The approach takes advantage of direct and indirect

relations between the histories of the users. Direct relations

are characterised by equal context parts between two users.

Indirect relations between two users e.g., U1 and U2 exist, if

the following two conditions are fulfilled:

• U1 and U2 do not have the same context parts,

• U3 features similarities of both U1 and U2.

CCP first transforms the underlying Collaborative Ubiq-

uitous Environment to a 3-order tensor structure with size

A ∈ ℜ3×5×3. (cf., Figure 5). Then HOSVD for tensor

dimensionality reduction is applied by reducing the dimension

size of the user to one. The resulting core tensor structure

is Σ ∈ ℜ1×5×3. By reapplying HOSVD to the core tensor

structure containing the approximated data the tensor structure

presented in Figure 6 containing new information is received.

The resulted tensor contains new relations between users,

context patterns and future contexts which are symbolised by

the new values. Because context patterns are not mapped to

multiple future contexts in this example the relations between

users, context patterns and future context in the resulted tensor

A′ are obvious. Otherwise, the future context with the highest

value that forms a relation to a given user and context pattern

will be predicted. For predicting future contexts for context

pattern FFX or BBD to U1, we can now use the new relations

provided by the resulted tensor to make a prediction. For

the pattern FFX we will predict Y and for BBD we will

predict the future context Z. The resulting prediction for BBD

is reasonable, because U1 shares the same context patterns

{EFG, BCC} with U3. The same applies to the prediction

for pattern FFX, because U1 has a direct relation to U3 and

U3 has a direct relation to U2 so U1 and U2 hold indirect

similarities. This illustrative example shows that CCP can be

used to provide further information to context histories of users

3

2

2

4 3

4

3

U1

U2

U3

XY

Z

AB

C

BC

C

FF

X

BB

D

EF

G

AB

C

BC

C

FF

X

BB

D

EF

G

AB

C

BC

C

FF

X

BB

D

EF

G

3

Fig. 5. Shows the tensor A ∈ ℜ3×5×3 that contains the information ofthe used sample data. The tensor consists of three users, five different contextpatterns and three different future contexts.

1.3

1.8

U1

U2

U3

XY

Z

AB

C

BC

C

FF

X

BB

D

EF

G

AB

C

BC

C

FF

X

BB

D

EF

G

AB

C

BC

C

FF

X

BB

D

EF

G

0.4

1.4

0.6

1.9

0.5

0.2

0.6

2.1

0.7

2.2

2.7

0.9

2.9

Fig. 6. Presents the resulted tensor A′ ∈ ℜ3×5×3 that contains new relationsbetween users, context patterns and future contexts.

by using existing direct or indirect relations to context histories

of other users. In the next section we will verify this result

by applying the CCP approach to a real dataset consisting of

movement patterns.

V. EXPERIMENTAL RESULTS

In this section we present experimental results of our CCP

approach that is based on real-world context data. We show

that context histories of additional users can be utilised to

allow context prediction even if the user himself, in this

case the research assistant in our introduction, does not have

suitable information in his history. Furthermore, we explore

how the prediction accuracy for so far unobserved context

patterns is affected by the number of used histories. Finally,

we compare the accuracy of our results to a local Alignment

context prediction approach that has access to the same context

history database using the Smith-Waterman-Algorithm [10].

A. Dataset

The dataset contains acceleration data recorded using the

accelerometer in a smartphone annotated with the movements

performed by test users. These were carried out in a way sim-

ilar to the experiments performed in our previous work [11].

Smartphones used for the recording of acceleration included

a Nokia N95 8GB, 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

[12] is used to transform the magnitude of the raw acceleration

data into a series of alphabetical symbols.

Each time series was normalized and split into windows

of 4 seconds. First, each window was transformed into a

piecewise aggregate approximation (PAA) representation of

440

GoDownstairs - baecdbbbeedfebceeaceebabfeaceeda - B1

GoDownstairs - cdcccccccbcdfaacddefbbcefacdcddb - B0

...

GoDownstairs - bacbfbabddebabbfdabdfdcabbfabcfe - B2

GoUpstairs - ebebbcefadebbdfeafebdfcaeccccddb - C1

...

GoUpstairs - ccdcdccbcefdcabfccbcfddaafdccbfd - C1

GoUpstairs - eafbbbceccbbfddbcdeabfcbfaaedccb - C2

...

...

Fig. 7. Illustration of acceleration data entries of a test dataset and their approximation.

the given normalized time series, then converted into symbol

strings with the distance matrix defined in Lin’s work. We

applied the SAX representation using string lengths of 32 and

a total of 6 symbols {a, b, c, d, e, f}. This enables the use of

a simple clustering approach where each movement pattern

is divided into maximum three sub clusters. Sub clusters

of ”go downstairs” are represented by {B0, B1, B2}, sub

clusters of ”go upstairs” are represented by {C0, C1, C2}, etc.

Henceforth, a maximum of 15 resulting different clusters are

used to represent the context information in the history of the

users. Figure 7 illustrates two time series each with a window

size of 4 seconds. Below the two acceleration curves a snippet

of a used test dataset is presented. The data snippet illustrates

the label, the SAX transformation of the acceleration data and

the label of the respective sub cluster.

For our experiments we used four context histories of

different users. Every context history containing approximately

1000 sub clustered and time-ordered contexts resulted from

the recorded movement behaviour of the users. To gain a

representative number of different evaluation sets, we used

different window sizes for the length of the context parts {3,

5, 7} to divide the four existing context histories. Moreover,

we generated additional evaluation sets by removing context

parts that occurred successively. Datasets without successive

context parts are called single-mode datasets, datasets with

successive context parts are called all-mode datasets.

B. Experimental Configuration

For the evaluation we apply the CCP and the local Align-

ment approach to different test datasets. A test dataset con-

sists of intersections of exactly two users’ context histories.

Intersections are context parts that occur in both histories.

If both users have ten equal context parts in their histories,

for example, the test dataset contains twenty intersections

entries. 10 intersections from the perspective of the first user

to the second user and 10 intersections from the reverse

perspective. The test datasets are used to simulate missing

context information in the context history of the corresponding

users. For every test dataset three training datasets exist that

are used to construct the prediction models for the applied

context prediction approaches.

The first training dataset contains the information of the

context histories on the two users the test dataset has been

generated from. The second training dataset extends the in-

formation of the first training dataset by adding the context

history information of a third user. The third dataset extends

the second by adding the history information 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 dataset is removed

temporally one after the other from the context history of the

corresponding user in the current training dataset.

Every time a single context part is removed temporally, the

prediction model is constructed anew with the reduced training

dataset and is used to forecast the next context of the context

pattern given by the current context part of the test dataset.

Finally, the predicted context is compared to the actual future

context that follows the context pattern.

C. Results

In this subsection we provide the results gained after ap-

plying the CCP and the local Alignment approach to different

test datasets. Altogether we generated 24 test datasets. The test

datasets result from four different context history combinations

of users, combined with three different window sizes for

the context parts and the two dataset modes. Each chart

presented in the Figures 8 to 11 shows four histogram bars

for every window size that indicate the different context

prediction accuracies. The blue bars indicate the accuracy of

the CCP approach for the different training datasets. The red

bar indicates the accuracy of the local Alignment approach.

We show only one result for the local Alignment approach

for every window size because local Alignment always leads

to the same accuracy results in our experiments despite of

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TABLE ITENSOR DIMENSIONALITY FOR THE DIFFERENT WINDOW SIZES OF THE FOUR TEST DATASETS. REMARK: THE TENSOR DIMENSIONALITY FOR ALL AND

SINGLE DATA MODE IS SIMILAR.

Wnd = 3 Wnd = 5 Wnd = 7

A1

A2

A3

Ψ A1

A2

A3

Ψ A1

A2

A3

Ψ

Fig. 8 2x44x11 3x63x11 4x68x11 54 2x104x11 3x136x11 4x183x11 34 2x123x11 3x184x11 4x250x11 18

Fig. 9 2x53x11 3x64x11 4x66x11 48 2x130x10 3x180x10 4x232x10 32 2x142x10 3x209x10 4x275x10 12

Fig. 10 2x54x11 3x59x11 4x67x11 44 2x125x11 3x160x11 4x205x11 28 2x125x11 3x176x11 4x239x11 10

Fig. 11 2x61x11 3x68x11 4x75x11 68 2x143x10 3x188x10 4x232x10 38 2x153x11 3x221x11 4x277x11 16

using different trainings datasets. This indicates that the local

Alignment approach already gets most of the information of

the two context histories the test dataset has been generated

from and does not benefit from additional context histories.

Table I presents the different sizes of the tensor models

created from the training datasets. A1

indicates the tensor

containing context histories of two users, etc. Furthermore, the

Table displays the size Ψ of the test datasets for the different

window sizes. To construct the approximated prediction mod-

els from the tensors containing the different training datasets,

in each case only the user dimension has been reduced to the

size of one. The accuracy of the context prediction process gets

worse dramatically, if the context patterns’ dimension or the

future contexts’ dimension of the tensors presented in Table I

has been reduced.

The results indicate two important cognitions. Firstly, the

results show that it is possible to forecast future contexts based

on an unknown context pattern by using additional context

histories of other users. Secondly, in most cases the prediction

results of the CCP approach can be improved by using more

than just one additional context history. The division of the

context histories in context parts with different window sizes

show that the prediction results for smaller window sizes

normally achieve less accuracy than for higher window sizes.

That is because the smaller the chosen window size the higher

the number of entries in the test dataset. In the comparison

of the single-mode datasets and the all-mode datasets we

recognise that in most cases the prediction for the all-mode

datasets achieved better results. Furthermore, CCP provides

more accurate prediction results than the local Alignment

approach for all examined test datasets.

VI. CONCLUSIONS

In this paper we introduced the Collaborative Context

Predictor (CCP) method. This approach tries to overcome

the problem of unknown or missing context information in

a single user’s context history by using existing relations

between context histories of several users. Experiments on

real-world movement data showed that CCP is able to obtain

quite accurate prediction results, even if the underlying context

information is missing in the context history of the respective

user. Furthermore our experiments have shown that CCP

obtains better results than the local Alignment predictor for

every test dataset. Next, we intend to add fuzziness to the

CCP approach for which context patterns in the histories of

the users do not have to match exactly to be considered as

existing relations.

ACKNOWLEDGMENT

The authors are involved in the VENUS research project.

VENUS is a research cluster at the interdisciplinary Re-

search 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-okonomischer Exzellenz”.

For further information, please visit: http://www.iteg.uni-

kassel.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.

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Fig. 8. Test datasets generated from the intersections of user 1 and user 2. Used with different window sizes and data modes.

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Fig. 9. Test datasets generated from the intersections of user 2 and user 3. Used with different window sizes and data modes.

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Wnd=3 Wnd=5 Wnd=7

Accu

racy in

%

Window Sizes

Based on test dataset of user 1 and user 3 (all data)

2User(CCP)3User(CCP)4User(CCP)

Alignment

Fig. 10. Test datasets generated from the intersections of user 1 and user 3. Used with different window sizes and data modes.

0

20

40

60

80

100

Wnd=3 Wnd=5 Wnd=7

Accura

cy in %

Window Sizes

Based on test dataset of user 2 and user 4 (single data)

2User(CCP)3User(CCP)4User(CCP)

Alignment

0

20

40

60

80

100

Wnd=3 Wnd=5 Wnd=7

Accura

cy in %

Window Sizes

Based on test dataset of user 2 and user 4 (single data)

2User(CCP)3User(CCP)4User(CCP)

Alignment

0

20

40

60

80

100

Wnd=3 Wnd=5 Wnd=7

Accura

cy in %

Window Sizes

Based on test dataset of user 2 and user 4 (all data)

2User(CCP)3User(CCP)4User(CCP)

Alignment

0

20

40

60

80

100

Wnd=3 Wnd=5 Wnd=7

Accura

cy in %

Window Sizes

Based on test dataset of user 2 and user 4 (all data)

2User(CCP)3User(CCP)4User(CCP)

Alignment

Fig. 11. Test datasets generated from the intersections of user 2 and user 4. Used with different window sizes and data modes.

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