Using Entropy Measures for Monitoring the Evolution of Activity Patterns Yushan Huang

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Using Entropy Measures for Monitoring the

Evolution of Activity Patterns

Yushan Huang

Dyson School of Design Engineering

Imperial College London

Care Research and Technology Centre

The UK Dementia Research Institute

London, UK

yushan.huang21@imperial.ac.uk

Hamed Haddadi

Dyson School of Design Engineering

Imperial College London

Care Research and Technology Centre

The UK Dementia Research Institute

London, UK

h.haddadi@imperial.ac.uk

Yuchen Zhao

Dyson School of Design Engineering

Imperial College London

Care Research and Technology Centre

The UK Dementia Research Institute

London, UK

yuchen.zhao19@imperial.ac.uk

Payam Barnaghi

Department of Brain Sciences

Imperial College London

Care Research and Technology Centre

The UK Dementia Research Institute

London, UK

p.barnaghi@imperial.ac.uk

Abstract—In this work, we apply information theory inspired

methods to quantify changes in daily activity patterns. We use

in-home movement monitoring data and show how they can

help indicate the occurrence of healthcare-related events. Three

different types of entropy measures namely Shannon’s entropy,

entropy rates for Markov chains, and entropy production rate

have been utilised. The measures are evaluated on a large-

scale in-home monitoring dataset that has been collected within

our dementia care clinical study. The study uses Internet of

Things (IoT) enabled solutions for continuous monitoring of in-

home activity, sleep, and physiology to develop care and early

intervention solutions to support people living with dementia

(PLWD) in their own homes. Our main goal is to show the

applicability of the entropy measures to time-series activity data

analysis and to use the extracted measures as new engineered

features that can be fed into inference and analysis models.

The results of our experiments show that in most cases the

combination of these measures can indicate the occurrence of

healthcare-related events. We also ﬁnd that different participants

with the same events may have different measures based on one

entropy measure. So using a combination of these measures in

an inference model will be more effective than any of the single

measures.

Keywords—entropy, healthcare, feature engineering, IoT

I. INTRODUCTION

Finding patterns in activity data collected by IoT has been

applied to various research ﬁelds, including object tracking [1],

intrusion detection [2], and healthcare [3]. Existing research

mainly focuses on using machine learning (ML) models and

algorithms to learn and analyse patterns from raw data [4].

Although such methods can ﬁnd the direct combination of

raw data points that can indicate interesting events, they are

not able to utilise statistical and useful information about

the data, such as the distribution of data points and the

uncertainty in such distributions. Determining the distribution

and uncertainty will introduce more useful information into

ML models and thus can potentially contribute to building

accurate prediction and inference models.

In this paper, we propose three measures that are constructed

based on entropy. Our goal is to provide measures to enhance

the ability of processing models to quantify the changes in

data patterns and improve the outcome of predictive and

analytical machine learning models. We empirically evaluated

these measures on the data that we have collected in an in-

home healthcare monitoring IoT platform (illustrated in Fig. 1)

to support PLWD. Our preliminary results indicate that, in

most cases, combining these new measures into data analysis

pipelines can suggest occurrences of certain healthcare-related

events. These measures show different suitability on different

participants’ data. So these measures as engineered features in

modern ML methods can improve the outcomes of inference

and predictive models.

II. SYSTEM AND DATA

We have developed a digital platform, called Minder, to

integrate in-home IoT sensors to collect physiological data,

sleep data, environmental data, and activity data in a privacy-

aware and secure manner. A list of the IoT devices in our

platform is shown in Table I. The dataset used in this study

includes 9,370 person-day activity data collected between

arXiv:2210.01736v2 [cs.LG] 5 Oct 2022

TABLE I

IOTDEVICES IN THE PLATFORM

Digital Marker IoT Device Frequency

Activity Passive infrared sensors Triggered by movement

Home device usage Smart plugs Triggered by device use

Body temperature Smart temporal thermometers Twice daily or continuous using a wearable device

Blood pressure and heart rate Wearable devices Twice daily

Weight and heart rate Smart scale with body composition and heart rate Once a day

Respiratory and heart rate during sleep Sleep mat Once a minute

Environmental light Light sensors Every 15 minutes

Environmental temperature Temperature sensors Once an hour

Fig. 1. An overview of our in-home IoT monitoring system. The system

allows integration of different in-home activity and physiology data. It also

provides a framework for deploying and validating analytical models.

December 2020 and March 2022. We have used the Minder

platform to collect remote monitoring data in a dementia

study. The study has received ethical approval and all the

data used and presented in this research has been anonymised.

The Minder platform provides an overview dashboard, which

allows a monitoring team to observe raw data and predicted

alarms raised by analytical models. The platform has four key

components: 1) sensors installed in participants’ homes (the

platform is designed to be device agnostic), 2) the back-end

system including Cloud infrastructure, storage, and analysis

tools, 3) the user interface for data visualisation and presenting

clinical information, environmental information, and alerts,

4) clinical intervention where healthcare practitioners use the

system/alerts and interact with the participants, caregivers and

respond to their healthcare needs.

In our system, activity data is collected using passive

infrared (PIR) sensors, which are installed in ﬁve locations in

the home: bathroom, bedroom, lounge, kitchen, and hallway.

A PIR sensor in a certain location is triggered when a person

passes by and sends an alert to the system at the same time,

which records the time and the location of the alert. The raw

data is time-series containing location and time information,

as Fig. 2 shows.

The data is labelled by our monitoring team who react to the

alerts generated on the platform and verify the alerts by con-

tacting PLWD or their caregivers. The labels contain different

healthcare-related events, including accidental falls, abnormal

Fig. 2. An example for raw Passive Infrared (PIR) data. The data is selected

from one participant. The x-axis shows the time of the day, and different

colours represent different locations in the house.

motor function behaviour, hospital admissions, Urinary Tract

Infections (UTIs), anxiety and depression, disturbed sleep

patterns, agitation, and confusion. We combine the activity

data and the labels from different participants to create the

dataset.

III. METHODOLOGY

We aim to capture and model complex features that cannot

be directly obtained through linear and nonlinear functions

in training models. Fig. 3 shows an example of a participant

with more routine activities and a participant with less routine

activities. We use entropy to capture the uncertainty from

two perspectives including location-based and route-based

changes.

A. Shannon’s entropy

If the occurrence at locations is regarded as random events,

we can consider measuring the extent of occurrence of

these random events. Shannon’s entropy [5] is a conventional

method to quantify information. We apply Shannon’s entropy

to represent changes in activity patterns. Suppose that there

are nlocations in a participant’s activity, denoted as X=

{x1, x2, . . . , xn}. The Shannon’s entropy of the activity data

is:

H(X) = −

i=1

P(xi) log P(xi)(1)

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UsingEntropyMeasuresforMonitoringtheEvolutionofActivityPatternsYushanHuangDysonSchoolofDesignEngineeringImperialCollegeLondon&CareResearchandTechnologyCentreTheUKDementiaResearchInstituteLondon,UKyushan.huang21@imperial.ac.ukHamedHaddadiDysonSchoolofDesignEngineeringImperialCollegeLondon&CareResearc...

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