Full text of DOI:10.1016/S1566-2535(02)00091-X

Information Fusion 3 (2002) 289–297
www.elsevier.com/locate/inffus
Combining parametric and non-parametric algorithms
for a partially unsupervised classification
of multitemporal remote-sensing images
*
Lorenzo Bruzzone , Roberto Cossu, Gianni Vernazza
Department of Information and Communication Technologies, University of Trento, Via Sommarive, 14, I-38050, Povo, Trento, Italy
Received 26 January 2002; received in revised form 3 June 2002; accepted 12 August 2002
Abstract
In this paper, we propose a classification system based on a multiple-classifier architecture, which is aimed at updating land-cover
maps by using multisensor and/or multisource remote-sensing images. The proposed system is composed of an ensemble of clas-
sifiers that, once trained in a supervised way on a specific image of a given area, can be retrained in an unsupervised way to classify a
new image of the considered site. In this context, two techniques are presented for the unsupervised updating of the parameters of a
maximum-likelihood classifier and a radial basis function neural-network classifier, on the basis of the distribution of the new image
to be classified. Experimental results carried out on a multitemporal and multisource remote-sensing data set confirm the effec-
tiveness of the proposed system.
Ó 2002 Elsevier Science B.V. All rights reserved.
Keywords: Multiple-classifier system; Unsupervised retraining algorithm; Maximum-likelihood classifier; Radial basis function neural network;
Expectation-maximization algorithm
1
. Introduction
classification methods capable of analysing the images
of the considered site for which no training data are
available, thus increasing the effectiveness of monitoring
systems based on the use of remote-sensing images.
Recently, the authors faced this problem by pro-
posing an unsupervised retraining technique for maxi-
mum-likelihood (ML) classifiers capable of producing
accurate land-cover maps even for images for which
ground-truth information is not available [6]. This tech-
nique allows the unsupervised updating of the parame-
ters of an already trained classifier on the basis of the
distribution of the new image to be classified. How-
ever, given the complexity inherent with the task of
unsupervised retraining, the resulting classifier may be
intrinsically less reliable and less accurate than the cor-
responding supervised one, especially for complex data
sets.
In this paper, in order to define a robust classifica-
tion system for an unsupervised updating of land-
cover maps, we propose: (i) to extend the unsupervised
retraining technique proposed in [6] to radial basis
function (RBF) neural network classifiers; (ii) to inte-
grate the resulting unsupervised retraining classifiers in
the framework of multiple-classifier systems. In greater
The increasing availability of remote-sensing images,
acquired periodically by satellite sensors on the same
geographical area, makes it extremely interesting to
develop monitoring systems capable of automatically
producing and regularly updating land-cover maps of
the considered site. The monitoring task can be ac-
complished by supervised classification techniques,
which have proven to be effective categorisation tools
[
1–5]. Unfortunately, these techniques require the
availability of a suitable training set (and hence of
ground-truth information) for each new image of the
considered area to be classified. However, in real ap-
plications, it is not possible to rely on suitable ground
truth information for each of the available images of the
analysed site. Consequently, not all the remote-sensing
images acquired on the investigated area at different
times can be used for updating the related land-cover
maps. In this context, it would be important to develop
*
Corresponding author. Tel.: +39-0461-882623/882056; fax: +39-
461-882671/881696.
E-mail address: lorenzo.bruzzone@ing.unitn.it (L. Bruzzone).
0
1
566-2535/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved.
PII: S1566-2535(02)00091-X

290
L. Bruzzone et al. / Information Fusion 3 (2002) 289–297
detail, the proposed system is based on two different
unsupervised retraining classification algorithms: a para-
metric ML classifier and a non-parametric RBF neural-
network classifier. Both techniques allow the existing
on several factors (e.g., differences in the atmospheric
and light conditions at the image-acquisition dates,
sensor non-linearities, different levels of soil moisture,
etc.) that alter the spectral signatures of land-cover
classes in different images and consequently the distri-
butions of such classes in the feature space.
‘
‘knowledge’’ of the classifiers (i.e., the parameters of the
classifiers obtained by supervised learning on a first im-
age, for which a training set is assumed available) to be
updated in an unsupervised way, on the basis of the
distribution of the new image to be categorised. The
combination of the above-mentioned classification al-
gorithms is used as a tool for increasing the accuracy
and the reliability of the classification maps obtained by
each single classifier. Classical approaches to classifier
combination are adopted. As compared to previous
works [6], the main novelty of this paper consists in the
original retraining technique proposed for the RBF
classifier and in the multiple-classifier architecture used
in the context of partially unsupervised classification.
The paper is organized into seven sections. In Section
It is worth noting that the proposed approach is
based on a separate analysis of the two images X
. Consequently, it does not require that the images are
accurately co-registrated.
1
and
X
2
3. Description of the architecture of the proposed
classification system
The proposed classification system is based on a
multiple-classifier architecture. The choice of this ar-
chitecture mainly depends on the intrinsic complexity of
the unsupervised retraining procedures, which may re-
sult in less reliable and less accurate classifiers than the
corresponding supervised ones, especially for complex
data sets. In this context, the use of a multiple-classifier
approach allows one to integrate the complementary
information provided by an ensemble of different clas-
sifiers, thus involving a more robust and reliable classi-
fication system.
2
the considered problem is formulated. The architec-
ture of the proposed system is described in Section 3.
The unsupervised retraining classifiers are described in
Section 4. Section 5 presents the strategies adopted for
the combination of the ensemble of unsupervised re-
training classifiers considered. Experimental results are
given in Section 6. Finally, in Section 7, discussion is
provided and conclusions are drawn.
The classifiers composing the ensemble are developed
within the framework of the Bayes decision theory.
Consequently, the decision rule adopted to classify a
1
j
generic pixel x of the image X can be expressed as [10]:
1
2
. Formulation of the problem
1
j
1
j
x 2 x if x ¼ arg maxfP ðx =x Þg
ð1Þ
k
k
1
i
1
1
1
2
1
B
2
1
2
2
2
B
xi2X
Let X ¼ fx ; x ; . . . ; x g and X ¼ fx ; x ; . . . ; x g
1
2
1
j
denote two multispectral images composed of B pixels
and acquired in the area under analysis at the time t and
, respectively. Let x be the 1 Â d feature vector asso-
where P ðx =x Þ is the estimate of the posterior proba-
1
i
1
j
1
bility of the class x
(1), the classification of the image X
mation of the posterior probabilities P
classes x
2 X. These estimates involve the computation
of a parameter vector # , which represents the ‘‘knowl-
i
at t , given the pixel x . According to
1
i
j
t
2
1
requires the esti-
ðx =X Þ for all
ciated with the jth pixel of the image X
dimensionality of the input space). Let X
variate random variable that represents the pixel values
i.e., the feature vector values) in X . Let us assume that
i
(where d is the
1
i
1
i
be a multi-
i
1
(
edge’’ of the classifier concerning the distributions of the
classes in the feature space (i.e., the status of the clas-
i
the same set X ¼ fx ; x ; . . . ; x g of C land-cover
1
2
C
classes characterizes the considered geographical area at
both t and t . This means that in our system only the
sifier at t ). The number and nature of the vector com-
1
1
2
ponents will be different depending on the specific
classifier used. In our system, we propose to consider
two different unsupervised retraining approaches: the
former is a parametric approach, which is based on the
ML classifier; the latter consists of a non-parametric
spatial and spectral distributions of such land-covers
classes are supposed to vary (i.e., the set of land-cover
classes that characterize the considered site is fixed over
time). This assumption is quite realistic in several real
applications of classification of remote-sensing data [7–
technique, which is based on RBF neural networks.
p
9
]. Finally, let us assume that a reliable training set Y is
1
Both techniques allow the parameter vectors # (corre-
sponding to the parametric approach) and # (corre-
sponding to the non-parametric approach), which are
1
n
1
available at t , whereas a training set is not available at
1
t
2
. This prevents the generation of the t
as the training of the classifier on the image X
performed. At the same time, it is not possible to apply
the classifier trained on the image X to the image X
2
land-cover map,
2
cannot be
1
obtained by supervised learning on the first image X , to
be updated in an unsupervised way.
1
2
In the proposed multiple-classifier approach, N dif-
ferent classifiers are trained at the time t by using the
information contained in the available training set Y . In
because, in general, the estimates of the statistical pa-
rameters of the classes at t do not provide accurate
1
1
1
approximations for the same terms at t . This depends
particular, a classical parametric ML classifier [10] and
2

L. Bruzzone et al. / Information Fusion 3 (2002) 289–297
291
N À 1 different architectures of non-parametric RBF
where the mixing parameters and the component den-
sities are the a priori probabilities and the conditional
density functions of the classes, respectively. In this
context, the retraining of the ML classifier at the time t2
becomes a mixture density estimation problem, which
can be solved by exploiting the iterative expectation-
maximization (EM) algorithm [11–14]. The iterative
equations to be used are the following:
neural networks [5] are used. As a result, a parameter
p
vector # corresponding to the parametric approach,
and the N À 1 parameter vectors # (r ¼ 1; . . . ; N À 1)
1
n;r
1
corresponding to the non-parametric RBF neural ap-
proach, are derived. Then, at time t
retrained in an unsupervised way by using the infor-
mation contained in the distribution pðX Þ of the new
image X . At the end of the retraining phase, a new
2
, the classifiers are
2
2
X
1
p
tþ1
t
2
j
P
ðx Þ ¼
P ðx =x Þ
ð4Þ
parameter vector # is obtained for the ML classifier
2
k
2
k
2
B
n;r
2
2
j
x 2X2
and N À 1 new parameter vectors # r ¼ 1; . . . ; N À 1
P
P
are obtained for the N À 1 RBF neural-network archi-
tectures considered. Finally, the results provided by
different unsupervised retraining classifiers are combined
by using a classical multiple-classifier approach.
t
2
2
j
2
P ðx
k
=x Þx
x 2X2
2
j
tþ1
j
l
¼ P
ð5Þ
ð6Þ
2
;k
t
2
2
P ðx
k
=x Þ
x 2X
2
2
j
j
t
2
j
2
j
tþ1
T
2
j
tþ1
2;k
2
j
P ðx
k
=x Þðx À l Þ ðx À l
Þ
x 2X2
2
2;k
tþ1
R
¼
P
2
;k
t
2
2
j
2
j
P ðx
k
=x Þ
x 2X2
4
. The proposed unsupervised retraining classifiers
where the superscripts t and t þ 1 refer to the values of
the parameters at the current and next iterations, re-
spectively, the superscript T refers to the vector trans-
pose operation, and the estimated posterior probability
The main idea of the proposed unsupervised re-
training approach is that rough estimates of the pa-
rameter values that characterize the classes considered at
the time t
2
can be obtained by exploiting the parameters
t
2
j
P ðx
k
=x Þ is equal to:
2
of the classifiers estimated at the time t by supervised
1
t
2
j
t
ÞP ðx
2
p ðx =x
i¼1
k
k
Þ
t
2
2
j
2
learning. Such estimates are then updated in an unsu-
pervised way by using the information contained in the
P ðx =x Þ ¼ P
ð7Þ
k
C
t
t
2
2
j
p ðx =x
i
ÞP ðx
i
Þ
2
distribution pðX
2
Þ of the new image X
2
. In the following,
t
2
2
where the density function p ðx =x
i
Þ is computed by
j
a detailed description of the proposed unsupervised re-
training technique for the RBF neural-network classifi-
ers is given. Concerning the retraining technique for the
ML classifier, we provide only a brief description since it
was already proposed in [6].
t
2;i
t
using the estimates of the terms l and R obtained at
current iteration.
2;i
For each class x 2 X, the estimates obtained at
i
convergence of the EM algorithm are the new parame-
2
ters of the ML classifier at the time t . Since the unsu-
pervised retraining approach for the ML classifier is not
the novel aspect of this paper, we refer the reader to [6]
for greater details on this method.
4.1. The proposed retraining technique for the ML
classifier
In the case of a parametric ML classifier, the vector of
parameters that should be estimated for classifying the
new image X is given by:
4.2. The proposed unsupervised retraining technique for
RBF neural-network classifiers
2
p
p
2;1
p
2;2
p
2;C
#2
¼ ½h ; P ðx Þ; h ; P ðx Þ; . . . ; h ; P ðx ފ
ð2Þ
2
1
2
2
2
C
The proposed non-parametric classifier is based on
Gaussian RBF neural networks, which consist of three
layers: an input layer, a hidden layer, and an output
layer (see Fig. 1). The input layer relies on as many
neurons as the input features. The input neurons just
propagate the input features to the next layer. Each one
of the Q neurons in the hidden layer is associated with a
Gaussian kernel function. The output layer is made up
of as many neurons as the classes to be recognised. Each
output neuron computes a simple weighted summation
over the responses of the hidden units for a given input
pattern (we refer the reader to [5] for more details on
RBF neural-network classifiers).
p
where h2 is the vector of the parameters that charac-
;i
terize the conditional density function p
class x (e.g., the mean vector l2;i and the covariance
matrix R2;i in the Gaussian case). For each class x
2
ðX
2
=x
i
Þ of the
i
i
2 X,
0
the initial values of both the prior probability P ðx
i
Þ and
2
0
2
the conditional density function p ðX =x Þ can be ap-
2
i
proximated by the values computed in the supervised
training phase at t : Then, such estimates can be im-
proved by exploiting the information associated with the
1
distribution p
the proposed method is based on the observation that the
statistical distribution of the pixel values in X can be
2
ðX
2
2
Þ of the new image X . In particular,
2
In the context of RBF neural classifiers, the condi-
tional densities of Eq. (3) can be written as a sum of
described by the following mixed-density distribution:
C
X
contributes due to the Q kernel functions u of the
p
2
ðX
2
Þ ¼
P
2
ðx
i
Þp
2
ðX
2
=x
i
Þ
ð3Þ
q
i¼1
neural architecture [14]:

292
L. Bruzzone et al. / Information Fusion 3 (2002) 289–297
chitecture of the proposed system (and, in particular,
some of the results provided by the ML classifier) for
estimating such parameters. For simplicity, let us as-
sume that all the Q kernel functions /2;q are character-
2
ized by the same width r . Under the above-mentioned
assumptions, it is possible to prove that the following
equations (derived by exploiting the EM algorithm) can
be applied iteratively to update the RBF neural-network
classifier parameters:
X
1
tþ1
t
2
j
P
ðu Þ ¼
P ðu =x Þ
ð12Þ
2
q
2
q
B
2
j
x 2X2
Fig. 1. Standard architecture of a supervised RBF neural-network
classifier.
P
t
2
2
j
2
j
2
P ðu =x Þx
x 2X2
q
tþ1
j
p
r
¼ P
ð13Þ
ð14Þ
2;q
t
2
j
2
P ðu =x Þ
x 2X2
2
q
j
Q
X
"
#
Q
p ðX Þ ¼
P ðu Þp ðX =u Þ
ð8Þ
1 X X
2
2
2
q
2
2
q
tþ1
t
2
2
j
2
j
tþ1
2;q
2
¼
P ðu =x Þkx À p
k
q¼1
2
q
dB
2
j
q¼1
x 2X2
where the mixing parameters and the component den-
sities are the a priori probabilities and the conditional
density functions of the kernels. Eq. (8) can be rewritten
as:
where the superscripts t and t þ 1 refer to the values of
the parameters at the current and next iterations, re-
spectively, and the estimated posterior probability
t
2
2
j
C
Q
P ðu =x Þ is given by:
q
XX
p
2
ðX
2
Þ ¼
P
2
ðx
i
=u ÞP
2
ðu Þp
2
ðX
2
=uqÞ
ð9Þ
t
2
j
t
2
q
q
p ðx =u ÞP ðu Þ
i¼1
2
q
q
t
2
2
i¼1 q¼1
P ðu =x Þ ¼ P
ð15Þ
q
j
Q
t
2
2
j
t
2
p ðx =u ÞP ðu Þ
i
i
where the mixing parameter P
2
ðx
i
=u Þ is the conditional
q
t
2
2
j
probability that the kernel u belongs to class x
i
. In this
where the density function p ðx =u Þ is computed by
q
i
t t
2;i 2
formulation, kernels are not deterministically owned by
classes; so the formulation can be considered as a gen-
eralization of a standard mixture model [14]. The value
using the estimates of the terms p and r obtained at
current iteration.
n
2
All the components of # are initialized according to
the values obtained in a supervised way on the t image.
It is possible to prove that at each iteration, the log-
i
q
of the weight w that connects the qth hidden unit to the
ith output node, can be computed as [14]:
1
i
likelihood function of the estimates increases until a
maximum is reached. Although the EM algorithm may
converge to a local maximum, its convergence is guar-
anteed [11–14]. The values of the parameters obtained at
convergence for each RBF neural classifier are used to
analyse the new image to be classified.
w ¼ Pðx =u ÞPðu Þ
ð10Þ
q
i
q
q
By analysing Eq. (9), it can be noticed that, as for the
ML classifier, the retraining of the RBF classifier at time
2
t becomes a parameter estimation problem. In partic-
ular, the parameter vector to be estimated is given by:
n
#2
¼½/ ;Pðu Þ;P ðx =u Þ;...;P ðx =u Þ;...;/ ;Pðu Þ;
2;1
1
2
1
1
2
C
1
2;Q
Q
P ðx =u Þ;...;P ðx =u ފ
ð11Þ
2
1
Q
2
C
Q
5
. Multiple-classifier strategies
where /2;q is the vector of parameters that characterises
the density function p ðX =u Þ (e.g., if Gaussian kernel
2
2
q
We propose the use of different combination strate-
functions are considered, /2 is composed of the mean
gies to integrate the complementary information pro-
vided by the ensemble of unsupervised retraining
parametric and non-parametric classifiers described in
the previous section. The use of these strategies for
combining the decisions provided by each single classi-
fier results in a more robust behaviour in terms of ac-
curacy and reliability of the final classification system.
As stated in Section 3, let us assume that a set of N
classifiers (an unsupervised retraining ML classifier and
N À 1 unsupervised retraining RBF neural classifiers
with different architectures) are retrained on the X2
image in order to update the corresponding parameters
;q
p
2;q and the width r2;q characterizing the qth kernel).
n
However, the parameter vector # is more complex to be
estimated than the parameter vector # related to the
ML classifier. In particular, the presence of the mixing
2
p
2
terms P ðx =u Þ do not allow the new estimates to be
2
i
q
accomplished in a fully unsupervised way. Hence, ad-
ditional information should be available in order to
compute such statistical terms. In the following, we will
assume to know the values of the mixing parameters
Pðx
i
=u Þ; we refer the reader to the Appendices A and B
q
for the description of a technique that exploits the ar-

L. Bruzzone et al. / Information Fusion 3 (2002) 289–297
293
by using the procedures described in Section 4. In this
context, several strategies for combining the decisions of
the different classifiers can be adopted [15,16]. We will
focus on three widely used combination strategies: the
majority voting [15], the combination by Bayesian average
servation of the previous one. However, in this case, the
strategy for combining classifiers consists in a winner-
takes-all approach: the land-cover class that has the
larger posterior probability among all classifiers is taken
as the class of the input pattern.
[
16], and the maximum posterior probability strategies. It
is worth noting that, in our case, the use of these un-
supervised combination strategies is mandatory because
6. Experimental results
2
a training set is not available at t , and therefore more
complex supervised approaches cannot be adopted.
The majority voting principle faces the combination
problem by considering the results of each single clas-
sifier in terms of the class labels assigned to the patterns.
Hence, a given input pattern receives N classification
labels from the multiple-classifier system, each label
corresponding to one of the C classes considered. The
combination method is based on the interpretation of
the classification label resulting from each classifier as a
In order to assess the effectiveness of the proposed
approach, different experiments were carried out on a
data set made up of two multispectral images acquired
by the thematic mapper (TM) multispectral sensor of
the Landsat 5 satellite. The selected test site was a sec-
tion (412 Â 382pixels) of a scene including Lake Mu-
largias on the Island of Sardinia, Italy. The two images
used in the experiments were acquired in September
1
995 (t
1
2
) and July 1996 (t ). Fig. 2shows channels 5 of
‘
‘vote’’ for one of the C land-cover classes. The data
both images.
class that receives the largest number of votes is taken as
the class of the input pattern.
The second method considered, the combination by
The available ground truth was used to derive a
training set and a test set for each image. Five land-
cover classes (i.e., urban area, forest, pasture, water
body, and vineyard), which characterize the test site at
the above-mentioned dates, were considered. A detailed
description of the training and test sets of both images is
given in Table 1. To carry out the experiments, we as-
sumed that only the training set associated with the
image acquired in September 1995 was available. It is
worth noting that the images considered were acquired
in different periods of the year. Therefore, in this case,
the unsupervised retraining problem turned out to be
rather complex.
Bayesian average strategy, is based on the observation
2
that for a given pixel x in the image X
2
the N classifiers
considered provide an approximation of the posterior
j
2
j
probability P ðx =x Þ for each class x 2 X. Therefore, a
2
i
i
possible strategy for combining these classifiers consists
in the computation of the average posterior probabili-
ties, i.e.,
N
X
1
ave
2
j
n
2
j
b
P2 ðx =x Þ ¼
P ðx =x Þ
ð16Þ
i
2
i
N
n¼1
n
2
b
where P ðx
i
=x Þ is the approximation of the posterior
An ML and two RBF classifiers (one with 60 hidden
neurons, i.e., RBF-1, the other with 80 hidden neu-
rons, i.e., RBF-2) were trained in a supervised way on
the September 1995 image to estimate the parameters
that characterize the density functions of the classes
2
j
2
j
probability P
2
ðx
i
=x Þ provided by the nth classifier. The
classification is then carried out according to the Bayes
rule by selecting the land-cover class associated with the
maximum average posterior probability.
The third method considered (i.e., the maximum
posterior probability strategy) is based on the same ob-
at the time t . For the ML classifier, the assumption
of Gaussian distributions was made for the density
1
Fig. 2. Channel 5 of the Landsat-5 TM images utilized for the experiments: (a) image acquired in September 1995; (b) image acquired in July 1996.

294
L. Bruzzone et al. / Information Fusion 3 (2002) 289–297
Table 1
Number of patterns in the training and test sets of both the September
995 and July 1996 images
Table 3
Classification accuracies exhibited by the considered classifiers on the
July 1996 test set after the unsupervised retraining
1
Land-cover class
Number of patterns
Land-cover class Classification accuracy (%) (July 1996 test set)
Training set
Test set
ML
RBF-1
RBF-2
Pasture
Forest
554
304
408
804
179
589
274
418
551
117
Pasture
Forest
94.06
87.22
93.06
99.83
98.54
98.56
100.00
98.90
98.56
Urban area
Water body
Vineyard
Urban area
Water body
Vineyard
100.00
64.10
100.00
31.6231.62
100.00
Overall
2249
1949
Overall
92.76
95.34
95.44
functions of the classes (this was a reasonable assump-
tion, as we considered TM images). In order to exploit
the non-parametric characteristic of the two RBF neural
classifiers, they were trained using not only the 6 avail-
able spectral channels, but also 5 texture features based
on the gray-level co-occurrence matrix (i.e., sum vari-
ance, sum average, correlation, entropy and difference
variance) [17]. These features were computed by using
a window size equal to 7 Â 7 and an interpixel dis-
accuracies provided by the considered unsupervised re-
training classifiers for the July 1996 test set are sharply
higher than the ones exhibited by the single classifiers
trained on the September 1995 image (i.e., 92.76% vs.
50.43%, 95.34% vs. 71.27%, 95.44% vs. 69.78% for the
ML, the RBF-1, the RBF-2classifiers, respectively). In
greater detail, the retrained classifiers exhibited high
accuracies on all land-cover classes, with exception of
the vineyard class, which is a minority one.
At this point, the three classifiers were combined ac-
cording to the strategies described in Section 5. In order
to evaluate the accuracy of the resulting classification
system, it was applied to the July 1996 test set. The
overall and class-by-class accuracies yielded are given in
Table 4. As one can see, the overall accuracies provided
by all the considered combination strategies (i.e.,
95.58%, 95.39%, and 95.75% for the majority voting, the
Bayesian average, and the maximum posterior proba-
bility strategies, respectively) are similar to the one
yielded by the best-performing classifier composing the
ensemble (i.e., 95.44% obtained by the RBF-2classifier).
It is worth stressing that the objective of the multiple-
classifier architecture is not only to increase the accuracy
of the classification system but also to increase its ro-
bustness. In particular, the combination strategy should
allow one to recover the possible failure of a single un-
supervised retraining classifier of the ensemble by ex-
ploiting the results provided by the other considered
classifiers. In order to assess this last issue, an experi-
ment was carried out in which the failure of the re-
tance equal to 1. After the supervised training on the X
1
image, the effectiveness of the classifiers was evaluated
on the test sets related to both images (see Table 2). On
the one hand, as expected, the classifiers provided high
overall classification accuracies for the test set related to
the September 1995 image (i.e., 90.97%, 81.79% and
8
1.74% for the ML, the RBF-1, and the RBF-2classi-
fiers, respectively). On the other hand, they exhibited
very poor performances on the July 1996 test set. In
particular, the overall classification accuracy provided
by the ML classifier for the July test set was equal to
5
0.43%, which is not an acceptable result. Also the ac-
curacies exhibited by the two RBF neural classifiers
considered are not sufficiently high (i.e., 69.78% and
7
1.27%).
At this point, the considered classifiers were retrained
on the t image (July 1996) by using the proposed un-
2
supervised retraining techniques. The ML and RBF re-
training processes converged in 11 and 15 iterations,
respectively, taking few minutes of processing on a Sun
Ultra80 workstation. The overall and class-by-class ac-
curacies exhibited by the different classifiers after the
retraining phase are given in Table 3. By a comparisons
of Tables 2and 3, one can see that the classification
Table 4
Classification accuracies exhibited by the proposed multiple-classifier
system on the July 1996 test set
Land-cover
class
Classification accuracy (%) (July 1996 test set)
Table 2
Overall classification accuracies exhibited by the considered classifiers
Majority
voting
Bayesian
average
Maximum posterior
probability
(trained in a supervised way on the September 1995 image) before the
unsupervised retraining
Pasture
Forest
100.00
98.90
98.56
100.00
34.18
99.83
98.90
98.56
99.32
98.54
98.08
Classification
technique
Overall classification accuracy (%)
Test set (September 1995) Test set (July 1996)
Urban area
Water body
Vineyard
100.00
.7 33 1.6242
100.00
ML
RBF-1
RBF-281.74
90.97
81.79
50.43
71.27
69.78
Overall
95.58
95.39
95.75

L. Bruzzone et al. / Information Fusion 3 (2002) 289–297
295
Table 5
intrinsically less reliable and less accurate than the cor-
responding supervised approaches, especially for com-
plex data sets. Therefore, the use of methodologies for
the combination of classifiers has been proposed in
order to increase the reliability and the accuracy of
single unsupervised retraining classifiers.
Classification accuracies exhibited by the proposed multiple-classifier
system on the July 1996 test set when the failure of the unsupervised
retraining of RBF-3 was simulated
Land-cover
class
Classification accuracy
(%) (July 1996 test set)
Majority
voting
Bayesian
average
Maximum posterior
probability
Although extensive experiments on other data sets
are necessary for a final validation of the method, the
results we obtained on the considered data set are very
interesting. In particular, they pointed out that the
proposed system is a promising tool for attaining high
classification accuracies also for images of a given area
for which an updated training set is not available.
The presented method is based on the assumption
that the estimates of the classifier parameters derived
from a supervised training on a previous image of the
considered area can represent rough estimates of the
class distributions in the new image to be categorised.
Then the EM algorithm is applied in order to iteratively
improve such estimates on the basis of the global density
function of the new image.
It is worth noting that the initial estimates usually
cannot be directly used to classify the new image to be
analyzed. In fact in practical situation, depending on
differences in the atmospheric or light conditions exist-
ing between the two acquisition dates, such initial esti-
mates may be significantly different from the true ones.
The proposed method copes with this situation, i.e., the
EM algorithm is able to improve the initial estimates so
that the classification of the new image can be accurately
performed. However, in order to minimize the possi-
bility that the retraining does not converge to accurate
estimates, if possible, we recommend the application of
a pre-processing phase aimed at reducing the differences
between images due to the above-mentioned factors
Pasture
Forest
98.47
98.90
98.56
100
96.43
98.90
97.84
100
90.83
99.27
98.08
100
Urban area
Water body
Vineyard
58.11
52.13
58.11
Overall
96.56
95.43
94.20
training process of one of the RBF classifiers (i.e.,
RBF-1) was simulated. To this end, the RBF classifier
with 60 hidden neurons, after being trained on the X1
2
image, was not retrained on the X image (let us indicate
this classifier as RBF-3). In this condition, the classifi-
cation accuracy exhibited by the RBF-3 classifier on the
July 1996 test set results equal to the one yielded by the
RBF-1 classifier on the same test set before the unsu-
pervised retraining phase (see Table 2). As already
observed, this overall accuracy (i.e., 71.27%) is not ac-
ceptable. At this point, the ML classifier and the RBF-2
and RBF-3 neural classifiers were combined according
to the strategies described in Section 5. The accuracies
exhibited by the resulting multiple-classifier system are
reported in Table 5. As one can see, even though RBF-3
provided low accuracy on the July 1996 test set, all the
combination strategies resulted in high classification
accuracies, so recovering the simulated failure of the
unsupervised retraining process. In greater detail, the
obtained accuracies are comparable to the ones achieved
by combining the three ‘‘well-retrained’’ classifiers (i.e.,
ML, RBF-1, and RBF-2).
(simple correction algorithms can be adopted).
At the present, the authors are addressing the prob-
lem of defining criteria suitable to identify the cases in
which the initial estimates of the class distributions are
so different from the true ones that may involve a failure
of the retraining process.
7
. Discussion and conclusions
In this paper, the problem of unsupervised retraining
of classifiers for the updating of land-cover maps has
been addressed in the framework of a multiple-classifier
system. The proposed system produces accurate land-
cover maps of a specific study area also from images for
which a reliable ground truth (and hence a suitable
training set) is not available. This is made possible by an
unsupervised updating of the parameters of an ensemble
of parametric and non-parametric classifiers on the basis
of the new image to be classified. In particular, an ML
parametric classifier and RBF neural network non-
parametric classifiers have been considered. However,
given the complexity inherent with the task of un-
supervised retraining, the resulting classifiers are
Acknowledgement
This research was supported by the Italian Space
Agency (ASI).
Appendix A. Estimation of the mixing parameters
P
classifiers
2
ðx
i
=u Þ for the retraining of RBF neural-network
q
In this appendix, we propose a method for estimating
the values of the mixing parameters P ðx =u Þ of the
2
i
q

296
L. Bruzzone et al. / Information Fusion 3 (2002) 289–297
RBF neural classifiers (see Section 4.2). These parame-
ters can be estimated by exploiting the multiple-classifier
architecture of the proposed system. In particular, they
can be derived by using the updated parameter vector of
DE¼Etþ1ðX
n
2
t
n
2
2
=# ÞÀE ðX
2
=# Þ¼
ꢀ
ꢁ
P
P
P
t
2
t
ðuq=x2j
Þ
Þ
Q
q¼1
tþ1
2
tþ1
2
p
ðx =u ÞP ðu Þꢀ
ðuq=x2j
X
2
j
q
q
2
¼
À
log
P
þ
Q
r¼1
t
2
2
j
t
2
j
½p ðx =u ÞP ðu ފ
r
2
r
x
6
the ML classifier. The strategy adopted is the following.
2
8
ꢀ
ꢁ9
P
Pt ðu =x2Þ
>
Q
tþ1
ðx =u ÞP ðu ÞPtþ1ðx
2
j
tþ1
2
t
q
j
2
>
C
B
q¼1
p
2
q
2
q
2
i
=u Þꢀ
q
Let L
2
be the set of pixels x that are most likely cor-
rectly classified by the ML classifier. This set can be
X
X
P
ðu =xj
Þ
j
2
q
À
log
P
Q
t
2
2
j
t
2
t
2
>
½p ðx =u ÞP ðu ÞP ðx
=u ފ
>
>;
i¼1 >: x22Li
r¼1
r
r
i
r
j
2
identified by analysing the estimates of the posterior
2
probability P
2
ðx
i
=x Þ provided by the ML classification
ð20Þ
j
2
j
t
n
2
tþ1
n
2
algorithm. Let us consider the jth pixel x of the image
X and let us assume that x is classified by the ML
2
where E ðX
2
=# Þ and E ðX
2
=# Þ are the error functions
2
j
computed with the parameters estimated at the current
t
2
j
classifier as belonging to the class x (i.e., x ¼
k
k
and next iterations, respectively. The terms P ðu =x Þ are
2
q
2
2
j
arg maxxi2XfP
2
ðx =x Þg). The pixel x is likely to be
i
j
correctly classified by the ML classifier (and thus is as-
introduced in order to apply the JensenÕs inequality.
Thanks to such inequality, the following upper-bound
can be obtained:
signed to the set L
2
and labelled as belonging to the class
x
k
) if its estimated posterior probability is above a given
2
Q
tþ1
2
j
tþ1
X X
p
ðx =u ÞP ðu Þ
t
2
j
2
q
2
q
DE 6 À x
P ðu =x Þ log P
þ
threshold (i.e., P
2
ðx
k
=x Þ P a, where 0:5 < a < 1 is a real
2
q
Q
r¼1
j
number usually close to 1). The set L is then used to
t
2
2
t
t
2
j
2
j
q¼1
p
ðx
j
=u
r
ÞP
2
ðu
r
ÞP
2
ðu
q
=x
Þ
6
2
"
C
B
Q
X X X
estimate the mixing parameters P ðx =u Þ according to
2
i
q
t
2
À
P ðu =x Þ ꢀ
2
q
j
the following iterative equation:
i¼1 x22Li q¼1
j
2
#
P
t
2
j
tþ1
ðx =u ÞP ðu ÞPtþ1ðx
2
j
tþ1
p
i
=u Þ
2
j
i
P ðu =x Þ
2
q
2
q
t
2
q
x 2L
2
q
tþ1ðx
2
ꢀ log P
ð21Þ
Q
t
2
2
j
t
2
t
2
2
j
P
i
=u Þ ¼ P
ð17Þ
2
q
t
2
2
j
r¼1
p
ðx
=u
r
ÞP
ðu
r
ÞP
2
ðx
i
=u
r
ÞP
ðu
q
=x
Þ
2
j
P ðu =x Þ
x 2L2
q
We aim at minimizing this bound with respect to the
values of the parameters computed at the next iteration.
Dropping the terms which depends only on the ‘‘old’’ pa-
rameters, the right-hand side of (21) can be rewritten as:
i
2
2
where L is the subset of L containing the pixels x
labelled as belonging to the class x
EM algorithm used for the unsupervised estimation of
the other RBF neural-network parameters (see Eqs.
2
j
: At each step of the
i
Q
X X
t
2
2
j
tþ1
2
j
tþ1
2
H ¼ Àx
P ðu =x Þ log½p ðx =u ÞP ðu ފ þ
(
12)–(14)), also the Eq. (17) is iterated in order to in-
q
2
q
q
2
j
q¼1
6
crease the accuracy in the estimation of the mixing pa-
rameters.
(
C
B
Q
X X X
t
2
2
j
À
P ðu =x Þꢀ
q
i¼1 x22Li q¼1
j
2
)
Appendix B. Derivation of the equations for estimating
the parameters of RBF neural-network classifiers
ꢀ log½p 2t þ1ðx =u ÞP ðu ÞP ðx =u ފ
2
j
tþ1
tþ1
ð22Þ
q
2
q
2
i
q
Eqs. (12)–(14) and (17) can be derived by maximizing
the following log-likelihood function:
and for the Gaussian case:
(
Q
X X
t
2
2
j
Q
H ¼ Àx
P ðu =x Þꢀ
X
X
q
n
2
2
j
WðX
2
=# Þ ¼
log
½p
2
ðx =u ÞP
2
ðu ފ
2
j
q¼1
q
q
6
2
j
q¼1
x
6
2L2
"
#)
2
j
tþ1
2;q
2
8
9
=
kx À p
k
"
#
tþ1
tþ1
C
<
Q
ꢀ log P ðu Þ À d log r
À
þ
X
X
X
2
q
2
2
tþ1
2
j
2ðr2
Þ
þ
log
p
2
ðx =u ÞP
2
ðu ÞP
2
ðx =uqÞ
i
q
q
:
;
(
i¼1
x22Li
q¼1
C
B
Q
j
2
X
X
X
t
2
2
À
P ðu =x Þꢀ
q
j
ð18Þ
i¼1 x22Li q¼1
j
2
"
which is equivalent to minimizing the error function
n
ꢀ log Ptþ1ðu
Þ þ log P 2t þ1ðx
=u
Þ
#)
EðX
2
=# Þ:
q
i
q
2
2
n
n
2
EðX =# Þ ¼ ÀWðX =# Þ
ð19Þ
2
2
2
2
tþ1
2
kx À p
k
À d log r t2 þ1
À
j
2;q
ð23Þ
This task can be achieved by means of the technique
described in [18]. In particular, let us consider the
change DE in the function (19) when replacing the pa-
rameter values of the current iteration with the one of
the next iteration:
tþ1
2
2
ðr
Þ
2
At this point it is possible to minimize H (and hence the
tþ1
n
2
error function E ðX =# Þ) with respect to the ‘‘new’’
2
parameters. Concerning the parameters r and p2;q the
2

L. Bruzzone et al. / Information Fusion 3 (2002) 289–297
297
minimization is straightforward and leads to Eqs. (13)
and (14). Concerning the parameters P ðu Þ and
remote-sensing images, IEEE Transactions on Geoscience and
Remote Sensing 39 (2001) 456–460.
2
q
[
[
7] F. Maselli, M.A. Gilabert, C. Conese, Integration of high and low
resolution NDVI data for monitoring vegetation in mediterranean
environments, Remote Sensing of Environment 63 (1998) 208–
218.
P ðx =u Þ the following constraints should be considered:
2
i
q
Q
X
P ðu Þ ¼ 1
ð24Þ
2
q
8] A. Grignetti, R. Salvatori, R. Casacchia, F. Manes, Mediterra-
nean vegetation analysis by multi-temporal satellite sensor data,
International Journal of Remote Sensing 18 (1997) 1307–1318.
q¼1
C
X
P
2
ðx =u Þ ¼ 1
i
ð25Þ
q
[9] M.A. Friedl, C.E. Brodley, A.H. Strahler, Maximizing land cover
accuracies produced by decision trees at continental to global
scales, IEEE Transactions on Geoscience and Remote-Sensing 37
i¼1
This can be easily done by introducing two Lagrange
multipliers. Accordingly equations (12) and (17) can be
obtained.
(
1999) 969–977.
[
[
10] J.T. Tou, R.C. Gonzalez, Pattern Recognition Principles, Addi-
son, Reading, MA, 1974.
11] A.P. Dempster, N.M. Laird, D.B. Rubin, Maximum likelihood
from incomplete data via the EM algorithm, Journal of Royal
Statistical Society 39 (1977) 1–38.
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