Feature Weighted Support Vector Machines for Writer-independent On-line

Signature Verification

Jacques Swanepoel and Johannes Coetzer

Department of Mathematical Sciences

Stellenbosch University

Stellenbosch, Western Cape, South Africa

{jpswanepoel,jcoetzer}@sun.ac.za

Abstract—In this paper we present a novel frameworkfor writer-independent on-line signature verification. Thisframework utilises a dynamic time warping-based dichotomytransformation and a writer-specific dissimilarity normalisationtechnique, in order to obtain a robust writer-independentsignature representation in dissimilarity space. Support vectormachines are utilised for signature modelling and verification.Linear and radial basis function kernels are investigated. Inthe case of the radial basis function kernel, both conventionaland feature weighted variants are considered.

We show that the non-linear kernel significantly outperformsits linear counterpart. We also show that the incorporation offeature weights into the non-linear kernel function consistentlyimproves verification proficiency.

When evaluated on the Philips signature database, whichcontains 1530 genuine signatures and 3000 amateur skilledforgeries from 51 writers, we show that equal error ratesof 1.26% and 3.52% are expected when 15 and 5 genuinereference samples are considered per writer. This performanceestimate compares favourably with those of existing systemsalso evaluated on this data set. Furthermore, there is sufficientevidence to suggest that further investigation into the featureset considered, as well as the feature weighting strategy utilised,may further improve performance.

Keywords-signature verification; writer-independent authen-tication; support vector machines; feature weighting;

I. INTRODUCTION

Handwritten signatures as a means of identity verification

is the most widely used behavioural biometric authentication

technique. In this paper we focus on on-line signature

verification. This problem is fundamentally different from

that of off-line signature verification (where signature data

is captured by digitising a pen-on-paper sample) in the

sense that an on-line signature is captured by means of an

electronic writing device and associated electronic writing

surface. The signature acquisition process therefore provides

spatial as well as temporal (or dynamic) information.

In recent years, the concept of writer-independent signa-

ture modelling has gained notable interest in the field of

off-line signature verification. This approach is fundamen-

tally different from traditional writer-dependent signature

modelling techniques and performs model construction in

dissimilarity space, as opposed to the more commonly

utilised feature space. The dissimilarity representation of

any questioned signature is obtained by comparing it to

a known genuine reference sample that belongs to the

claimed owner. The authentication of a questioned signature

associated with any writer is thereby reduced to a two-class

problem. Writer-independent signature modelling has been

shown to outperform the writer-dependent approach in two

key areas: (1) Since a single, universal signature model is

constructed using pooled data obtained from several different

writers, this approach successfully addresses the issue of

data scarcity i.e. an efficient model can be constructed even

when limited training samples are available; (2) Since model

training only occurs after the signature data is collected in a

controlled environment, this approach is able to facilitate

training with skilled forgeries – a property that is not

practically feasible within a writer-dependent framework.

To the best of our knowledge, no existing publications

investigate the use of a writer-independent strategy within

the context of on-line signature verification. In this paper,

we initiate such an investigation and present our findings as

a proof of concept.

A wide variety of writer-dependent on-line systems are

proposed in the literature. Comprehensive surveys of these

systems can be found in [1] and [2], whilst a historical

perspective is given in [3]. It is clear from these surveys that

many pattern recognition techniques have been successfully

employed for the purpose of on-line signature verification.

Popular feature extraction techniques include the utilisation

of function-features (such as pen position, velocity, acceler-

ation, pressure, etc.) and global parameter-features (such as

the average, minimum and maximum of the aforementioned

function-features, as well as total time duration, number

of pen up or pen down samples, etc.). Popular classifica-

tion techniques include simple distance classifiers, dynamic

programming, neural networks and hidden Markov models

(HMMs).

The HMM-based systems proposed in [4]–[7] are of

particular interest to this study, since these systems also

consider the Philips signature database for evaluation pur-

poses. Their reported results are therefore fit for comparison

to those reported for the systems presented in this paper.

2014 14th International Conference on Frontiers in Handwriting Recognition

2167-6445/14 $31.00 © 2014 IEEE

DOI 10.1109/ICFHR.2014.79

434

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Figure 1. Schematic representation of a typical system presented in this paper. The sets ST and SE denote the signatures considered for training andevaluation respectively, whilst RT and RE denote their associated genuine reference signatures.

II. SYSTEM OVERVIEW

The design of a typical system presented in this paper is

conceptually illustrated in Figure 1.

Following successful signature acquisition, both spatial

and temporal features are extracted from the captured signa-

ture data. The resulting feature set is subsequently converted

into a dissimilarity vector, by matching its associated feature

vectors to those extracted from a known genuine reference

sample. A dynamic time warping (DTW) algorithm [8]

is used for matching. The resulting dissimilarity vector

is then normalised using the writer-specific dissimilarity

normalisation technique proposed in [9].

The entire set of normalised dissimilarity vectors, ex-

tracted from both genuine (positive) and forged (negative)

samples belonging to a set of guinea-pig writers, is used

to train a support vector machine (SVM) classifier [10].

We consider linear, radial basis function (RBF) and feature

weighted RBF kernels [11], [12]. The trained SVM is finally

used to accept/reject any subsequently presented questioned

signatures.

During experimentation, system proficiency is gauged

using the equal error rate (EER) performance metric. Sig-

nature samples belonging to different writers are used for

training and evaluation purposes.

III. SIGNATURE REPRESENTATION

A. Feature extraction

Since on-line signatures are captured using specialised

hardware, several key measurements are recorded during the

signature acquisition process. For the systems presented in

this paper, these measurements are represented by the 5-tuple

(x, y, p, θx, θy), sampled at a rate of up to 200Hz [4]. After

successful recording of the signing event, the signature is

therefore represented by the T -dimensional feature vectors

x and y (horizontal and vertical pen-positions respectively),

p (axial pen-pressure), as well as θx and θy (pen-tilt in the xand y directions respectively), where T denotes the number

of sampled points.

Although these feature vectors may suffice for basic

model construction, various additional descriptors can be

derived from the captured data. For example, from the spatial

feature x it is possible to derive the dynamic features vx

and ax (velocity and acceleration, respectively, in the xdirection). Similarly, vy and ay can be obtained from y.

These dynamic features are considered valuable throughout

the literature, since they proved to be considerably more

difficult to mimic than spatial signature characteristics, even

when the forger possesses forensic expertise [4], [13].

Several additional features may also be derived from the

captured data, as detailed in e.g. [4], [7], [14]. An in-depth

investigation of supplementary features, however, is deemed

outside the scope of this paper.

For initial signature representation, the systems presented

in this paper therefore consider the T × 9 feature set

X = [p, x, y, vx, vy , ax, ay , θx, θy] , (1)

where T represents the number of samples associated with

the signature in question.

B. Dichotomy transformation

In a writer-dependent modelling framework, the extracted

feature sets (detailed in the previous section) may be used

to construct a separate signature model for each writer

enrolled into the system. In order to obtain a suitable writer-

independent representation, however, a dichotomy transfor-

mation (i.e. the process that converts the signature represen-

tation from feature space to dissimilarity space) is required.

The systems presented in this paper quantify the dis-

similarity between two feature vectors through a DTW

algorithm. DTW is particularly well suited for this task,

since: (1) it is able to calculate the distance between feature

vectors with different dimensions, as is usually the case for

on-line signature data; (2) prior to the distance calculation,

the algorithm non-linearly aligns individual features based

on their similarity, thereby compensating for minor discrep-

ancies in signature data belonging to the same writer (i.e.

intra-class variability).

Given a T (k) ×D feature set X(k), extracted from a

reference signature belonging to a specific writer, any other

T (q) ×D feature set X(q), extracted from a signature that is

claimed to belong to the same writer, can be converted into

a D-dimensional dissimilarity vector z(k,q) by calculating

the dissimilarity between each pair of corresponding feature

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vectors as follows,

z(k,q) =

D⋃d=1

D(x(k)d ,x

(q)d ), (2)

where⋃

denotes the vector concatenation operator, whilst

D(x(k)d ,x

(q)d ) denotes the DTW-based distance between

x(k)d ∈ X(k) and x

(q)d ∈ X(q).

This DTW-based approach was shown in [15] to sig-

nificantly outperform the more commonly used Euclidean

distance in the construction of robust dissimilarity vectors.

IV. SIGNATURE MODELLING

In order to construct a writer-independent model, samples

of genuine signatures and skilled forgeries are collected

from a set of so-called guinea pig writers. These writers

are considered representative of the general public, and their

signatures are used for training purposes only.

Given a set of K reference signatures and N labelled

training signatures (that include an equal number of pos-

itive and negative samples) for each of the Ω guinea-

pig writers, the relevant dissimilarity vectors are generated

for each writer by computing z(k,n) for k = {1, 2, . . . ,K}and n = {1, 2, . . . , N}. We henceforth refer to dissimilarity

vectors that represent genuine signatures and forgeries as

being positive and negative respectively. Furthermore, let

Z+ and Z− denote the sets that contain the positive and

negative dissimilarity vectors obtained from all the guinea-

pig writers.

A. Dissimilarity normalisation

The sets Z+ and Z− provide a suitable platform for

obtaining a decision boundary in dissimilarity space. How-

ever, it is advisable to incorporate a preprocessing stage,

in this case dissimilarity normalisation, into the signature

modelling framework. Dissimilarity normalisation aims to

address the following potential issues: (1) Since the feature

vectors obtained during signature acquisition are highly de-

pendent on the handwriting style (e.g. velocity, acceleration

and pressure) of the writer in question, the dissimilarity

sets obtained by considering several different writers may

contain dissimilarity vectors of arbitrary magnitude – and

may therefore be irregularly distributed in dissimilarity

space; (2) Since the negative samples considered for model

construction represent skilled forgeries, a certain degree of

class overlap in dissimilarity space is a distinct possibility.

In order to address these issues, the systems presented

in this paper perform dissimilarity normalisation using the

writer-specific normalisation strategy proposed in [9].

For every writer ω, the D-dimensional statistics

μ(ω) and σ(ω) are determined by considering the

N (ω) = (K2 −K)/2 unique dissimilarity vectors obtained

when every reference signature belonging to writer ω is

compared to every other reference signature belonging to

the same writer as follows,

μ(ω)d =

1

N (ω)

K∑i=1j>i

z(i,j)d , (3)

σ(ω)d =

√√√√√ 1

N (ω) − 1

K∑i=1j>i

(z(i,j)d − μ

(ω)d

)2

. (4)

The normalised dissimilarity vector z̄ is subsequently ob-

tained using a modified logistic function as follows,

z̄ =

D⋃d=1

[1 + exp

(R

(ω)d −

6zd

R(ω)d

)]−1

, (5)

R(ω)d = μ

(ω)d + σ

(ω)d . (6)

This writer-specific normalisation strategy was shown in

[15] to improve overall class separability in dissimilarity

space, thereby significantly increasing verification profi-

ciency.

B. Weighted kernel support vector machines

The primary objective of an SVM-based classifier is to de-

termine the hyperplane in dissimilarity space that maximally

separates the positive and negative classes. This hyperplane

is described by the weight vector w and bias b. When

the two classes are not linearly separable, a mapping φ(z)is often employed in order to transform the input data to

kernel space, where a more effective hyperplane may be

determined. Popular choices for the kernel function

K(z(i), z(j)) = φ(z(i))′φ(z(j)), (7)

where ′ denotes the vector transpose operator, include linear,

polynomial and radial basis function (RBF) kernels. The

SVM-based decision boundary is therefore described by

f(z̄) = w′φ(z̄) + b. (8)

A notable advantage provided by the SVM-based ap-

proach is the fact that one can easily introduce the concept of

feature weighting by simply modifying the kernel function

[11], [12]. For instance, a weighted RBF kernel may be

obtained as follows,

K(z(i), z(j)) = exp

(−γ

D∑d=1

αd(z(i)d − z

(j)d )2

), (9)

where αd denotes the weight associated with the dth feature,

whilst γ > 0 denotes the kernel width. The use of trivial

weights, where αd = 1 for d = 1, 2, . . . , D, corresponds to

the conventional RBF kernel.

In this paper we consider two fundamentally different

feature weighting strategies, namely the F -score and the

linear SVM weighting methods, as discussed in [11]. In

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the former strategy, the weight associated with each feature

equals its inter-to-intra-class-variability-ratio. In the latter

strategy, the positive and negative classes are first used to

train a conventional linear SVM. The systems presented

in this paper employ the sequential minimal optimisation

(SMO) algorithm [16] for SVM training. The feature weights

used for the subsequent weighted RBF kernel are given by

α = wLIN, where wLIN denotes the weight vector obtained

for the linear SVM.

V. VERIFICATION

Following the acquisition of a questioned signature,

claimed to belong to writer ω, the relevant feature set is

constructed as discussed in Section III-A. This feature set is

then compared to that of each of the K reference signatures

belonging to writer ω, in order to produce a set of normalised

DTW-based dissimilarity vectors.

Each normalised dissimilarity vector is subsequently pre-

sented to the trained SVM, yielding a signed distance mea-

sure relative to the corresponding decision boundary. The

logistic function is used to convert each distance measure

into a partial confidence score s ∈ [0, 1]. The set of Kpartial confidence scores is then averaged, yielding the final

confidence score s∗ as follows,

s∗ =1

K

K∑k=1

[1 + exp

(−f(z̄

(ω)(q,k))

)]−1

. (10)

Finally, a threshold τ ∈ [0, 1] is imposed on s∗, such that

the questioned signature is accepted as genuine if and only

if s∗ ≥ τ .

VI. EXPERIMENTS

A. Data

System evaluation is performed using the well-known

Philips signature database [4]. This data set contains

1530 genuine signatures and 3000 amateur skilled forgeries

obtained from 51 writers. These forgeries may be sub-

categorised as either home-improved (1530 samples) or over-

the-shoulder (1470 samples). The home-improved forgeries

were produced by forgers who had in their possession an

off-line sample (i.e. paper copy) of the genuine signature, as

well as ample time to practice its reproduction. The over-the-

shoulder forgeries were produced by forgers who witnessed

a legitimate signing event and then attempted to reproduce

the signature immediately afterwards.

B. Protocol

In order to ensure that data from different writers are

used for model training and evaluation, the data set is

partitioned into two disjoint subsets prior to experimentation.

This strategy avoids potential model overfitting and therefore

produces an unbiased system performance estimate. These

partitions, referred to as the training set and evaluation

set, contain the signatures of 34 writers and 17 writers

respectively.

During model training, only the training set is considered.

For every writer, 15 genuine signatures are reserved as a ref-

erence set, whilst 15 genuine signatures and 15 forgeries are

included into the training data. These signatures are used to

obtain a total of 225 positive and 225 negative dissimilarity

vectors. The entire set of positive and negative dissimilarity

vectors, obtained from all 34 writers in the training set, is

used to determine the optimal decision boundary, which is

retained for subsequent verification. Note that, although it

is not reasonable to assume that 15 reference samples will

be available for every writer enrolled into the system during

deployment, it is entirely reasonable to consider 15 reference

samples during training, since these samples are collected

within a controlled environment and are used for training

purposes only.

During system evaluation, only the evaluation set is

considered. For every writer, K genuine signatures are

reserved as a reference set, whilst 30−K genuine signatures

and 60 forgeries are considered for verification. The entire

set of genuine signatures and forgeries, obtained from all

17 writers in the evaluation set, is used to gauge system

performance.

Since only 17 of the 51 writers are considered for

evaluation, the protocol utilised in this paper employs 3-

fold cross validation and 10-fold data randomisation, which

proceeds as follows: (1) The data set is partitioned into

three equal subsets, each containing the signatures from 17

writers; (2) Each subset, in turn, is used as an evaluation set,

whilst signatures from the remaining 34 writers constitute

the training set; (3) The order of the writers is randomised

and the process is repeated. The reported results therefore

represent the average performance for 30 independent trials.

C. Results

We evaluate our SVM-based verification protocol for

several kernel function configurations. These include the

linear (LIN), radial basis function (RBF), F -score weighted

RBF (FS-WRBF) and linear support vector weighted RBF

(LSV-WRBF) variants. The performance metric μ(K)EER, which

denotes the average equal error (EER) rate achieved for a

specific value of K, is presented in Table I.

It is clear from Table I that the linear kernel is signif-

icantly outperformed by its RBF-based counterparts. It is

also clear that there exists a strong correlation between the

reference set size K and system performance. This is an

expected result, since the number of reference signatures

available per writer plays a key role during several phases

of model construction. Finally, it becomes apparent that the

weighted kernels prove superior to the conventional RBF

kernel. Although this superiority may not be significant, it

is undoubtedly consistent.

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Table IAVERAGE EERS (%) OBTAINED WHEN THE PHILIPS EVALUATION SET IS CONSIDERED.

μ(K)

EER

KAVE

3 5 7 9 11 13 15

LIN 8.16 7.08 6.13 5.82 5.17 4.78 4.52 5.95

RBF 4.55 3.67 2.62 2.38 1.89 1.47 1.29 2.55

FS-WRBF 4.42 3.54 2.60 2.26 1.77 1.37 1.26 2.46

LSV-WRBF 4.34 3.52 2.59 2.23 1.74 1.36 1.26 2.44

AVE 5.37 4.46 3.49 3.17 2.64 2.24 2.08 3.35

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Figure 2. (a)–(b) Average feature weights considered by the FS-WRBF and LSV-WRBF kernels respectively. The feature indices correspond to the featureset column numbers defined in (1), namely X = [p, x, y, vx, vy , ax, ay , θx, θy ].

We find that, although two fundamentally different

weighting strategies are considered, there is no clear dis-

tinction between the performances yielded by the differ-

ently weighted RBF kernels. This is an interesting result,

especially when one analyses the different feature weights

considered by the two strategies, as illustrated in Figure 2.

Although both strategies recognise e.g. y, vx and vy as

highly discriminant features, there is a notable difference

in the weights assigned to e.g. x and ay . Another point

of interest is raised when one considers the fact that it is

reported in [4] that both of the pen-tilt features are amongst

the most discriminant features in their system. This assertion

is in stark contrast with the evidence presented in Figure 2,

where θx and θy rank amongst the least discriminant features

when either strategy is considered.

We compare the results reported in this paper to those

reported in the literature for systems also evaluated on the

Philips database. These include the systems presented in [4]–

[7], as discussed in Section I. The reader is reminded that,

although these systems were evaluated on the same data set,

there are slight differences in the experimental protocols

considered for evaluation. Nevertheless, the experimental

conditions are similar enough to perform a sensible com-

parison. This comparison is presented in Table II.

From Table II we observe that, for K = 15, both WRBF-

based systems outperform the system presented in [4], whilst

they are marginally outperformed by the systems presented

Table IIEERS (%) REPORTED FOR SELECTED EXISTING SYSTEMS EVALUATED

ON THE PHILIPS DATABASE.

SystemEER (%)

K = 5 K = 15[4] (1998) - 1.90[5] (2000) - 1.02[6] (2004) 3.54 0.95[7] (2007) 3.25 -FS-WRBF 3.54 1.26

LSV-WRBF 3.52 1.26

in [5] and [6]. For K = 5, there is no clear distinction

between the performance of our systems and that of [6],

whilst they are marginally outperformed by the system

presented in [7].

This is a promising result, considering the comparatively

rudimentary feature set considered by the systems presented

in this paper. It is reasonable to assume that the development

of a more sophisticated feature extraction process should

almost certainly improve system performance. Furthermore,

if pen-tilt features do indeed contain valuable information, as

asserted in [4], it is reasonable to believe that the utilisation

of an alternative feature weighting strategy, specifically one

that successfully quantifies the significance of the pen-tilt

features, could potentially improve system performance.

438

VII. CONCLUSION

In this paper we demonstrated that: (1) A DTW-based

algorithm is able to successfully convert a writer-dependent

on-line signature feature set into a writer-independent dis-

similarity vector, provided that a genuine reference sam-

ple is available for comparison; (2) The incorporation of

feature weights into the SVM kernel consistently results

in superior verification performance; (3) The utilisation of

both aforementioned techniques produces a novel writer-

independent on-line signature verification system of which

the performance compares favourably with that of existing

systems evaluated on the same database. As a proof of

concept, the systems presented in this paper are therefore

deemed successful.

Furthermore, additional topics that warrant further inves-

tigation are identified. Firstly, the investigation of alternative

feature weighting strategies is deemed warranted. Candidate

strategies include linear discriminant analysis (LDA), as

employed in [4], the receiver operating characteristic (ROC)

based approach proposed in [12], as well as the FSDD

feature ranking algorithm proposed in [17]. Also, a large

number of additional features may be derived from the orig-

inally captured signature data. Such an expanded feature set

should be well suited for use in a feature weighted modelling

framework, since the role of relatively less discriminating

features are minimised during model construction.

The incorporation of alternative feature weighting strate-

gies, into an expanded feature set, is currently under inves-

tigation.

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