![](bg4.png)
detach from the tail of the ordered list a series of
template sequences which actually belong to the
same class. This increases the uniformity and
consistency of initial clusters, allowing a better
result after the merging procedure. In fact, there is
no implementation of a process of cluster split or
deletion of an item from a cluster: when a template
is added to a cluster, it is never removed from it. If
the initial clusters, produced by E-AC are very
heterogeneous (i.e. contain templates belonging to
different classes), the final result, will be hopelessly
affected by this. In a final experiment, the merging
step was reapplied to the final clustering with
increasing thresholds, in an iterative way. With
LDA, the procedure initially generated 104 clusters,
to which merging was applied with threshold 0.2 to
obtain the first final clustering (the procedure used
for Table 2). The merging procedure was applied
again to the set of clusters obtained so far, with a
higher threshold 0.3, and again to the set of clusters
obtained with a threshold 0.4. Table 3 shows the
performance in terms of number of clusters and
performance indices for the various iterations. The
same procedure was applied with FACE obtaining
the results in Table 4.
Table 3: Performance indices for the sequence of iterations
of the merging step when E-AC is applied with LDA FET.
FET Cl.s RM FMI P R
it-0
104 0.9736 0.4087 0.84 0.20
it-1
84 0.9729 0.3927 0.79 0.19
it-2
60 0.9771 0.5077 0.78 0.33
it-3
45 0.9806 0.5856 0.71 0.48
Table 4: Performance indices for the sequence of iterations
of the merging step when E-AC is applied with FACE
FET.
FET Cl.s RM FMI P R
it-0
62 0.9777 0.5227 0.81 0.34
it-1
50 0.9813 0.6237 0.79 0.49
it-2
39 0.9833 0.6790 0.71 0.65
Table 3 and Table 4 show that the different
applications of the merging procedure consistently
fuse together the clusters with similar templates, as
indicated by the growth of the value of Recall.
However, the reduction of Precision shows that
merging may put elements of different classes within
the same cluster.
E-AC is slightly slower than K-Means, but this
can be fixed by suitable computation optimizations.
5 CONCLUSIONS
Clustering is a promising solution to address the
problem of biometric recognition with a large scale
database. K-means Clustering is a very popular
technique to address the problem, but needs the
parameter k a-priori. Our technique achieves better
results even without this information.
REFERENCES
Bhatnagar J., Kumar A.(2009). On Estimating Some
Performance Indices for Biometric Identification.
Pattern Recognition, vol. 42( 5), pp. 1805-1818.
De Marsico M., Nappi M., Riccio D. (2012). Entropy in
Biometric Face Template Analysis. In: Campilho,
Aurélio and Kamel, Mohamed (eds.)
Proceedings of
International Conference on Image Analysis and
Recognition – ICIAR 2012. Lecture Notes in Computer
Science
, Vol. 7325, pp. 72-79.
De Marsico M., Nappi M., Riccio D., Wechsler H.
(2012). Robust Face Recognition for Uncontrolled
Pose and Illumination Changes.
IEEE Trans. on
Systems, Man and Cybernetics, Part A: Systems and
Humans
, vol.PP, no.99, pp.1-15, doi:
10.1109/TSMCA.2012.2192427
Fowlkes E. B., Mallows C. L. (1983). A Method for
Comparing Two Hierarchical Clusterings.
J. of the
American Statistical Association,
78(383), 553–569.
Kirby M., Sirovich L. (1990). Application of the Karhunen
Loeve procedure for the characterization of human
faces.
IEEE Trans. on Pattern Analysis and Machine
Intelligence
Vol.12, pp.103–108.
Maltoni D., Maio D., Jain A. K., Prabhakar S. (2003).
Handbook of Fingerprint Recognition. Springer.
Phillips P. J., Wechsler H., Huang J., Rauss P.(1998). The
FERET Database and Evaluation Procedure for Face
Recognition Algorithms, Image and Vision Computing
Journal, Vol. 16(5), pp. 295-306.
Rand W. M. (1971). Objective criteria for the evaluation
of clustering methods.
J. of the American Statistical
Association
Vol, 66(336), 846–850.
Singh, J. K. (2009). A Clustering and Indexing Technique
suitable for Biometric Databases. MSc Thesis, Indian
Institute Of Technology Kanpur, Kanpur, India.
Turk M., Pentland A. (1991) Eigen Faces for Recognition.
J. of Cognitive Neuroscience, Vol. 3(1), pp. 71-86
Wiskott, L., Fellous, J. M., Krüger, N., von der Malsburg,
C. (1996). Face Recognition by Elastic Bunch Graph
Matching.
IEEE Trans. on Pattern Analysis and
Machine Intelligence
, Vol. 19(7,) pp.775-779
Zhao H., Yuen P.C. (2008). Incremental linear
discriminant analysis for face recognition. IEEE
Trans. on Systems, Man and Cybernetics – Part B:
Cybernetics
. Vol. 38, pp. 210–221
EntropybasedBiometricTemplateClustering
563