=Paper=
{{Paper
|id=Vol-528/paper-2
|storemode=property
|title=Using Gaussian Spatial Processes to Model and Predict Interests in Museum Exhibits
|pdfUrl=https://ceur-ws.org/Vol-528/paper2.pdf
|volume=Vol-528
|dblpUrl=https://dblp.org/rec/conf/ijcai/BohnertZS09
}}
==Using Gaussian Spatial Processes to Model and Predict Interests in Museum Exhibits==
https://ceur-ws.org/Vol-528/paper2.pdf
Using Gaussian Spatial Processes to
Model and Predict Interests in Museum Exhibits
Fabian Bohnert, Ingrid Zukerman, and Daniel F. Schmidt
Faculty of Information Technology, Monash University
Clayton, VIC 3800, Australia
{fabianb,ingrid,dschmidt}@infotech.monash.edu.au
Abstract viewing times rather than explicit ratings, and (3) predictions
differing from recommendations (we do not want to recom-
This paper adapts models from the area of spatial mend exhibits that visitors are going to see anyway). We turn
statistics to the task of predicting a user’s inter- the first challenge into an advantage by exploiting the fact
ests (i. e., implicit item ratings) within a recom- that physical distances between exhibits are meaningful, en-
mender system in the museum domain. We de- abling the use of walking distance between exhibits to calcu-
velop a model based on Gaussian spatial processes, late (content) distance. This supports the direct, interpretable
and discuss two ways of computing item-to-item application of spatial processes by using a simple paramet-
distances in the museum setting. Our model was ric Gaussian spatial process model (with the ensuing low
evaluated with a real-world dataset collected by variance in parameter estimates), compared to more complex
tracking visitors in a museum. Overall, our model non-parametric approaches, e. g., [Schwaighofer et al., 2005].
attains a higher predictive accuracy than nearest- The second challenge, which stems from the variable seman-
neighbour collaborative filters. In addition, the tics of viewing times (time t for different exhibits could mean
model variant using physical distances outperforms interest or boredom), is naturally addressed by SPM’s struc-
that using distances computed from item-to-item ture. The third challenge can be addressed by (a) using SPM
similarities. to build a model of a visitor’s interests in unseen exhibits,
(b) inferring a predictive model of a visitor’s pathway through
1 Introduction the remainder of the museum [Bohnert et al., 2008], and
Spatial processes (random fields) are a subclass of stochastic (c) combining these models to recommend exhibits of interest
processes which are applied to domains that have a geospa- that may be overlooked if the predicted pathway is followed.
tial interpretation, e. g., [Diggle et al., 1998; Banerjee et al., SPM was evaluated with a real-world dataset of time spans
2004]. They are typically used in the field of spatial statistics spent by museum visitors at exhibits (viewed as implicit rat-
to model spatial associations between a set of observations ings). We compared our model’s performance to that of (1) a
made at certain locations, and to predict values at locations baseline model which delivers a non-personalised prediction,
where no observations have been made. This paper applies and (2) a nearest-neighbour collaborative filter incorporat-
such models to the prediction of a user’s interests or item rat- ing performance-enhancing modifications, e. g., [James and
ings in recommender systems (RS). We develop our Spatial Stein, 1961; Herlocker et al., 1999]. Our results show that
Process Model (SPM) by adapting a Gaussian spatial process SPM significantly outperforms both models.
model to the RS scenario, and demonstrate our model’s ap- The paper is organised as follows. In Section 2, we discuss
plicability to the task of predicting implicit ratings in the mu- related research. Section 3 describes our domain and dataset.
seum domain. The use of spatial processes requires a measure Our spatial processes approach for modelling and predicting
of distance between items in addition to users’ ratings. This exhibit interests is developed in Section 4. In Section 5, we
measure, which is non-specific (e. g., it may be a physical or present the results of our evaluation, followed by a discussion
a conceptual distance), can be readily obtained in most cases. in Section 6 and our conclusions in Section 7.
For example, distances could be computed from feature vec-
tors representing the items (similarly to content-based RS), 2 Related Research
from item-to-item similarities (similarly to item-to-item col- Recommender systems (RS) are designed to direct users to
laborative filtering [Sarwar et al., 2001]), or from physical personally interesting items in situations where the amount
distance. In this paper, we explore the latter two measures. of available information exceeds the users’ processing capa-
Our application scenario is motivated by the need to au- bility [Resnick and Varian, 1997; Burke, 2002]. Typically,
tomatically recommend exhibits to museum visitors, based such systems (1) use information about a user (i. e., a user
on non-intrusive observations of their actions in the physi- model) to predict ratings of items that the user has not yet
cal space. Employing RS in this scenario is challenging due considered, and (2) recommend suitable items based on these
to (1) the physical nature of the domain, (2) having exhibit predictions. Collaborative modelling techniques constitute
one of the main model classes applied in RS [Albrecht and dation techniques that do not require such an explicit domain
Zukerman, 2007]. They base their predictions upon the as- knowledge representation [Albrecht and Zukerman, 2007].
sumption that users who have agreed in their behaviour in the
past will agree in the future.
3 Domain and Dataset
The greatest strength of collaborative approaches is that
they are independent of any representation of the items being The G ECKO project endeavours to develop user modelling
recommended, and work well for complex objects, for which and personalisation techniques for information-rich physical
features are not readily apparent. The two main collaborative spaces, relying on non-intrusive observations of users’ be-
approaches are memory-based and model-based. Previous haviour [Bohnert et al., 2008]. Developing such non-intrusive
research has mainly focused on memory-based approaches, user modelling and personalisation techniques for museums
such as nearest-neighbour models (classic collaborative fil- requires datasets about visitor behaviour in the physical mu-
tering), e. g., [Herlocker et al., 1999]. The main drawback of seum space (i. e., visitor pathways). Datasets that are suitable
memory-based algorithms is that they operate over the entire for the development phase can be obtained by manually track-
user database to make predictions. In contrast, model-based ing museum visitors. Such a data collection methodology is
approaches use techniques such as Bayesian networks, latent- clearly inappropriate for model deployment, but it facilitates
factor models and artificial neural networks, e. g., [Breese et model development by eschewing issues related to technol-
al., 1998; Bell et al., 2007], to first learn a statistical model ogy selection and instrumentation accuracy.
in an offline fashion, and then use it to make predictions and Museums such as Melbourne Museum (Melbourne, Aus-
generate recommendations. This decomposition can signifi- tralia) display thousands of exhibits distributed over many
cantly speed up the recommendation generation process. separate galleries and exhibitions. Normally, visitors do not
Personalised guide systems in physical domains have of- require recommendations to travel between individual, logi-
ten employed adaptable user models, which require visitors cally related exhibits in close physical proximity. Rather, they
to explicitly state their interests in some form. For example, may prefer recommendations regarding physically separated
the GUIDE project [Cheverst et al., 2002] developed a hand- areas. In order to gather data for assessing predictive models
held tourist guide for visitors to the city of Lancaster, UK. that support appropriate recommendations, we grouped Mel-
It employed a user model obtained from explicit user input bourne Museum’s individual exhibits into semantically co-
to generate a dynamic and user-adapted city tour, where the herent and spatially confined exhibit areas. This task, which
order of the visited items could be varied. In the museum do- was performed with the assistance of museum staff, yielded
main, the CHIP project [Aroyo et al., 2007] investigates how 126 exhibit areas. Figure 1 depicts the site map of Melbourne
Semantic Web techniques can be used to provide personalised Museum showing these exhibit areas, together with one of the
access to digital museum collections both online and in the visitor pathways we collected.
physical museum, based on models that require an explicit To obtain our dataset, we manually tracked visitors to Mel-
initialisation. bourne Museum from April to June 2008, using a custom-
Less attention has been paid to predicting preferences made tracking tool running on laptop computers [Bohnert and
from non-intrusive observations, and to utilising adaptive user Zukerman, 2009]. In total, we recorded over 170 visitor path-
models that do not require explicit user input. In the museum ways. We only tracked first-time adult visitors travelling on
domain, adaptive user models are usually updated from a their own, to ensure that neither prior knowledge about the
user’s interactions with the system, the focus being on adapt- museum nor other visitors’ interests influenced a visitor’s de-
ing content presentation as opposed to predicting and rec- cisions about which exhibits to view. Prior to the data col-
ommending exhibits to be viewed. For example, HyperAu- lection, we briefed our trackers on the usage of our tracking
dio [Petrelli and Not, 2005] dynamically adapted the pre- software, the layout of the museum, and its digital represen-
sented content and hyperlinks to stereotypical assumptions tation on the site map. Additionally, we clarified what should
about a user, and to what a user has already accessed and be considered a viewing event. After the data collection, the
seems interested in. The augmented audio reality system for visitor pathways were post-processed using a post-processing
museums ec(h)o [Hatala and Wakkary, 2005] treated user in- tool we developed. For instance, we removed tracking events
terests in a dynamic manner, and adapted its user model on that could not have possibly occurred, e. g., visitor transitions
the basis of a user’s interactions with the system. The col- from one end of the museum to the other and back within
lected user modelling data were used to deliver personalised a few seconds, or transitions outside the museum walls and
information associated with exhibits via audio display. The back. We also removed incomplete visitor pathways, e. g.,
PEACH project [Stock et al., 2007] developed a multimedia due to a laptop computer running out of battery, or a vis-
handheld guide which adapts its user model on the basis of itor leaving unexpectedly. The resulting dataset comprises
both explicit visitor feedback and implicit observations of a 158 complete visitor pathways in the form of time-annotated
visitor’s interactions with the device. This user model was sequences of visited exhibit areas, with a total visit length
then used to generate personalised multimedia presentations. of 291:22:37 hours, and a total viewing time of 240:00:28
These systems, like most systems in the museum domain, hours. The dataset also contains demographic information
rely on knowledge-based user models in some way, and about the visitors, which was obtained by means of post-visit
hence, require an explicit, a-priori engineered representation interviews conducted by our trackers. In total, we obtained
of the domain knowledge. In contrast, our research investi- 8327 viewing durations at the 126 exhibit areas, yielding an
gates non-intrusive statistical user modelling and recommen- average of 52.7 exhibit areas per visitor (41.8% of the exhibit
(a) Melbourne Museum – Ground level (b) Melbourne Museum – Upper level
Figure 1: Visitor pathway visualised on a site map of Melbourne Museum
Table 1: Dataset statistics as viewing time correlates positively with preference and in-
terest [Parsons et al., 2004]. Hence, viewing time can be used
Mean Stddev Min Max as an indirect measure of interest. We propose to use log
viewing time (instead of raw viewing time), due to the fol-
Visit length (hrs) 1:50:39 0:47:54 0:28:23 4:42:12
lowing reasons. When examining our dataset (Section 3), we
Viewing time (hrs) 1:31:09 0:42:05 0:14:09 4:08:27
found the distributions of viewing times at exhibits to be pos-
Exhibit areas / visitor 52.70 20.69 16 103 itively skewed (we use the terms ‘exhibit’ and ‘exhibit area’
Visitors / exhibit area 66.09 25.36 6 117 synonymously in the remainder of this paper). Thus, the usual
assumption of a Gaussian model did not seem appropriate. To
select a more appropriate family of probability distributions,
areas). Hence, on average 58.2% of the exhibit areas were we used the Bayesian Information Criterion (BIC) [Schwarz,
not viewed by a visitor. This indicates that there is potential 1978]. We tested exponential, gamma, normal, log-normal
for pointing a visitor to relevant but unvisited exhibit areas. and Weibull distributions. The log-normal family fitted best,
Table 1 summarises further statistics of the dataset. with respect to both number of best fits and average BIC score
Clearly, the deployment of an automated RS in a museum (averaged over all exhibits). Hence, we transformed all view-
requires suitable positioning technologies to non-intrusively ing times to their log-equivalent to obtain approximately nor-
track visitors, and models to infer which exhibits are being mally distributed data. This transformation fits well with the
viewed. Although our dataset was obtained manually, it pro- idea that for high viewing times, an increase in viewing time
vides information of the type that may be inferred from sens- indicates a smaller increase in the modelled interest than a
ing data (the work described in [Schmidt et al., 2009] links similar increase in the context of low viewing times.
sensory and manually obtained information). Additionally,
the results obtained from experiments with this dataset are 4.2 Spatial Statistics in the Context of Our
essential for model development, as they provide an upper Application Scenario
bound for the predictive performance of our model. Spatial statistics is concerned with the analysis and predic-
tion of geographic data [Banerjee et al., 2004]. Utilising spa-
tial processes, the field deals with tasks such as modelling the
4 Using Gaussian Spatial Processes to Model associations between observations made at certain locations,
and Predict Visitors’ Exhibit Interests and predicting values at locations where no observations have
In this section, we first describe how we use viewing time to been made. The assumption made for spatial processes, that
quantify interest in exhibits (Section 4.1), and discuss the ap- correlation between observations increases with decreasing
plicability of spatial process models [Banerjee et al., 2004] site distance, fits well with our RS scenario, where viewing
to the prediction of a visitor’s interest in exhibits in our RS times are usually more correlated the more related exhibits
scenario (Section 4.2). We then propose a model-based col- are. Hence, by introducing a notion of spatial distance be-
laborative approach based on the theory of Gaussian spa- tween exhibits to functionally specify this correlation struc-
tial processes for predicting a visitor’s (log) viewing times ture, we can use spatial process models for predicting view-
(viewed as exhibit interests) from non-intrusive observations ing times (i. e., exhibit interests). We use s1 , . . . , sn to de-
of his/her (log) viewing times at visited exhibits (Section 4.3). note the locations of exhibits i, j ∈ I = {1, . . . , n} in a
space providing such a distance measure, i. e., ksi − sj k. For
example, ksi − sj k can be computed from feature vectors
4.1 From Viewing Time to Exhibit Interest
representing the items (similarly to content-based RS), from
In an information-seeking context, people usually spend more item-to-item similarities (similarly to item-to-item collabora-
time on relevant information than on irrelevant information, tive filtering [Sarwar et al., 2001]), or from physical distance.
In this paper, we explore the two latter options: Item-to-Item viewed exhibits 2, 3, 7 and 9, then µ1 = (µ2 , µ3 , µ7 , µ9 ) and
Distance and Physical Distance. σ1 = (σ2 , σ3 , σ7 , σ9 ).
• Item-to-Item Distance (I2I). Item-to-item collaborative Similarly to spatial processes, SPM assumes a special cor-
filtering [Sarwar et al., 2001] utilises a database of rat- relation structure between the viewing times of different ex-
ings to compute item-to-item similarities, and predicts hibits. In our experiments, we use a powered exponen-
a current user’s rating of an unseen item from his/her tial [Banerjee et al., 2004]:
ratings of those items that are most similar to the item ν
ρ(ksi − sj k; φ, ν) = exp (− (φksi − sj k) ) ,
in question. Inspired by how item-to-item similarities
are computed in this process, we use the observed log where φ > 0 and 0 < ν < 2. That is, ρ(ksi − sj k; φ, ν)
viewing times to derive the I2I distance measure as fol- models the correlation between the log viewing times of ex-
lows. We first transform the log viewing times into z- hibits i and j (ρ(ksi − sj k; φ, ν) depends on the sites si
scores by normalising the values for each visitor sepa- and sj of exhibits i and j only through the distance
rately. This ensures that varying viewing behaviour does ksi − sj k). Let H(φ, ν) be a correlation matrix with com-
not affect the similarity computation.1 Secondly, we cal- ponents (H(φ, ν))ij = ρ(ksi − sj k; φ, ν) collecting all these
culate item-to-item similarities using Pearson’s correla- correlations, and let Hu (φ, ν) denote a visitor u’s correlation
tion coefficient on the normalised log viewing times of matrix (dimension nu × nu ). That is, Hu (φ, ν) corresponds
exhibits i and j (using only the normalised log viewing to H(φ, ν) without the rows and columns
for unvisited ex-
times of those visitors that have viewed both exhibits i hibits. Also, let θ = µ, σ, τ 2 , φ, ν be a vector representing
and j). The resulting similarity value from within the in- the 2n + 3 model parameters, where τ 2 denotes the variance
terval [−1, 1] is finally transformed into a distance mea- of non-spatial error terms necessary to fully specify the model
sure by mapping it onto a value in [0, 1] (a similarity (these terms model non-spatial variation in the data). Then,
value of −1 yields a distance of 1, and a similarity of 1 modelling the data using Gaussian spatial processes (a de-
yields a distance of 0). tailed derivation appears in [Bohnert P et al., 2009]), r given θ
m
• Physical Distance (PD). Museums are carefully themed is multivariate normal of dimension u=1 nu . As the view-
by curatorial staff, such that closely-related exhibits are ing times of different visitors u = 1, . . . , m are independent,
in physical proximity. Based on this observation, we the model simplifies to
hypothesise that physical walking distance between ex-
ru | θ ∼ N (µu , Σu ) for all u = 1, . . . , m, (1)
hibits is inversely proportional to their (content) simi-
larity. Thus, we use physical walking distance PD as 2
where Σu = σu 1nu Hu (φ, ν)σu 1nu + τ 1nu is a visitor u’s
a measure of distance between exhibits. Specifically, covariance matrix, and 1nu is the identity matrix of dimen-
a SVG file-based representation of Melbourne Museum sion nu × nu .
was used to calculate the walking distances by mapping We employ Bayesian inference using SPM’s likelihood
the site map (Figure 1) onto a graph structure which pre- function derived from Equation 1 to estimate θ from r (in
serves the physical layout of the museum (i. e., prevent- particular, we use slice Gibbs sampling [Neal, 2003]). This
ing paths from passing through walls or ceilings). We solution offers attractive advantages over the classic frequen-
normalised the resulting distances to the interval [0, 1]. tist approach, such as the opportunity of incorporating prior
knowledge into parameter estimation via the prior distribu-
4.3 Our Gaussian Spatial Process Model tion, and capturing the uncertainty about the parameters via
In this section, we utilise theory from the area of spatial the posterior distribution.
statistics (Section 4.2) to formulate a Gaussian spatial process Given the model parameters θ = µ, σ, τ 2 , φ, ν , our
model, called Spatial Process Model (SPM), for predicting a model is fully specified, and we can use standard multivari-
museum visitor’s interests in unseen exhibits (i. e., log view- ate normal theory to predict a current visitor a’s log viewing
ing times) from his/her viewing behaviour at visited exhibits. times of unseen exhibits, say ra,1 , from a vector of observed
Let U = {1, . . . , m} be the set of all visitors, and log viewing times ra,2 . This is because (ra,1 , ra,2 ) | θ is nor-
I = {1, . . . , n} be the set of all items. Typically, for a vis- mally distributed (similarly to Equation 1). If we use the fol-
itor u ∈ U , we have viewing times for only a subset of I, say lowing notation
for nu exhibits. Denoting a visitor’s log viewing time vec-
Σa,11 Σa,12
ra,1 µa,1
tor with ru , we collect all observed logPviewing times into a |θ ∼ N , T ,
m ra,2 µa,2 Σa,12 Σa,22
vector r = (r1 , . . . , rm ) of dimension u=1 nu . Associated
with each exhibit i ∈ I is a log viewing time mean µi and then the conditional distribution p (ra,1 |ra,2 , θ) is normal
a standard deviation σi . Let µ = (µ1 , . . . , µn ) be the vector with mean vector and covariance matrix
of mean log viewing times, and σ = (σ1 , . . . , σn ) the vector
of standard deviations. Furthermore, µu and σu are the vec- E (ra,1 |ra,2 , θ) = µa,1 + Σa,12 Σ−1
a,22 (ra,2 − µa,2 ) ,
tors of means and standard deviations respectively for only Cov (ra,1 |ra,2 , θ) = Σa,11 − Σa,12 Σ−1 T
a,22 Σa,12 ,
those exhibits viewed by a visitor u. For example, if visitor 1
where E (ra,1 |ra,2 , θ) represents a personalised prediction
1
We also tested a variant of the I2I measure without visitor-wise of the log viewing times ra,1 . Additionally, a measure
normalisation. However, this variant yielded inferior results. of confidence in this prediction can be easily derived from
Cov (ra,1 |ra,2 , θ), i. e., by using the variances on the diago- was followed to obtain samples of θ for both SPM variants,
nal of this matrix. i. e., for both distance measures I2I and PD (Section 4.2). We
Being a model-based approach, SPM offers advantages then used the posterior means estimated from these samples
over memory-based collaborative filters. For instance, the to compute predictions by conditioning a multivariate normal
model parameters θ = µ, σ, τ 2 , φ, ν have a clear inter- distribution (Section 4.3). We improved SPM-I2I’s predic-
pretation, and the confidence measure provided by the model tive performance by using the (non-personalised) mean log
supports an informed interpretation of the model’s predic- viewing time µi as a prediction whenever the conditioning
tions. Additionally, recommendation generation is sped up by would have been based on fewer than K log viewing times
decoupling the model-fitting phase from the prediction phase. (in our case, K = 19). This modification was not applied to
SPM-PD. For CF, predictions were computed from the rat-
5 Evaluation ings of the nearest neighbours; and for MM, we used µi , esti-
mated from the appropriate reduced dataset, as a prediction.
This section reports on the results of an evaluation performed We performed two types of experiments: Individual Ex-
with our dataset (Section 3), including comparison with a hibit and Progressive Visit.
nearest-neighbour collaborative filter.2
• Individual Exhibit (IE). IE evaluates predictive perfor-
5.1 Experimental Setup mance for a single exhibit. For each observed visitor-
exhibit area pair (u, i), we removed the observation rui
To evaluate the predictive performance of our Spatial Process
from the vector of visitor u’s log viewing durations, and
Model (SPM), we implemented two additional models: Mean
computed a prediction r̂ui from the other observations.
Model (MM) and Collaborative Filter (CF). MM, which we
This experiment is lenient in the sense that all available
use as a baseline, predicts the log viewing time of an ex-
observations except the observation for exhibit area i are
hibit area i to be its (non-personalised) mean log viewing
kept in a visitor’s viewing duration vector.
time µi . For CF, we implemented a nearest-neighbour col-
laborative filtering algorithm, and added modifications from • Progressive Visit (PV). PV evaluates performance as a
the literature that improve its performance, such as shrink- museum visit progresses, i. e., as the number of viewed
age to the mean [James and Stein, 1961] and significance exhibit areas increases. For each visitor, we started with
weighting [Herlocker et al., 1999]. Additionally, to ensure an empty visit, and iteratively added each viewed exhibit
that varying exhibit area complexity does not affect the simi- area to the visit history, together with its log viewing
larity computation for selecting the nearest neighbours (view- time. We then predicted the log viewing times of all yet
ing time increases with exhibit complexity), we transformed unvisited exhibit areas.
the log viewing times into z-scores by normalising the values For both experiments, we used the mean absolute error
for each of the exhibit areas separately. Visitor-to-visitor dif- (MAE) to measure predictive accuracy as follows:
ferences with respect to their mean viewing durations were
removed by transforming predictions to the current visitor’s 1 XX
MAE = P |rui − r̂ui |,
viewing-time scale [Herlocker et al., 1999]. Refer to [Bohn- u∈U |Iu | u∈U i∈Iu
ert and Zukerman, 2009] for a detailed description of CF. We
tested several thousand different parameterisations, but in this where Iu denotes a visitor u’s set of exhibit areas for which
paper, we report only on the performance of the best one. predictions were computed. For IE, we calculated the total
Due to the relatively small dataset, we used leave-one-out MAE for all valid visitor-exhibit area pairs; and for PV, we
cross validation to evaluate the performance of the different computed the MAE for the yet unvisited exhibit areas for all
models. That is, for each visitor, we trained the models with visitors at each time fraction of a visit (to account for different
a reduced dataset containing the data of 157 of the 158 visit visit lengths, we normalised all visits to a length of 1).
trajectories, and used the withheld visitor pathway for test-
ing. To train and instantiate the SPM variants (i. e., SPM-I2I 5.2 Results
and SPM-PD), we obtained a sample of θ = µ, σ, τ 2 , φ, ν Table 2 shows the results for the IE experiment, where both
from p(θ|r) by performing slice Gibbs sampling [Neal, 2003] spatial models (SPM-I2I and SPM-PD) outperform both MM
on the training data. For each of the 129 free model parame- and CF. Specifically, SPM-I2I achieves an MAE of 0.7756
ters,3 we used (uninformative) independent uniform prior dis- (stderr 0.0068), and SPM-PD attains an MAE of 0.7548
tributions. We used every 20-th sample after a burn-in phase (stderr 0.0066), outperforming SPM-I2I as well. The pair-
of 1000 iterations as a sample of θ from p(θ|r), and stopped wise performance differences are statistically significant with
the sampling procedure after 8000 iterations. Thus, in total, p 0.01 for all model pairings.
we obtained 350 samples of θ from p(θ|r). This procedure The performance of SPM-PD, SPM-I2I, CF and the base-
2
line MM for the PV experiment is depicted in Figure 2. CF
For our experiments, we ignore travel between exhibit areas, outperforms MM slightly (statistically significantly for visit
and collapse multiple
q viewing events of one area into one event. fractions 0.191 to 0.374 and for several shorter intervals later
3 2
We set σi = σr,i − τ 2 to speed up the sampling process, on, p < 0.05). More importantly, both SPM-I2I and SPM-PD
2
where σr,i denotes the sample variance of the log viewing times at perform significantly better than MM and CF. For SPM-I2I,
exhibit i, calculated from the observed log viewing times rui . This this performance increase is statistically significant for visit
reduces the number of free parameters from 255 (126×2+3) to 129. fractions 0.189 to 0.960 when comparing to MM, and except
Table 2: Model performance for the IE experiment (MAE) 6 Discussion
MAE Stderr SPM offers advantages over other model-based approaches in
that, unlike neural networks (and memory-based techniques),
Mean Model (MM) 0.8618 0.0071
it returns the confidence in a prediction, and its parameters
Collaborative Filter (CF) 0.7868 0.0068
have a clear interpretation; unlike Bayesian networks, our
Spatial Process Model using I2I
model does not require a domain-specific adaptation, such
(SPM-I2I) 0.7756 0.0068
as designing the network topology. In addition, the dis-
Spatial Process Model using PD
tance measure endows our model with capabilities of hybrid
(SPM-PD) 0.7548 0.0066
RS [Burke, 2002; Albrecht and Zukerman, 2007] by seam-
lessly supporting the incorporation of other types of models
0.92
MM
(e. g., content-based). The distance measure also alleviates
CF the cold-start problem. The new-item problem is addressed
0.90 SPM−I2I
SPM−PD by utilising the (distance-based) correlation between this item
0.88 and the other items. The new-user problem is similarly han-
MAE
dled through the correlation between items rated by a user
0.86 and the other items (when utilising Physical Distance as the
distance measure, our model can make useful personalised
0.84
predictions after only one item has been rated).
0.82 Our dataset is relatively small compared to other real-world
0.0 0.2 0.4 0.6 0.8 1.0
visit fraction RS applications. Although a high number of ratings per user
slows down the slice Gibbs sampler due to repeated inversion
Figure 2: Model performance for the PV experiment (MAE) of matrices of high dimension, employing our model with
larger datasets should not represent a problem in practice.
for a few short intervals, for visit fractions 0.375 to 0.902 This is because the number of ratings per user is usually small
when comparing to CF. In comparison, SPM-PD performs compared to the number of users and items, and the compu-
significantly better than both MM and CF for visit fractions tational complexity of evaluating the likelihood function de-
0.019 to 0.922 (statistically significantly, p < 0.05). Ad- pends only linearly on the number of users in the database.
ditionally, SPM-PD outperforms SPM-I2I until visit fraction
0.660 (statistically significantly, p < 0.05). Drawing atten- 7 Conclusions and Future Work
tion to the initial portion of the visits, SPM-PD’s MAE de-
creases rapidly, whereas the MAE for MM and CF remains In this paper, we utilised the theory of spatial processes to de-
at a higher level. Generally, the faster a model adapts to velop a model-based approach for predicting users’ interests
a visitor’s interests, the more likely it is to quickly deliver in exhibits (i. e., implicit item ratings) within a RS in the mu-
(personally) useful recommendations. Such behaviour in the seum domain. We applied our model to a real-world dataset
early stages of a museum visit is essential in order to build collected by tracking visitors in a museum, using two mea-
trust in the RS, and to guide a visitor in a phase of the visit sures of item-to-item (content) distance: (1) distances com-
where such guidance is most likely needed. A similar im- puted from item-to-item similarities (as in item-to-item col-
provement in performance cannot be observed for SPM-I2I, laborative filtering), and (2) physical walking distance. For
which suggests that a visitor’s exhibit interests observed in both distance measures, our model attains a higher predictive
close physical proximity are better predictors of interests in accuracy than nearest-neighbour collaborative filters. Addi-
unseen exhibits than interests in exhibits with positively cor- tionally, the model variant using physical distances outper-
related viewing times. As expected, MM performs at a rela- forms that using distances computed from item-to-item sim-
tively constant MAE level. For CF, SPM-I2I and SPM-PD ilarities. Under the realistic Progressive Visit setting, our
we expected to see an improvement in performance (rela- model using physical distance to measure item-to-item dis-
tive to MM) as the number of visited exhibit areas increases. tance rapidly adapts to a user’s ratings (starting from as little
However, this trend is rather subtle (it can be observed when as one rating), thus alleviating the new-user problem common
plotting the models’ performance relative to MM). Addition- to collaborative filtering. This is not the case for the model
ally, for all four models, there is a performance drop towards variant based on distance computed from item-to-item simi-
the end of a visit. We postulate that these phenomena may be larities, which suggests that a visitor’s interests observed for
explained, at least partially, by the increased influence of out- exhibits in close physical proximity are better predictors of
liers on the MAE as the number of exhibit areas remaining to interests in unseen exhibits than those interests for exhibits
be viewed is reduced with the progression of a visit. This in- with positively correlated viewing times.
fluence in turn offsets potential gains in performance obtained In the future, we intend to hybridise our model by incor-
from additional observations. Our hypothesis is supported by porating content-based item features into our distance mea-
a widening in the standard error bands for all models as a sure, and to explore hybrids of models utilising a variety of
visit progresses, in particular towards the end (not shown in item-to-item distances. We also plan to extend our model
Figure 2 for clarity of presentation). However, this behaviour to fit non-Gaussian item ratings, e. g., [Diggle et al., 1998;
requires further, more rigorous investigation. Yu et al., 2006].
Acknowledgments [Hatala and Wakkary, 2005] M. Hatala and R. Wakkary.
Ontology-based user modeling in an augmented audio re-
This research was supported in part by grant DP0770931 ality system for museums. User Modeling and User-
from the Australian Research Council. The authors thank Adapted Interaction, 15(3-4):339–380, 2005.
Carolyn Meehan and her team from Museum Victoria for
their assistance; and David Abramson, Jeff Tan and Blair [Herlocker et al., 1999] J.L. Herlocker, J.A. Konstan, A.
Bethwaite for their help with the computer cluster. Borchers, and J.T. Riedl. An algorithmic framework for
performing collaborative filtering. In Proceedings of the
22th Annual International ACM SIGIR Conference on Re-
References search and Development in Information Retrieval (SIGIR-
[Albrecht and Zukerman, 2007] D.W. Albrecht and I. Zuker- 99), pages 230–237, 1999.
man. Introduction to the special issue on statistical and [James and Stein, 1961] W. James and C.M. Stein. Estima-
probabilistic methods for user modeling. User Modeling tion with quadratic loss. In Proceedings of the Fourth
and User-Adapted Interaction, 17(1-2):1–4, 2007. Berkeley Symposium on Mathematical Statistics and Prob-
[Aroyo et al., 2007] L. Aroyo, N. Stash, Y. Wang, P. Gorgels, ability, vol. 1, pages 361–379, 1961.
and L. Rutledge. CHIP demonstrator: Semantics-driven [Neal, 2003] R.M. Neal. Slice sampling. The Annals of
recommendations and museum tour generation. In Pro- Statistics, 31(3):705–767, 2003.
ceedings of the Sixth International Conference on the Se- [Parsons et al., 2004] J. Parsons, P. Ralph, and K. Gallager.
mantic Web (ISWC-07), pages 879–886, 2007. Using viewing time to infer user preference in recom-
[Banerjee et al., 2004] S. Banerjee, B.P. Carlin, and A.E. mender systems. In Proceedings of the AAAI Workshop
Gelfand. Hierarchical Modeling and Analysis for Spatial on Semantic Web Personalization (SWP-04), pages 52–64,
Data. Chapman & Hall/CRC, 2004. 2004.
[Petrelli and Not, 2005] D. Petrelli and E. Not. User-centred
[Bell et al., 2007] R. Bell, Y. Koren, and C. Volinsky. Chas-
design of flexible hypermedia for a mobile guide: Reflec-
ing $1,000,000: How we won the Netflix progress
tions on the HyperAudio experience. User Modeling and
prize. ASA Statistical and Computing Graphics Newslet-
User-Adapted Interaction, 15(3-4):303–338, 2005.
ter, 18(2):4–12, 2007.
[Resnick and Varian, 1997] P. Resnick and H.R. Varian.
[Bohnert and Zukerman, 2009] F. Bohnert and I. Zukerman. Recommender systems. Communications of the ACM,
Non-intrusive personalisation of the museum experience. 40(3):56–58, 1997.
In Proceedings of the 1st and 17th International Confer-
ence on User Modeling, Adaptation, and Personalization [Sarwar et al., 2001] B. Sarwar, G. Karypis, J.A. Konstan,
(UMAP-09), pages 197–209, 2009. and J.T. Riedl. Item-based collaborative filtering recom-
mendation algorithms. In Proceedings of the 10th Inter-
[Bohnert et al., 2008] F. Bohnert, I. Zukerman, S. Berkov- national Conference on the World Wide Web (WWW-01),
sky, T. Baldwin, and L. Sonenberg. Using interest and pages 285–295, 2001.
transition models to predict visitor locations in museums. [Schmidt et al., 2009] D.F. Schmidt, I. Zukerman, and D.W.
AI Communications, 21(2-3):195–202, 2008.
Albrecht. Assessing the impact of measurement uncer-
[Bohnert et al., 2009] F. Bohnert, D.F. Schmidt, and I. Zuk- tainty on user models in spatial domains. In Proceedings
erman. Spatial processes for recommender systems. In of the 1st and 17th International Conference on User Mod-
Proceedings of the 21st International Joint Conference on eling, Adaptation, and Personalization (UMAP-09), pages
Artificial Intelligence (IJCAI-09), 2009. 210–222, 2009.
[Breese et al., 1998] J.S. Breese, D. Heckerman, and C. [Schwaighofer et al., 2005] A. Schwaighofer, V. Tresp, and
Kadie. Empirical analysis of predictive algorithms for col- K. Yu. Learning Gaussian process kernels via hierarchi-
laborative filtering. In Proceedings of the 14th Interna- cal Bayes. In Advances in Neural Information Processing
tional Conference on Uncertainty in Artificial Intelligence Systems 17 (NIPS-04), pages 1209–1216, 2005.
(UAI-98), pages 42–52, 1998. [Schwarz, 1978] G.E. Schwarz. Estimating the dimension of
[Burke, 2002] R. Burke. Hybrid recommender systems: Sur- a model. The Annals of Statistics, 6(2):461–464, 1978.
vey and experiments. User Modeling and User-Adapted [Stock et al., 2007] O. Stock, M. Zancanaro, P. Busetta,
Interaction, 12(4):331–370, 2002. C. Callaway, A. Krüger, M. Kruppa, T. Kuflik, E. Not, and
[Cheverst et al., 2002] K. Cheverst, K. Mitchell, and N. C. Rocchi. Adaptive, intelligent presentation of informa-
tion for the museum visitor in PEACH. User Modeling
Davies. The role of adaptive hypermedia in a context-
and User-Adapted Interaction, 18(3):257–304, 2007.
aware tourist guide. Communications of the ACM,
45(5):47–51, 2002. [Yu et al., 2006] S. Yu, K. Yu, V. Tresp, and H.-P. Kriegel.
Collaborative ordinal regression. In Proceedings of
[Diggle et al., 1998] P.J. Diggle, J.A. Tawn, and R.A. Moy- the 23rd International Conference on Machine Learning
eed. Model-based geostatistics. Applied Statistics, (ICML-06), pages 1089–1096, 2006.
47(3):299–350, 1998.