Filtered Random Hybrid Strokes (FRHS): Filtering Time-Series

Considering Velocity Profile

Stefania Bello

, Alessia Monaco

, Luca Musti

, Giuseppe Pirlo

and Gianfranco

Semeraro

2,3 e

Digital Innovation srl, 70125, Bari, Italy

Department of Computer Science, University of Studies of Bari “Aldo Moro”, Via Edoardo Orabona,

4, 70125 Bari, BA, Italy

University School for Advanced Studies IUSS Pavia, Palazzo del Broletto, Piazza Della Vittoria, 15, 27100 Pavia, PV, Italy

gianfranco.semeraro@iusspavia.it

Keywords: Random Hybrid Strokes, Kinematic Theory, Handwriting, Early Dementia Identification, Bi-LSTM.

Abstract: This paper proposes an improvement to the data augmentation technique, Random Hybrid Stroke

(RHS), widely used in handwriting analysis for the early detection of dementia. This improvement involves

the application of a filtering method to handwriting time series, redefining the concept of a ’stroke’ based on

insights derived from kinematic theory. Specifically, a trait is considered as the segment joining successive

local mini- mum and local maximum points with respect to the lognormal velocity profile. Experimental

evaluations were conducted using a dataset consisting of 23 different writing tasks (Mini-COG, MMSE, etc.)

for the early detection of dementia using K-Fold cross-validation with K set to 10. The proposed

improvement demonstrates promising results, showing an increase in performance over a wide range of

writing tasks and representing a significant contribution, in particular, for the Mini-COG, MMSE and Trail

Matrix Tests.

INTRODUCTION

The progressive deterioration of brain cells gives rise

to noticeable impacts on memory, thinking, behav-

ioral, and emotional skills. Such brain cells’ deterio-

rations is collectively characterized as dementia

(Pat- terson, 2018),(Gauthier et al., 2022). This

condi- tion often progresses into more severe

forms, such as Alzheimer’s Disease (AD),

Parkinson’s Disease (PD), or Lewy Body Dementia.

The prevalence of Alzheimer’s disease is on a steady

rise, with approx- imately one new case reported

every three seconds, according to the World

Alzheimer Report (Patterson, 2018).

The impairment of brain cells results in increased

difficulty performing daily life activities due to cog-

nitive, functional, and behavioral decline (Impedovo

https://orcid.org/0009-0002-7714-0178

https://orcid.org/0000-0002-7484-3321

https://orcid.org/0009-0008-8337-1275

https://orcid.org/0000-0002-7305-2210

https://orcid.org/0000-0003-1666-8323

and Pirlo, 2018),(De Stefano et al., 2019). Among

these activities, handwriting is profoundly affected

by the degradation of brain cells (De Stefano et al.,

2019).

Handwriting, being a complex biometric trait,

serves various analytical purposes, ranging from se-

curity (Zhang et al., 2016)(Faundez-Zanuy et al.,

2021) (Castro et al., 2023b) to health (Gattulli et al.,

2022),(Gattulli et al., 2023),(Dentamaro et al.,

2021a),(Dentamaro et al., 2021b),(Erdogmus and

Kabakus, 2023),(D’Alessandro et al., 2023).

The evaluation of a patient’s health status can be

conducted by utilizing a diverse set of data sources.

The set of data sources include images of hand-

writing tasks (Lemos et al., 2018) , such as draw- ing

and writing text (offline handwriting) (Dentamaro et

al., 2021a), (Impedovo et al., 2012), time-series data

associated with pen movements during handwrit- ing

tasks (online handwriting) (Gattulli et al., 2022),

(Cilia et al., 2022), (Angelillo et al., 2019b) and also

videos capturing gait (Dentamaro et al., 2020)

(Cheriet et al., 2023), audio recordings (Dentamaro

et al., 2023), among others.

Bello, S., Monaco, A., Musti, L., Pirlo, G. and Semeraro, G.

Filtered Random Hybrid Strokes (Frhs): Filtering Time-Series Considerding Velocity Proﬁle.

DOI: 10.5220/0012567500003654

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 13th International Conference on Pattern Recognition Applications and Methods (ICPRAM 2024), pages 961-968

ISBN: 978-989-758-684-2; ISSN: 2184-4313

961

This work is focused the analysis of online hand-

writing considering the health domain. The online

handwriting analysis allows a non-invasive analysis

through the use of digital tablets and digital pens

(Gat- tulli et al., 2022) (Cilia et al., 2022), (Angelillo

et al., 2019a).

More in detail, tablets are capable to capture pen-

tip movements on-surface, as well as in-air move-

ments (within a range from the tablet surface that

varies accordingly to the tablet), saving simpler in-

formations as x and y coordinates, pressure on the

surface, button-status (if the pen is touching ”1” or

not ”0” the surface), timestamp and more complex

in- formation as velocity, azimuth and altitude

(Gattulli et al., 2023) (Impedovo and Pirlo, 2018)

(Faundez- Zanuy et al., 2021).

The objective of this work is to introduce an en-

hancement to the data augmentation technique

known as Random Hybrid Stroke (Gattulli et al.,

2022) (Zhang et al., 2016). This enhancement

involves ap- plying a filtering method to the

handwriting time- series, altering the definition of a

stroke based on in- sights derived from the

Kinematic Theory.

The organisation of this work is as follows: Sec-

tion 2 provides an overview of related work in the

field so as to explain the insight behind this pa- per.

Section 3 explains the methods employed in this

study. The dataset is discussed in detail in Section 4.

Section 5 presents the experimental set-ups, bench-

marking results and a comprehensive discussion. Fi-

nally, Section 6 focuses on the conclusions drawn

from the study.

RELATED WORKS

2.1

Kinematic Theory in Handwriting

Analysis

The integration of kinematic theory represented a

sig- nificant milestone in the evolution of

handwriting analysis. Studies such as (Plamondon,

1995) and (O’Reilly and Plamondon, 2009) laid the

foundation for understanding the kinematic aspects

of motor con- trol in writing and they formulated the

matematical model of the kinematic theory called

Sigma Log- Nomral (ΣΛ). Of particular interest is

the concept that the result of writing, i.e. a graphic

sign as characters of numbers, is considered to be

composed of primi- tives called strokes . Indeed,

accordingly to kinematic theory (Plamondon, 1995),

(Ferrer et al., 2018), these primitives are identified

through their velocity profile. Each stroke, in fact,

has a lognormal velocity profile, characterised by a

bell-shaped pattern. This discovery in kinematic

theory is of fundamental importance, as it can be

applied to any movement performed by hu- mans,

as, for example, in the analysis of walking from videos

(Dentamaro et al., 2020) (Castro et al., 2023a)

(Dentamaro et al., 2021c). In the context of writing,

in a sequence of strokes that make up a graphic stroke,

such as letters and numbers, each stroke is delimited

by its minimum points in velocity profile.

2.2

Random Hybrid Stroke (RHS)

Zhang X (2016) introduced the Random Hybrid

Stroke (RHS) technique to improve handwriting

anal- ysis in the context of security (Zhang et al.,

2016). RHS is based on random sampling of fixed-

length stroke sub-sequences, making the stroke

sequences independent of user and writing task, thus

showing promise in user identification. In the work

of Zhang X. (2016), a different concept of stroke

was also adopted, defining it as the segment joining

two suc- cessive points. Furthermore, strokes are

distinguished as real or imaginary, depending on

whether the seg- ment was traced entirely on the

tablet or partly or en- tirely at a distance from the

tablet. The innovation of the RHS technique lies in

its ability to perform data augmentation to facilitate

the training of deep learn- ing models, instead of

different SoA technique that focus on generate

artificial data sampling the data dis- tribution, as the

LICIC (Dentamaro et al., 2018)

2.3

Proposed Enhancement

In the study conducted by Gattuli V (2022), the Ran-

dom Hybrid Stroke (RHS) technique was used to

analyse handwriting with the specific aim of

detecting early signs of dementia. The work

conducted by Gat- tulli V. (2022) made it possible to

transfer a technique that originated in the context of

safety into the con- text of health, in accordance with

Faundez-Zanuy’s (2021) statement that there are

competing tasks in handwriting analysis that belong

to both the safety and health domines (Gattulli et al.,

2022) (Faundez- Zanuy et al., 2021). Thus, the

application of the RHS allowed for the augmentation

of data in such a way that deep learning architectures

could also be used.

The central aspect of this work concerns the

devel- opment of a filtered version of hybrid random

traits. This enhancement focuses on refining the

definition of stroke through a filtering process

applied to the time series of coordinates and

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—

−

— −

pressures. The filtering procedure involves the

identification and selection of successive local

maxima and minima in the time se- ries. These

specific points play a crucial role as they indicate the

beginning, the point of maximum veloc- ity and the

conclusion of a stroke. Consequently, the definition

of a run, initially proposed by (Zhang et al., 2016), is

redefined as the segment located between two

consecutive important points.

The primary objective of this redefined approach

is to improve the performance and effectiveness of

early dementia detection in the field of handwriting

analysis.

METHODS

In this section is described the used method to per-

form the experiments of this work. Specifically, it

was used a Bi-Directional Long Short Term Memory

with Self-Attention (Vaswani et al., 2017) (Bi-

LSTM) us- ing the two versions of Random Hybrid

Stroke (RHS) (Zhang et al., 2016) technique.

3.1

Random Hybrid Strokes

The Random Hybrid Strokes technique is based on

the processing of handwriting data. The data must be

time-series containing position coordinates (x, y)

and button status (0 for in-air movements and 1 for

on- surface movements). An example of the time-

series is given in Eq. 1, and its graphical

representation is shown in Figure 1. The time-series

are pre-processed to obtain information about

strokes, defined as the line between two points,

rather than mere position and button status.

S = [(x1, y1, bs1), (x2, y2, bs2), ..., (xn, yn, bsn)]

(1)

Hence, the difference between successive pairs

of co- ordinates and the multiplication of button

status are computed.

∆S = [(∆x1, ∆y1, b˜s1), ..., (∆xn, ∆yn, b˜sn)] (2)

where ∆xi = xi xi−1, ∆yi = yi yi−1, and b˜si = bsi

bsi 1. This leads to obtaining two types of strokes:

real strokes, where b˜si is 1, representing

strokes drawn on the surface, and imaginary

strokes, where b˜si is 0, representing strokes drawn

with at least one of the two points with button status

as 0. Finally, random sub-sampling from the stroke

sequences ∆S is performed. This results in a set of

fixed-length stroke sub-sequences, represented in

Eq. 3.

Figure 1: Example of handwriting trait. In the images points

with different button status (”1” or ”0”) are rappresented as

black and white points. Strokes between points are high-

lighted if ”real strokes” or ”imaginary” strokes accordingly

to the description.

3.2

Filtered Hybrid Strokes

In this work, is proposed an upgrade of RHS. Such

upgrade is inspired by the Sigma-LogNormal (ΣΛ)

Model(O’Reilly and Plamondon, 2009) of the human

movement and the Kinematic Theory (Plamondon,

1995). The Sigma-LogNormal analyze the velocity

profile of a timeseries of coordinates and ensemble

with the Kinematic-Theory state that when a person

perform a movement, as drawing a single straight line,

the velocity profile is similar to a Normal distribution.

Similarly, in this work the time-series of coordi-

nates is firstly transformed looking the velocity pro-

file of the movement performed by the pen. Secondly,

only local maxima and local minimum are collected

by the velocity profile and then the referencing coor-

dinates and button status. The intuition is that in this

way it is possible to maintain only the most significant

point to use for the reaming steps of Random Hybrid

Strokes (explained above).

An example is reported in Figure 2.

Figure 2: In the figure are represented the log-normal of

the velocity profile of strokes. Hence, a stroke is identified

between successive local minimum. The highlighted points

RHSi = [∆S[i,i+size], ∆S[ j, j+size], ...] (3)

where i and j indicate different starting points from

the n points, and size represents the length of sub-

sequences. In conclusion, the Random Hybrid

Stroke technique uses both imaginary and real

strokes, giv- ing the name ”Hybrid” to this

technique. It considers strokes as data information,

Filtered Random Hybrid Strokes (Frhs): Filtering Time-Series Considerding Velocity Proﬁle

963

hence the term ”Stroke,” and employs random sub-

sampling of fixed lengths of the stroke series, giving

rise to the term ”Random.”

are them that are selected

during the filtering.

3.3

Deep Learning

The used model to perform experiments using both

RHS-based techniques is a Bi-Directional Long

Short Term Memory with Self-Attention (Bi-

LSTM).

Table 1: Classes division of “HAND-UNIBA” and its Bal-

anced version.

HAND-UNIBA Balanced HAND-UNIBA

Class

° Patients Class

° Patients

Healthy 56 Healthy 49

Mil

17 Disease

Firs

This model is characterized by the use of two layer

of LSTM that analyse the time-series in two

different time-direction: forward and backward,

differently form other work as (Impedovo et al.,

2019). Than the Self-Attention is applied in order to

retain the most significant information. Finally, a

Dense Layer is used to extract the prediction in

”healthy” or ”pa- tient”. The whole structure is

represented in Figure 3

Figure 3: In the figure are represented the deep learning

model used in this work. It is a Bi-Directional Long Short

Term Memory with the Self-Attention

DATA

In this work is used the Balanced version of

”HAND- UNIBA” data-set used in the previous

work [early de- mentia]. Such version was obtained

firstly, merging in a single class (patient or diseased)

person with mild or fist-stage dementia, and

secondly selecting the same amount of healthy

person from the original data-set. In this way, the

Balanced version of ”HAND- UNIBA” data-set,

referred also as ”Balanced-Hand”, contain 49

healthy and 49 diseased person. Such in- formation

are also reported in Table 1.

Each one of the 98 patients has performed 23

tasks. Multiple tasks were conducted because in this

way it could be possible to encompass both cogni-

tive and functional assessments. The recorded tasks

belonged to various categories, including the Mental

5 RESULTS

In this section the experimental set-ups and obtained

results are presented and discussed.

Regarding the labeling phases, patients with the

disease are assigned the class label ”1”, while

healthy patients are designated as the class with the

label ”0”. Then, it is applied One-Hot Encoding.

All the experiments were performed utilizing the

same data-set, patient label encoding, and a

consistent methodology for the training/testing

phases, specifi- cally employing K-Fold Cross

Validation with K set to 10.Such experimentation

was performed 10 times to average the evaluation

metrics, providing a more robust assessment of the

proposed method.

The division into folds is applied to the users.

Subsequently, during training, each Random Hybrid

Stroke (RHS) is considered separately. However,

dur- ing the testing phase, all predictions for a single

user are averaged, and then an argmax is applied to

iden- tify the predicted class.

In terms of the model architecture, the Bi-

directional Long Short-Term Memory (Bi-LSTM)

was configured with 30 units for each LSTM, 2

units, and Softmax as the activation function for the

Dense Layer. The training of the model utilized a

batch size of 32, employed Adam as the optimizer,

and binary cross-entropy as the loss function.

In the domain of neural degenerative disease pre-

diction, classification errors are of paramount impor-

tance. Hence, metrics, such as precision (Eq 4) and

recall (Eq 5), are useful to evaluate if the model is

capable of predicting the correct class, avoiding be-

haviors like giving the same prediction always (pre-

cision) and determining if the model can distinguish

between the two classes (recall). The terms in equa-

tions 4 and 5 are: TP for True Positive (for correctly

predicted instances of the positive class), FP for

False Positive (for instances of the negative class

predicted as positive), FN for False Negative (for

instances of the positive class predicted as negative).

𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 =

𝑇𝑃

𝑇𝑃 + 𝐹𝑃

(4)

𝑟𝑒𝑐𝑎𝑙𝑙 =

𝑇𝑃

𝐹𝑁

(5)

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Table 2: Tasks and their descriptions.

Abbreviation

Description User request Category

CDT

Clock drawing test Draw a clock with numbers in it, then draw the clock hands at

11.10 a.m

Mini-COG

Sentence

drawing test

Think and then write a sentence

MMSE

IPC

Pentagons

drawing test

Copy the shape of this design

MMSE

First matrix test

Mark all the numbers “5” in the matrix, without correcting the

barriers already made

Trail

Second matrix

test

Mar

all the numbers “2” an

“6” in the matrix, without

correcting the barriers already made

Trail

Third matrix

test

Mark all the numbers “1”, “4” and “9” in the matrix,

without correcting the barriers already made

Trail

TMT1

First trail-making test

Connect the circles following the order of the numbers.

For example, 1–2-3, and so on. Perform the exercise as quickly as

possible and never lift the pen. In case of error, correct immediately

Trail

TMT2

Second trail-

making test

Connect the circles alternatel

following the orde

of the

numbers and the order of the letters of the alphabet. For example,

1-A-2-B-3-C, and so on. Perform the exercise as quickly as

possible and never lift the pen. In case of error, correct immediately

Trail

TMTT1

Trail test 1

Connect the circles following the order of the numbers.

For example, 1-2-3, and so on. Perform the exercise as quickly as

possible and never lift the pen. In case of error, correct immediately

Trail

TMTT2

Trail test 2

Connect the circles alternately following the order of the

numbers and the order of the letters of the alphabet. For example,

1-A-2-B-3-C, and so on. Perform the exercise as quickly as

possible and never lift the pen. In case of error, correct immediately

Trail

Writing the word test

Write the word “Ciao” in italics, resting your wrist on the tablet

Additional tests

Connecting Two

vertical points tests

Link the vertical points with a straight line four times by

going back and forth

Additional tests

Connecting two

horizontal points tests

Link the horizontal points with a straight line four times

by going back and forth

Additional tests

Square copy task

Copy the square drawing shown

Additional tests

First signature

acquisition

Sign your signature here

Additional tests

Second signature

acquisition

Sign your signature here

Additional tests

Spiral copying test Copy the shape of this design

Additional tests

Retrace spiral test Retrace the shape of this design

Additional tests

CHK Bank check copying

task

Look at the fields on the completed check and copy them

back to the blank check below

Additional tests

LE Write “le”

repetitions

Write a sequence of “L” and “E” in italics, for example

“LELELELE”

Additional tests

MOM Writing the word test Write the word “MAMMA” in italics inside the three

boxes, from top to bottom

Additional tests

Writing the word test Write the word “FINESTRA” in italics

Additional tests

DS Listen and write

sen tence

Listen and write in italics what you will hear. (The sentence

“Oggi e` una bella giornata” will be dictated)

Additional tests

Filtered Random Hybrid Strokes (Frhs): Filtering Time-Series Considerding Velocity Proﬁle

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Table 3: Tasks and their descriptions.

Tas

° People Pe

forming the Task

Ratio People Pe

forming the Task

CDT 97 98,98%

SW 98 100%

IPC 97 98,98%

M1 98 100%

M2 98 100%

M3 98 100%

TMT1 96 97,96%

TMT2 82 83,67%

TMTT1 97 98,98%

TMTT2 89 90,82%

98 100%

VP 98 100%

HP 98 100%

SC 98 100%

S1 97 98,98%

S2 97 98,98%

CS 97 98,98%

TS 97 98,98%

CHK 98 100%

LE 97 98,98%

MOM 98 100%

98 100%

DS 98 100%

Status Assessment of Older Adults (Mini-COG),

Mini Mental State Examination (MMSE),

Attentional Matrix, Trail Making Test, and several

additional assessments. An extended description is

in Table 2.

Both versions of HAND-UNIBA data-set

contain, for certain task and for certain users, time-

series with less than 50 points. Hence, such

information were not used to perform experiments.

The raw number of people and the percentage of

people performing a task is reported in Table 3.In

order to consider both metrics (precision and recall),

the F1-score (Eq 6) is used, which is the har- monic

mean that allows understanding the predictive

capability of the model. All three metrics are in the

range

[

]

Because

both

classes

are

considered,

the average of F1-scores, computed firstly

considering the class ”1” as positive and then the

class ”0” as positive, is used to compare performance

between the proposed method and the previous

version.

𝐹1  𝑆𝑐𝑜𝑟𝑒 = 2

𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛  𝑟𝑒𝑐𝑎𝑙𝑙

𝑝𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 + 𝑟𝑒𝑐𝑎𝑙𝑙

(6)

The experimental results are reported in Table 4.

Specifically, the column RHS refers to the exper-

iments performed using the original Random Hy-

brid Strokes technique. Meanwhile, the column

FRHS refers to the proposed Filterd Random Hy-

brid Strokes. Finally, the column Task report the

task name. The reported values are the average F1-

scores with the associated standard deviation, and

the better value are highlighted with bold font.

It is noticeable that the performance difference

ranges from about 0.3% to approximately 7%.

Specif- ically, the most significant variance occurs

in the task cdt, where FRHS outperforms RHS, and

in s1, where RHS yields better results than FRHS.

RHS demon- strates superior performance in tasks

ds, hp, m1, m3, s1, sc, ts, and w. Therefore, in tasks

related to dic- tation, connecting two horizontal

points four times, the first and third tasks using

Attentional Matrix, the first signature, the square

copy task, the retracing spi- ral task, and the writing

of the fixed word test, RHS emerges as the better

alternative.

Table 4: Results obtained from the previous experiments.

RHS FRHS

Task

Mean STD Mean STD

0,55161 0,09186 0,62234 0,05778 cd

0,71060 0,02118 0,71124 0,04098 ch

0,64047 0,03287 0,66566 0,03388 cs

0,71473 0,01774 0,70250 0,02094 ds

0,65846 0,02043 0,68427 0,02908

0,66886 0,03534 0,66111 0,02325 hp

0,64749 0,04568 0,70385 0,02476 ipc

0,72229 0,02878 0,72948 0,02477 le

0,68166 0,02662 0,66744 0,02062 m1

0,72473 0,02962 0,72706 0,02072 m2

0,71750 0,02926 0,70536 0,02959 m3

0,68032 0,03348 0,69668 0,03497 mo

0,72105 0,01448 0,65310 0,04027 s1

0,70535 0,01171 0,72960 0,03038 s2

0,69778 0,02359 0,68690 0,01940 sc

0,69516 0,02177 0,70934 0,02039 sw

0,75781 0,01010 0,76006 0,01569 tmt1

0,62890 0,02552 0,66623 0,01907 tmt2

0,68579 0,02351 0,70167 0,03024 tmtt1

0,75652 0,01456 0,76399 0,01633 tmtt2

0,63088 0,02028 0,60728 0,01929 ts

0,67202 0,02655 0,69947 0,04107 vp

0,71994 0,01958 0,69170 0,02527

Considering tasks in the Mini-COG, MMSE, and

trail-making tests (tmt1, tmt2, tmtt1, and tmtt2),

the proposed FRHS demonstrates better performance

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than the original RHS. Furthermore, FRHS exhibits

superior performance in tasks chk, cs, h, le, m2, mom,

s2, and vp.

These results indicate that the proposed method

achieves better outcomes for the majority of the hand-

writing tasks. Additionally, in specific categories

such as Mini-COG, MMSE, and Trail Making Test,

the proposed method FRHS outperforms the original

RHS.

6 CONCLUSIONS

In conclusion, this study introduced a new tech-

nique for the early detection of neurodegenerative

dis- eases through handwriting analysis.

Specifically, the method proposed by this work, a

filtered version of the Random Hybrid Strokes

technique called Filtered Random Hybrid Strokes

(FRHS), aims to improve early dementia prediction

performance from hand- writing data.

In fact, the results obtained show that, for most

tasks, FRHS outperforms the original RHS. Further-

more, it is noteworthy that the proposed technique

improves prediction performance for all writing

tasks belonging to the Mini-COG, MMSE and Trail

Matrix Test categories.

Hence, the proposed technique not only outper-

forms the existing approach in terms of f1-scores,

but also proves to be particularly good for filtering

and data augmentation. Ultimately, FRHS holds

great promise for improving early dementia

diagnosis and handwriting analysis.

ACKNOWLEDGEMENTS

This article and related research have been

conducted during and with the support of the Italian

National Inter-University Ph.D. course in

Sustainable Develop- ment and Climate Change.

Furthermore, this article and related research

have also been conducted with the support and

funding of the Ministero della Salute’s project

”AmICA: Assis- tenza olistica Intelligente per

l’aCtive Ageing in eco- sistemi indoor e outdoor”

project, under Traiettoria 1, specifically ”Active

Healthy Ageing - Tecnolo- gie per l’invecchiamento

attivo e l’assistenza domi- ciliare” (T1-MZ-09).

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