Eigenbehaviour as an Indicator of Cognitive Abilities

Angela Botros1, Narayan Schütz1, Christina Röcke1, Robert Weibel1, Mike
Martin1, René Müri1, Tobias Nef1,*

1 ARTORG Center for Biomedical Engineering Research, Gerontechnology and
Rehabilitation, University of Bern, Bern, Switzerland
2 University Research Priority Program (URPP) ”Dynamics of Healthy Aging”,
University of Zurich, Andreasstrasse, Zurich, Switzerland
3 Department of Geography, University of Zurich, Zurich, Switzerland
4 Department of Psychology, University of Zurich, Binzmühlestrasse, Zurich,
Switzerland
5 Department of Neurology, Inselspital, University Hospital of Bern,
University of Bern, Switzerland
*<EMAIL_ADDRESS>
## Abstract

With growing usage of machine learning algorithms and big data in health
applications, digital biomarkers have become an important key feature to
ensure the success of those applications. In this paper, we focus on one
important use-case, the long-term continuous monitoring of the cognitive
ability of older adults. The cognitive ability is a factor both for long-term
monitoring of people living alone as well as an outcome in clinical studies.
In this work, we propose a new digital biomarker for cognitive abilities based
on location eigenbehaviour obtained from contactless ambient sensors. Indoor
location information obtained from passive infrared sensors is used to build a
location matrix covering several weeks of measurement. Based on the
eigenvectors of this matrix, the reconstruction error is calculated for
various numbers of used eigenvectors. The reconstruction error is used to
predict cognitive ability scores collected at baseline, using linear
regression. Additionally, classification of normal versus pathological
cognition level is performed using a support-vector-machine. Prediction
performance is strong for high levels of cognitive ability, but grows weaker
for low levels of cognitive ability. Classification into normal versus
pathological cognitive ability level reaches high accuracy with a AUC = 0.94.
Due to the unobtrusive method of measurement based on contactless ambient
sensors, this digital biomarker of cognitive ability is easily obtainable. The
usage of the reconstruction error is a strong digital biomarker for the binary
classification and, to a lesser extent, for more detailed prediction of
interindividual differences in cognition.

## Introduction

The monitoring of cognitive ability of people is a task to assess the health
state of adults. This holds true for both conducting clinical trials [2, 21,
5], as well as home-monitoring for elderly people [12, 17]. In both cases,
continuous long-term monitoring can complement the existing point-in-time
examinations, done by medical professionals in a clinic [10].

For the measurement of cognitive abilities, there are a range of different
tests. The Mini-Mental State Exam (MMSE) is an assessment to test for mild
cognitive impairment (MCI), Alzheimer’s disease (AD) and other cognitive
issues [4]. This test has a maximum cognitive ability score of 30. A cutoff is
used to distinguish between normal cognitive ability and people with dementia.
A generally accepted cutoff score for the MMSE is 24 [4], but a more
differentiated interpretation is suggested with adaptive cutoffs depending of
the peoples age and education [8]. Another test to detect cognitive impairment
is the Montreal Cognitive Assessment (MoCA) [11]. This test has a maximum
score of 30, too. The cutoff to distinguish between people with normal
cognitive ability and people with MCI or AD is set at 26 [7]; but this value
has been up for debate [11]. Other evaluations usually cover a selection of
individual tasks, such as the Halstead-Reitan neuropsychological test battery
[14].

Pervasive computing is a methodology that is promising for long-term
monitoring of cognitive abilities. It could provide safety and security for
independently living individuals, while still maintaining simplicity and -
depending on the exact chosen technology - privacy. Several studies have
provided evidence for both acceptance by the people and usefulness of such
systems [19, 16, 9, 1, 6, 20].

Stucki et al. have developed and tested a sensor system based on ambient and
object sensors to track activities of daily living (ADL) [19]. They have shown
that this system is able to track ADL reliably, both in healthy individuals
and people with AD. Schütz et al. were able to track physical health reliably
over a year, using a pervasive sensor system [16]. Their system consisted of
ambient, object and wearable sensors and was used for the monitoring of older
adults, living alone. Another multi faceted system consisting of ambient and
object sensors was used by Lyons et al. to monitor older people [9]. Over the
span of eight years they monitored their participants with the goal to
continually asses the cognitive status. Alam et al. have used wearable sensors
to track physiological data in order to assess cognitive ability trajectories
in the context of dementia [1].

With regards to the cognitive ability, Urwyler et al. have shown that the
daily routine of a a person diagnosed with Alzheimer’s dementia is far less
regular and more chaotic than the daily behaviour of age-matched healthy
individuals [20]. They have monitored people living alone using passive
infrared (PIR) sensors, a type of sensor detecting movement while maintaining
maximal privacy. Based on the results of Urwyler et al., we hypothesise, that
the regularity of people’s movement patterns at home is correlated to their
cognitive ability and thus influences the eigenvectors constructed from their
behaviour matrix.

The idea that certain medical conditions can affect daily behaviour has been
studies by Paraschiv-Ionescu et al.m where they monitored physical activities
of chronic pain patients over multiple days, and compared the data to those of
healthy pain-free people. They specifically noted the change in complexity of
physical activities between chronic-pain patients and pain-free patients, with
the latter showing a more complex behaviour [13].

For the analysis of the behaviour regularity we suggest a method based on
eigen-decomposition of behavioural matrices, a method introduced by Eagle et
al. [3]. They used the approximate localisation data obtained from cell phones
of 100 participants. An eigenvalue decomposition on this data provided insight
into the students’ behaviour, organisational group and circle of friends. The
idea to use principal component analysis to analyse the underlying structure
of data is not new, it was notably used in [18], where principal component
analysis is conducted to represent faces.

In the current work, we introduce a method to assess older adults’ cognitive
ability, based on movement patterns obtained through unobtrusive ambient
sensor technology. We evaluate this method based on data obtained from 48
individuals above the age of retirement.

## Materials and Methods

### Participants

The data presented in this study stems from two studies, the StrongAge Cohort
Study and the MOASIS MobiPro Study. Both studies were conducted based on the
principles declared in the Declaration of Helsinki and approved by the
University Ethics Committee. All participants signed and handed in an informed
consent before study participation.
The StrongAge Cohort Study is a home-monitoring study, where community
dwelling seniors (inclusion criterion $\geq 80$ years) were equipped with
pervasive computing systems for approximately one year [16]. The recruitment
aimed to represent a naturalistic sample of alone living older adults in
central Switzerland, irrespective of their cognitive ability.
The MOASIS MobiPro Study is a home-monitoring study, where community dwelling
seniors (inclusion criterion $\geq 65$ years, MMSE score $\geq 27$) were
equipped with pervasive computing systems for approximately four weeks [15].
The aim of the study was to assess mobility, physical and social acitivity
patterns in relation to health and well-being in healthy older adults. For the
current analysis, only alone living participants of the MOASIS MobiPro Study
were selected.

### Data collection

In this study, passive infrared (PIR) sensors (DomoSafety SA) were used to
monitor the participants in their respective homes. The PIR sensors were
placed in order to cover the relevant living spaces: bedroom, kitchen,
bathroom, living room and entrance area. These sensors recorded presence or
absence of movement with a frequency of $0.5Hz$. In addition to the PIR
sensors, door sensors were placed on the entrance door and the fridge to
assess time outside of home as well as kitchen usage. The sensors were
installed in the participants’ homes at the beginning of the study and
disassembled again at the end. At the beginning of the respective studies,
participants’ cognitive ability was assessed with a diverse battery of tests,
including the MMSE. The MMSE score was used in this project as measure of
cognitive ability. The sensor based activity and mobility monitoring in the
StrongAge Cohort Study was done for up to a year. The monitoring in the MOASIS
study was over a span of four weeks. To avoid any biases, the data from the
StrongAge Cohort Study was sub-sampled. Both time-points of measurement as
well as number of days distributions were matched. The obtained data is not
publicly available due to local Swiss data regulations.

### Behaviour Matrix and Eigendecomposition

The PIR sensor data consists of time and duration of activation for all
sensors. Based on this, the location of the people in their apartment
throughout each day was obtained. The set of locations is
$K=\\{bedroom,~{}bathroom,~{}livingroom,~{}kitchen,~{}entrance,~{}outside\\}$.
A visual representation of the locations as estimated by the sensors is given
in Figure 1(a). For the eigenbehaviour, every day of data is subdivided into
$S$ time windows, each of length $\Delta t=\frac{24h}{S}$. Different number of
$S$ were assessed, with $S:=\\{24,48,96,144,288\\}$ resulting in window
lengths from 5 minutes $(S=288)$ up to one hour $(S=24)$. For every time
window, the percentage of presence in every room was calculated.

For every person $i$, a location matrix $X^{i}$ was computed. Every row is a
day of measurement, with a total height of $D^{i}$-measurement days for person
$i$. In the columns, the percentages of presence for every time window and
location are given. The locations are stacked horizontally, i.e. the first $S$
columns represent the first location, and the columns $\\{(k-1)\cdot
S,(k-1)\cdot S+1,\ldots,k\cdot S-1\\}$ represent the time windows of location
$K$ for $k=1\ldots|K|$. The resulting $X^{i}$ is a $|D^{i}|\times S\cdot|K|$
matrix. This is also shown in Figure 1(b).

In every individual cell $X^{i}[d_{j},k\cdot S+n]$, the percentage of presence
in the corresponding location $K$ on day $d_{j}$ in the time window
$[\frac{24h}{\Delta t}n,\frac{24h}{\Delta t}(n+1)]$ is given. This
fragmentation was the same for all people.

(a)

(b)

Figure 1:  In a) is shown a representation of multiple days, with different
room-locations colour-coded. In b), the structure of matrix $X^{i}$ is
explained. Along the columns, sub-matrices $A_{k}$ are stacked. Every sub-
matrix $A_{k}$ contains the presence percentages of location $k$. Its width is
$S$ and its height is $D_{i}$, the total measurement days of person $i$. The
total matrix $X^{i}$ consists of the horizontally stacked matrices $A_{k}$.

The $j-th$ row of $X^{i}$ is $\Gamma^{i}_{j}$ and represents exactly one day,
or one point in an ($S\cdot|K|$)-dimensional space. The average location-
vector of person $i$ is
$\Psi^{i}=\frac{1}{D^{i}}\sum_{d=1}^{D^{i}}\Gamma^{i}_{j}$. The deviation of
an individual day from the average day is
$\Phi^{i}_{j}=\Gamma^{i}_{j}-\Psi^{i}$. The location deviation matrix is
$\hat{X}^{i}=[\Phi^{i}_{1},\cdots,\Phi^{i}_{D^{i}}]\in\mathbb{R}^{D^{i}\times(S\cdot|K|)}$.
To analyse the different behaviours for every person $i$, principal component
analysis is performed on the collection of vectors $\Phi^{i}_{j}$. The
covariance matrix $C^{i}$ of person $i$ is based on this set:

$C^{i}=\hat{X}^{i}(\hat{X}^{i})^{T},~{}~{}\textrm{s.t.}~{}~{}c^{i}[n,m]=\sum_{d=1}^{D^{i}}\Phi^{i}_{d}[n]\Phi^{i}_{d}[m]$
(1)

From the covariance matrix $C^{i}$ of person $i$, the Eigenvectors $v^{i}_{l}$
and Eigenvalues $\lambda^{i}_{l}(C^{i})$ can be computed. They represent the
principal components of the deviation vectors $\Phi^{i}_{j}$.
Based on the set of Eigenvectors $v^{i}_{l}$ and Eigenvalues
$\lambda^{i}_{l}(C^{i})$ of person $i$, the matrix $\hat{X}^{i}$ can be
reconstructed again. Depending on the number of Eigenvectors and Eigenvalues
that are used for the reconstruction, the resulting reconstructed matrix will
deviate from the original one. The difference between the reconstructed matrix
and the original matrix is the reconstruction error. We will refer to the
reconstruction error obtained from using only the first eigenvector as the
first reconstruction error, and the reconstruction error obtained from using
the first $n$ eigenvectors as the $n-th$ reconstruction error. Due to a
differing number of measurement days $D^{i}$, the matrices $\hat{X}^{i}$ have
varying size. To normalize the reconstruction error, the sum of the absolute
deviations is divided by size of the matrix $D^{i}\cdot S\cdot|K|$. This gives
a mean deviation per matrix segment.

### Prediction and classification of cognitive ability

In order to assess the influence of age on the prediction of the cognition
score, the partial correlation of the cognition score and the reconstruction
error was computed, with age as the other confounding variable.

The cognition score was predicted with a linear regression, using the
reconstruction error and age as features. As a baseline, a regression was
trained using only age, no reconstruction error. Cross-validation is used for
evaluation, due to the small sample size. The root-mean-squared deviation
$RMSD=\frac{1}{N}\sum_{i}((y_{i}-\hat{y}_{i})^{2})$ of the predicted score
$\hat{y}_{i}$ and true score $y_{i}$ over all $N$ measured people describes
the measurement of accuracy.

Besides the cognition-prediction, a more general classification was performed,
where the participants were divided into two groups; those with a score at or
above 26, and those with a score below 26. As a reference, a score at or above
26 is considered normal, while a score below this value indicates mild to
severe cognitive impairment [11]. For the cross-validation, the split was done
with two-thirds of the data (= 32 samples) in the training set and one third
(=16 samples) in the validation set, with the two sets stratified. The
receiver-operating-characteristic (ROC) and its area under the curve (AUC)
were calculated for all cross-validation folds. The mean ROC and the
confidence interval ($\pm std)$ were evaluated for final assessment.

The optimization parameters were the number of eigenvectors used for the
reconstruction and the size of the time window $S$. For both prediction and
classification, a simultaneous grid-search was performed in a leave-one-out
evaluation for parameter optimization.

All preprocessing and calculations were done using the Python programming
language version 3.6.9 (Python Software Foundation). Correlations and
significances thereof were calculated using the Python package scipy.stats,
version 1.3.1. Figures and graphical illustration were created using the above
mentioned Python programming language, as well as Inkscape version 1.0.

## Results

In this study, data from a total of 48 people were evaluated (38 women, 13
men). The participants were all above retirement age with mean age of 81.08
(SD 9.73) and mean cognition score was 23.88 (SD 4.54). The age distribution
is close to uniformly distributed between the ages of 65 and 98. The
Kolmogorov-Smirnov-statistic, when comparing the age values to the uniform
distribution is $D=0.064$ with a $p$-value of 0.989. Both age and cognition
distributions are shown in Figure 2(b) and 2(a). The people were monitored on
average for 30.6 days (SD 3.6) - excluding start and end day of measurements.

(a)

(b)

Figure 2: In a), the age distribution of the participants is depicted. It
follows closely a uniform distribution. In b), the score of the cognitive test
is depicted.

The partial correlations of the three parameters age, cognition and first
reconstruction error were computed. The results are presented in Table 1.
There was a slight positive correlation between age and the reconstruction
error at $\rho=0.27$ which was not significant. Age has a noticeable negative
correlation with the score, which was significant at $p<0.01$. The
reconstruction error and the score had the strongest correlation, at
$\rho=-0.42$. This correlation was highly significant, at $p<0.005$.

Table 1: Partial correlation of cognitive-score, reconstruction error and age.
∗p-value $<0.01$; ∗∗p-value $<0.005$. | $\rho$
---|---
Age vs Reconstruction error | $0.27$
cognitive ability vs Age | $-0.38^{*}$
Cognition score vs Reconstruction error | $-0.42^{**}$

Based on the behaviour matrix, the reconstruction errors were computed. They
decreased for increasing number of included eigenvectors up up til their
vanishing point when $|D_{i}|$ eigenvectors were used for the reconstruction.
This is depicted in Figure 3(a), where the segmentation was set at $S=24$
resulting in one hour long time segments. For other segmentations the
structure of the reconstruction errors looked similar.

(a)

(b)

(c)

Figure 3: In a), the normalized reconstruction error for increasing number of
used eigenvectors is depicted. In b), the RMSD of a linear regression for
different reconstruction errors is shown. In c), the optimal window size
$\Delta t$ is evaluated. Lowest RMSD is obtained at $\Delta
t=60min\leftrightarrow S=24$.

First, the results of the parameter optimization are presented. As a baseline,
the RMSD of the baseline was computed - the linear regression which was based
only on age as a feature and no reconstruction error. This resulted in a RMSD
of 3.74, higher than any of the regressions including the reconstruction
errors. The RMSD for the cognitive ability prediction was computed for all
reconstruction errors and is shown in Figure 3(b) up to the $10th$
reconstruction error. The best performance, i.e. lowest RMSD, was obtained
when using the $7th$ reconstruction error. This is shown in Figure 3(b), where
the segmentation is set at $S=24$. For all other $S=\\{48,96,144,288\\}$,
similar results were obtained, with the $7th$ reconstruction error being the
best choice for the prediction.
In Figure 3(c), the RMSD is depicted for $S=\\{24,48,96,144,288\\}$ equivalent
to window sizes of $\Delta t=\\{60min,30min,15min,10min,5min\\}$. The $7th$
reconstruction error was used in this figure. For $S=288$, the RMSD is
substantially higher than for the other chosen window sizes. The results for
$S=\\{24,48,96\\}$ are very close together, but the lowest RMSD is obtained
for $S=24$, i.e. $\Delta t=60min$.

(a)

(b)

Figure 4: In a) linear regression based on the optimal window size $\Delta
t=60min$ and the optimal $7th$ reconstruction error is shown. In b) the violet
line is the mean ROC of the classification. The thin lines indicate all
individual runs. The average AUC is 0.93

The linear regression model was evaluated in a leave-one-out cross-evaluation.
In Figure 4(a), the true and predicted scores are depicted together with the
coefficient of determination $R^{2}=0.42$. The black line indicates optimal
prediction performance. The RMSD of this linear regression with window size
$\Delta t=60min$ and using the $7th$ reconstruction error was $RMSD=3.42$. For
higher scores, the predictions were more concise, while for lower scores the
prediction became worse and spread out.

The model performance for the classification task was evaluated and an ROC
curve was calculated. The mean of the ROC, based on a k-fold cross-validation
is shown in Figure 4(b). The AUC of the mean ROC was $AUC=0.93$, but the
variation between individual evaluations was high. The standard deviation of
the multiple ROC runs is shown as well.

## Discussion

In this work, we have shown, how PIR-sensor based location information could
be used to gain insights into the cognitive ability of the older individuals
monitored over one month. Based on the location information, an
eigendecomposition was made which is sensitive to the regularity in the
behaviour patterns. The more predictable and regular the participants moved
around in their apartment, the fewer eigenvectors were required to reconstruct
their behaviour. Lower cognitive abilities has been found to be associated
with a loss of routine [20]. A loss of routine, or more erratic behaviour, is
harder to map onto fewer eigenvectors. The reconstruction error will be larger
than compared to regular and predictable behaviour.

In our evaluation, we have looked at two usages of the reconstruction error in
order to predict the cognitive ability. First, we conducted a prediction of
the cognition score, based on the reconstruction error. Second, we did a
classification into a healthy group versus a group with mild to sever
cognitive impairment.

For both the prediction as well as the classification of the score, two
parameters were optimized, the window-length $S$ and the choice of
reconstruction error. The error for the time window of length 60 minutes is
the smallest, but only by a small margin as compared to the other time windows
of length 10 minutes up to 30 minutes. For the time window of length 5 minutes
($S=288$), the error increases substantially. It is likely that in our
everyday routine, there is a lower boundary on our time precision. A boundary,
under which it is no longer possible to distinguish between routine behaviour
and erratic or chaotic behaviour. For example, if we set an alarm for getting
up in the morning, the time we actually get up might still differ by a few
minutes, influenced by our mood, our sleep quality or something else. By
checking different window lengths, it seems this time window is between five
and ten minutes. This would mean, that in our routine behaviour, we tend to be
exact down to a lower resolution of 10 minutes. Another consideration is the
computational time. The computation of the eigenvalues is considerably more
demanding for a $|K|\cdot S\times|K|\cdot S=5\cdot 144\times 5\cdot 144$
matrix than for a $5\cdot 24\times 5\cdot 24$ matrix, and thus the choice of
time resolution should take the computational resources into consideration.

The other parameter that was optimized was the choice of reconstruction error.
In the work of Eagle et al. [3], the number of eigenvectors needed to achieve
a certain level of reconstruction was used to distinguish between different
population groups. In a similar matter, we looked for the best number of
eigenvectors needed for the reconstruction error being able to best
distinguish interindividual differences in cognition. The most common every
day structural routines are covered by the first few eigenvectors. Due to
repeating structures of different time frames - hourly, daily and weekly - too
few eigenvectors would not be able to cover all of this behaviour. On the
other hand, when adding too many eigenvectors for the reconstruction, they no
longer explain predictable behaviour but actual behavioural noise. This
behavioural noise is probably best explained by our own timely inaccuracies as
discussed in the previous paragraph as well as disturbances from the outside
world. Interestingly, the optimal number of eigenvectors found in our analysis
was always seven. While this could be coincidental, it could just as well hint
to the periodicity of the weekly behaviour patterns. A similar discovery was
made by [3], where certain eigenvectors cover specific behavioural aspects,
such as weekends or breaks.

For the subgroup classification, the data was split into two groups. The group
with a cognition score at or above 26, and the group with a cognitive ability
below 26. The rationale behind this split was the close relationship to the
cognitive ability. A cognitive ability at or above 26 is commonly considered
to coincide with normal cognitive ability, whereas a cognitive ability below
26 is connected to MCI or AD [11]. The resulting AUC is surprisingly large.
But considering the comparably small set, 32 data points in the training set
and 16 data points in the test set, this value should be taken with a grain of
salt. There is still room for variance, and the evaluations would best be
repeated with larger data sets. Due to the small sample size, further
splitting of the data into a third group with cognitive ability below 17, as
suggested for AD [11] could not reasonably be performed.

Our method shows good prediction behaviour for higher cognition scores, but
worse performance when the actual cognitive ability score is below 20. On one
hand, we have fewer data points in that area to train a model with, which
could explain this lower performance. On the other hand, there are numerous
different reasons for low cognitive ability score; reduced language
comprehension, working memory, concentration and attention are some of the
abilities needed to reach high scores. As the evaluation does not
differentiate between the different causes for lower scores, their effect on
the movement behaviour is variable. This is not taken into consideration in
this evaluation. In a future study, more thorough evaluation of the
participants and classification of their cognitive ability could improve on
these results.

While not all causes for a lower cognitive ability score might lead to a
change in movement patterns, there might also be factors present causing
changing patterns, that are not represented through cognitive abilities. An
example was given by Paraschiv-Ionescu et al. in their study covering chronic
pain and its effect on physical activity patterns [13]. Furthermore, there is
a reasonable chance, that some causes for lower a cognitive ability score
might even favor the regularity of patterns and increase them. These
uncertainties indicate the limitations of this method.

In our study, we have used participants’ chronological age as an additional
feature to improve our predictions. But we have only looked at people above
the age of 65 years. We do not expect this method to be directly applicable to
a younger population. As most younger adults are likely to have a cognitive
ability around 30, a saturation effect is expected to kick in, making the
usage of linear regression as a model no longer a good choice. Nevertheless,
the usage of the reconstruction error might still be a valuable feature for
other models.

The data we have used in this study covers around four weeks of monitoring.
The cognitive ability of people is not expected to change within It would be
interesting to assess, whether longer monitoring periods could either improve
the prediction of cognition, or alternatively be used to monitor change in the
cognitive abilities.

## Funding

This research was funded by the Hasler Foundation grant number 16072.

## Ethics

The study was conducted according to the guidelines of the Declaration of
Helsinki, and approved by Ethics Committee of the Canton of Bern, Switzerland
(KEK-Nr. 406/16).

## Declaration of Interest

The authors declare no conflict of interest. The funders had no role in the
design of the study; in the collection, analyses, or interpretation of data;
in the writing of the manuscript, or in the decision to publish the results.

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