Engineering, 2013, 5, 84-87
doi:10.4236/eng.2013.55B017 Published Online May 2013 (http://www.scirp.org/journal/eng)
Handwriting Classification Based on Support Vector
Machine with Cross Validation
Anith Adibah Hasseim, Rubita Sudirman, Puspa Inayat Khalid
Faculty of Electrical Engineering, Universiti Teknologi Malaysia, Johor Bahru, Johor, Malaysia
Received 2013
ABSTRACT
Support vector machine (SVM) has been successfully applied for classification in this paper. This paper discussed the
basic principle of the SVM at first, and then SVM classifier with polynomial kernel and the Gaussian radial basis func-
tion kernel are choosen to determine pupils who have difficulties in writing. The 10-fold cross-validation method for
training and validating is introduced. The aim of this paper is to compare the performance of support vector machine
with RBF and polynomial kernel used for classifying pupils with or without handwriting difficulties. Experimental re-
sults showed that the performance of SVM with RBF kernel is better than the one with polynomial kernel.
Keywords: Support Vector Machine; Handwriting Difficulties; Cross-Validation
1. Introduction
The field of handwriting has been of interest from a vari-
ety of aspects; its entity, indications and aesthetic. In the
beginning, the development of handwriting and the fac-
tors that affect handwriting performance were investi-
gated [1,2], but later whole words were addressed. Most
of the systems reported in the literature until today in-
volved screening measures in identifying pupils who are
at risk of handwriting difficulties and also addressed the
absence of an appropriate tool for monitoring beginning
handwriting development. More importantly, automated
handwriting analysis has been given more attention in the
hunt for quantitative features and key indicators in
monitoring beginning handwriting skill development.
Such automated handwriting analysis include recogniz-
ing the writer (e.g. [3]), the text written (e.g. [4]), move-
ment and procedure (e.g. [5,6]), or even semantic content
of the text (e.g. [7]). More or less each of these issues can,
and have been investigated either offline or online related
to the available data.
Up to sixty percent of children’s typical school day is
allocated to fine motor activities, with writing being the
predominant task during these time periods [8]. These
tasks all require the foundational skill of basic handwrit-
ing proficiency to allow teachers to accurately assess
students’ understanding and comprehension of instruc-
tional material. If students do not possess basic hand-
writing proficiency, it can limit their ability to success-
fully complete a majority of classroom tasks. In addition,
it has also been suggested that students with handwriting
problems need to focus more attention on the physical
process of writing, thus limiting use of higher order cog-
nitive skills, planning and generation of content [9]. Thus,
handwriting proficiency is an important foundation upon
which success with later writing tasks depends. Due to
the number of every day school tasks which involve
writing, unsuccessful mastery of handwriting skill can
negatively influence later success in school.
1.1. Support Vector Machine
Support Vector Machine (SVM) is a new classification
technique based on the statistical learning theory pro-
posed by Vapnik in 1995 [10]. It can successfully solve
over-fitting, local optimal problem and is especially
suitable for small-sample and high-dimensional nonlinear
case. Besides, it already showed good results in the
medical diagnostics, optical character recognition, elec-
tric load forecasting and other fields.
Kernel Fuction
In general, a radial basis function is one of the most
popular kernel and reasonable first choice. The reason
why is, this kernel nonlinearly
Given the linearly separability sample set (xi, yi) where
i = 1,…, n. If taking the simplest case; 2 class classifica-
tion, then x∈Rn, y ∈ { + 1, − 1} is the classes number.
The commonly form of the linear decision function is:
f(x) = w. x + b (1)
Sometimes linear classifiers are not complex enough;
therefore SVM maps the data into a higher dimensional
space, unlike the linear kernel which can handle the case

A. A. HASSEIM ET AL. 85
when the relation between class labels and attributes is
nonlinear [11]. Formally, pre-process the data with:
x →φ(x) (2)
and then learn the map from φ(x) to y:
f(x) = w. φ(x) + b (3)
However, the dimensionality of φ(x) can be very large,
making w hard to represent explicitly in memory, and
hard to solve. The Representer theorem (Kimeldorf &
Wahba, 1971) shows that (for SVMs as a special case):
1
()
m
ii
i
x
w 

 (4)
for some variables α. Instead of optimizing w directly we
can thus optimize α. The decision rule is now:

1
()( ).
m
ii
i
f
xxx  


b

(5)
If the dot product (x. xi) is replaced by the kernel func-
tion K(x, x′), the optimal decision function is as follows:

1
() ,
m
ii
i
fxKxx b 


 (6)
In this project, 2 kinds of common kernel function are
used. The first one is Gaussian radial basis function
(RBF):
2
2
(,) exp()
i
i
x
x
Kx xg

 (7)
and the other one is polynomial kernel:

(,). 1
d
ii
Kx xxx


 
(8)
Classical techniques utilizing radial basis functions
employ some method of determining a subset of centre.
Typically a method of clustering is first employed to se-
lect a subset of centre. An attractive feature of the SVM
is that this selection is implicit, with each support vectors
contributing one local Gaussian function, center at that
data point.
1.2. Cross Validation (CV)
Currently, cross-validation has been widely used for es-
timating the performance of neural networks and other
applications such as support vector machine and k-nearest
neighbor. Cross-validation is a statistical method of
evaluating and comparing learning algorithms. The basic
idea of cross-validation is splitting the data, which is
consists of dividing the available training data into two
sets. The first set is used to train the network, while the
other is used to evaluate the performance of the trained
network. In typical cross-validation, the training and
validation sets must cross-over in successive rounds such
that each data point has a chance of being validated
against. The basic form of cross-validation is k-fold
cross-validation. Other forms of cross-validation are spe-
cial cases of k-fold cross-validation or involve repeated
rounds of k-fold cross-validation.
Advantages of this method are as follows: 1) Average
classification accuracies of k SVM classifiers are used to
evaluate the SVM classifier parameters performance
which can improve the generalization ability of the SVM
classifier with the optimized parameters; 2) k-fold
cross-validation method can ensure all the sample data be
involved in the SVM classifier training and validation, it
can make full use of the limited sample data; 3) no matter
how the data gets divided, every data point is used as a
test set exactly once, and gets to be in a training set k-1
times. The disadvantage of this method is that the train-
ing algorithm has to be rerun from scratch k times, which
means it takes k times as much computation to make an
evaluation.
2. Methodology
The data was obtained from Khalid et al in [13]. The data
is composed of 120 samples which contain 2 features
(that is The standard deviation of pen pressure when
drawing RU, p-value < 0.0001 and z-value = minus
4.319 and Ratio of time taken to draw HR and HL,
p-value < 0.0001 and z-value = minus 5.205.) and two
group of writers (that is below average printers (test
group) and above average printers (control group)).
Firstly, the data is portioned into k equally sizes seg-
ments or folds. In this project, we used 10-fold cross
validation (k = 10) as it is the most common used for data
mining and machine learning. As shown in Figure 1, the
darker section of the data are used for training while the
remaining data; lighter sections are used for validate the
model. This process is repeated 10 times until all sections
have been validated.
Model Parameter Selection
Two models; SVM of polynomial kernel function and
RBF kernel are chose in looking for performance com-
parison. Performance of the SVM depends on the choice
of parameters. The optimal selection of these parameters
is a nontrivial issue. According to study, the important of
RBF kernel is need to find parameter C and g. SVM of
polynomial kernel function chooses different parameter
C and d. The penalty factor C, is used to improve gener-
alized capability when C is increasing while g and d are
the adjustable parameter of study machine in the experi-
ment and they are used to adjust experienced error value.
The parameter slightly influences classification result
when a smaller amount of training samples are used [12].
After training SVM, the best value C and g can be
used to classify children with handwriting problems. For

A. A. HASSEIM ET AL.
86
Tr ain
Tr ain
Model
Model
Test Test
Result
Result
Train
Model
Test
Result
Figure 1. Procedure of 10-fold cross validation.
Table 1. Accuracy of Prediction based on SVM with RBF
Kernel.
the SVM with polynomial kernel, there are two parame-
ters: C and d. The SVM with RBF kernel has also two
parameters: g and C. In order to know different per-
formance each parameter produces to outputs, we select
three values for each parameter just like choosing the
number of hidden nodes in the neural networks.
Accuracy of Predictions (%)
Feature g/C
0.01 0.1 1
1 83.33 91.67 83.33
10 93.33 91.67 91.67 Feature 1
100 91.67 91.67 91.67
1 91.67 92.80 91.67
10 91.67 91.67 83.33 Feature 2
100 91.67 86.67 83.33
3. Results and Discussion
Table 1 and Table 2 present the recognition results using
the SVM with polynomial kernel, RBF kernel respec-
tively. The classification was considered correct if the
output from the model was similar to the one that had
been judged by the teachers (using Handwriting Profi-
ciency Screening Questionnaire (HPSQ)). In this paper,
we used the classification error (rejection of genuine
category) as the metric.
Table 2. Accuracy of Prediction based on SVM with Poly-
nomial Kernel.
According to Table 1, as can be seen the percentage of
correct prediction of feature 1 is in decreasing when the
variation g varies from 0.01 to 0.1. While it is in reverse
direction when the variation g varies from 0.1 to 1.The
results confirmed that the best value of the variation g
near 0.1. When the coefficient of penalty C is increased,
the accuracy of prediction is in decreasing. Different
from feature 1, feature 2 is seen to be decreasing in per-
centage of correct prediction when g varies from 0.01 to
1 and when C increases in the value.
Accuracy of Predictions (%)
Feature g/d
0.01 0.1 1
3 86.67 86.67 91.67
5 83.33 86.67 83.33 Feature 1
10 66.67 71.67 83.33
3 86.67 86.67 86.67
5 83.33 83.33 86.67 Feature 2
10 61.67 71.67 86.67
In the other hand, the result from Table 2 shows in
different from Table 1. It is clear that, when the variation
g increases in the value from 0.01 to 1, both percentage
of corrects prediction for feature 1 and feature trends to
decrease. While when the variation d varies from 3 to 10,
the accuracy of prediction is increasing. This exhibits
SVM good generalization performance.
The results reported here have shown that the per-
formance of SVM with RBF kernel is better than SVM
with polynomial kernel. We use SVM (RBF kernel) with

A. A. HASSEIM ET AL. 87
changing C and g to simulate and to classify children
with and without handwriting problem based on drawing
tasks.
4. Conclusions
SVM RBF and polynomial have been used in this study
to select those who are at risk of handwriting difficulty
due to the improper use of graphic rules. Cross-validation
method is adopted to choose parameter in order to gain
preferable classificatory result. In this paper, we have
testified that the performance of SVM with RBF kernel is
better than the one with polynomial kernel. Experiment
simulative results indicate: average accuracy of classifi-
catory testing based on SVM RBF algorithm reaches
more than 93%. The data is apparently high compared
with SVM polynomial algorithm.
5. Acknowledgements
This work was supported by the Malaysia Ministry of
Higher Education and Universiti Teknologi Malaysia
under Vote Q.J130000.2623.09J28.
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