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T
f
G PE
=+
(3)
T
(4)
Z
=
UQ
+
F
Where
B
and
U
are the matrices containing the extracted latent vectors, the
matrices P and Q represent loadings, and the matrices E and F are the residuals. Based
on the nonlinear iterative partial least squares (NIPALS) algorithm [9] for learning the
latent space, PLS finds weight vectors p and q such that
cov( ,
bu
)
2
=
max cov(
G Z
)
2
(5)
fp
,
q
pq
==
1
Where b and u are the column vectors of B and U respectively and
cov(b,u)
is the
sample covariance. The regression coefficients between the two sets of variables
G
and
Z
can be estimated by PLS regression formulation [10]
WGUBGG BZ
=
TT T
(
T
)
−
1
T
(6)
f
f
f
f
Using
W
, we can predict labels of the query feature vector
∧
zf W
=
T
(7)
t
t
z
∧
ℜ
c
is an indicator variable, ideally containing 1 at only one location
(indicating the class membership) and 0 at all other locations. However
z
∧
contains
some non-zero value at each location due to the noise in the data and approximation
Where
t
z
∧
is considered as
errors in the regression process. The location of the maximum of
the predicted label for
f
.
Using this method, for each test sample, we can obtain
c
regression values
z
∧
from all the PLS classifiers. The category corresponding to the maximum value of
z
∧
is decided to be the recognition result.
4
Experimental Results
The infrared data in this essay were collected by using an infrared camera Thermo
Vision A40 supplied by FLIR Systems Inc [4]. The training database comprises 500
thermal images of 50 individuals which were carefully collected under the similar
conditions in November 17, 2006: environment under air-conditioned control with
temperature around 25.626.3
℃
. The test database comprises 500 thermal images of
50 individuals were obtained under the same conditions of the training database. The
original resolution of each image is 240×320. In our experiments, the face image is
normalized to the size of 80×60.
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