In: Wagner W., Szekely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
temporal partitioning of Earth AOD through the competition of 
gating regression models (Radosavljevic et al, 2008). To 
address the spatio-temporal dependence the algorithm takes 
information about location and time of data points as inputs for 
gating function and performs competition among specialized 
predictors for each point in the dataset. It starts by randomly 
dividing the dataset into two disjoint subsets. A specialized 
predictor is then trained on each subset. Iteratively data are 
reassigned with some weight to each predictor. Weight is 
determined based on gating output and accuracy of regression 
models. Predictors and gating network are then retrained taking 
into account new assignment. 
2.2 AOD Retrieval across Multiple Accuracy Measures 
Well known accuracy measures such as Mean Squared Error 
(MSE) are often not informative enough because (1) retrieval 
error increases with AOD, (2) distribution of AOD is skewed 
towards small values, and (3) there are many outliers. Instead, 
domain scientists use an array of accuracy measures to gain 
better insight into the retrieval accuracy. For example, the Mean 
Squared Relative Error (MSRE) makes larger absolute errors 
more tolerable when predicting large AOD than when 
predicting small AOD. Ideally, one would like to have a 
retrieval algorithm that provides good accuracy with respect to 
these alternative accuracy measures. 
To address this issue we considered training of neural networks 
that minimize MSRE instead of MSE. In order to construct a 
predictor that is also accurate with respect to MSE and several 
other accuracy measures, we proposed an approach that builds 
an ensemble of neural networks, each trained with slightly 
different MSRE measure (Radosavljevic et al, 2010a). The 
outputs of the ensemble are then used as inputs to a meta-level 
neural network that produces the actual AOD predictions. 
2.3 Uncertainty Analysis of AOD Retrieval 
In this task our objective was to explore if neural networks can 
provide estimates about retrieval uncertainty in addition to 
providing accurate retrievals. Uncertainty estimation for the 
confidence of retrieval requires modeling of the whole 
conditional distribution of the target variable. A standard 
approaches for neural network uncertainty estimation assume 
constant noise variance. However, this assumption is not valid 
for AOD retrieval where noise is heteroscedastic (variance of 
noise is input-dependent). This is why we explored the 
Bayesian approach for uncertainty estimation, based on the 
previous work by Bishop and Quazaz. We also considered 
alternatives based on the bootstrap technique that are more 
tractable for large data sets. 
A neural network-based regression assumes that target y is 
related to input vector x by stochastic and deterministic 
components. The stochastic component is a random variation of 
target values around its mean caused by heteroscedastic noise 
with zero-mean Gaussian distribution and input-dependent 
variance. The deterministic component determines a functional 
relationship between attributes and prediction. Our goal was to 
estimate both the stochastic and deterministic component as 
good as possible. 
In (Ristovski et al, 2009) we have evaluated three approaches 
for estimating the stochastic component. The first was based on 
training a neural network to predict squared error from 
attributes. We used a standard Mean Squared Error (MSE) 
criterion to train this network. The second approach assumed 
heteroscedastic noise and defined the conditional target 
distribution. The uncertainty estimation neural network is 
obtained by maximizing the corresponding log-likelihood. The 
second method assumes that the conditional mean is exactly 
estimated by the bootstrap committee. Since this is only an 
estimate, in the third approach we also considered the model 
uncertainty. In this approach error occurs due to both 
uncertainty in the model and noise in target. 
2.4 Selection of Sites for Ground Based Observations 
Ground based AOD stations are often located without a 
rigorous statistical design. Decisions are typically based on 
practical circumstances (e.g. overrepresentation in urban 
regions and industrialized nations) and according to domain 
experts’ assumptions about the importance of specific sites. 
Given these circumstances, our aim was to evaluate 
performance of the current design of AERONET sensor 
network and to apply data mining techniques to assist in future 
modifications of the sensor network. 
In (Radosavljevic et al, 2009) we assumed that there is a 
pending budget cut for maintenance of the existing AERONET 
sites. The objective was to remove a fraction of the AERONET 
sites while making sure that the utility of the remaining sites is 
as high as possible. We made a simplifying assumption that 
operational costs for each AERONET site around the globe are 
equal. Common to most selection techniques originating from 
the spatial statistics is a tendency to overlook the time 
dimension of data collected by the sensor network. Therefore, 
we considered series of observations and proposed to optimize 
AERONET sensor selection based on the concept of retrieval 
accuracy. Each AERONET site provides a time series which we 
used for training a regression model to retrieve future AOD. 
Sites that can be removed are those whose observations are best 
predicted by the model built on data from the remaining sites. 
In (Das et al, 2009) our objective was to determine appropriate 
locations for the next set of ground-based data collection sites 
as to maximize accuracy of AOD prediction. Ideally, a new site 
should capture the most significant unseen aerosol patterns and 
should be least correlated with the previously observed patterns. 
We proposed achieving this aim by selecting the locations on 
which the existing prediction model is most uncertain. Several 
criteria were considered for site selection, including uncertainty, 
spatial diversity, temporal similarity, and their combination. 
Spatial diversity selects sites that are farthest away from the 
existing sites. The traditional approach in active learning is to 
label the most uncertain data points. In our application, instead 
of selecting an individual data point, we select a site. To address 
this, we defined uncertainty of a site as the average uncertainty 
over all its observations. For this purpose, we trained a number 
of neural networks on data obtained from the existing 
AERONET sites using the bootstrap method. Then we used 
these neural networks to predict the value of AOD at all satellite 
observations over potential AERONET sites. We measured the 
variance among the network predictions and considered this 
variance as the uncertainty of prediction at the individual data- 
points. The selected sites are those with the highest measured 
uncertainty. One drawback of the site uncertainty selection is 
that a global measure like average uncertainty might fail to 
compare the similarity in temporal variation of the uncertainty 
among sites. Each of the potential sites can be regarded as a