International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
HYPERSPECTRAL DATA CLASSIFICATION USING FACTOR GRAPHS
Aliaksei Makarau, Rupert Müller, Gintautas Palubinskas, and Peter Reinartz
German Aerospace Center (DLR)
German Remote Sensing Data Center (DFD) bzw. Remote Sensing Technology Institute (IMF)
82234 Oberpfaffenhofen, Germany
{aliaksei.makarau, rupert.mueller, gintautas.palubinskas, peter.reinartz}(@dir.de
Commission VII/3
KEY WORDS: Hyper spectral, Classification, Training, Reference Data
ABSTRACT:
Accurate classification of hyperspectral data is still a competitive task and new classification methods are developed to achieve desired
tasks of hyperspectral data use. The objective of this paper is to develop a new method for hyperspectral data classification ensuring
the classification model properties like transferability, generalization, probabilistic interpretation, etc. While factor graphs (undirected
graphical models) are unfortunately not widely employed in remote sensing tasks, these models possess important properties such as
representation of complex systems to model estimation/decision making tasks.
In this paper we present a new method for hyperspectral data classification using factor graphs. Factor graph (a bipartite graph consisting
of variables and factor vertices) allows factorization of a more complex function leading to definition of variables (employed to store
input data), latent variables (allow to bridge abstract class to data), and factors (defining prior probabilities for spectral features and
abstract classes; input data mapping to spectral features mixture and further bridging of the mixture to an abstract class). Latent
variables play an important role by defining two-level mapping of the input spectral features to a class. Configuration (learning) on
training data of the model allows calculating a parameter set for the model to bridge the input data to a class.
The classification algorithm is as follows. Spectral bands are separately pre-processed (unsupervised clustering is used) to be defined
on a finite domain (alphabet) leading to a representation of the data on multinomial distribution. The represented hyperspectral data
is used as input evidence (evidence vector is selected pixelwise) in a configured factor graph and an inference is run resulting in the
posterior probability. Variational inference (Mean field) allows to obtain plausible results with a low calculation time. Calculating the
posterior probability for each class and comparison of the probabilities leads to classification. Since the factor graphs operate on input
data represented on an alphabet (the represented data transferred into multinomial distribution) the number of training samples can be
relatively low.
Classification assessment on Salinas hyperspectral data benchmark allowed to obtain a competitive accuracy of classification. Employ-
ment of training data consisting of 20 randomly selected points for a class allowed to obtain the overall classification accuracy equal
to 85.3294 and Kappa equal to 0.8358. Representation of input data on a finite domain discards the curse of dimensionality problem
allowing to use large hyperspectral data with a moderately high number of bands.
graphical model type is not so wide for remotely sensed data in-
terpretation.
1 INTRODUCTION
Development of new methods for single/multisensory data clas-
sification leads to an improvement of the data classification and In this paper a new approach for hyperspectral imagery super-
a more precise identification of land-cover classes. Nevertheless,
requirements on the methods such as transferability, integration
into complex systems, or augmenting ability motivate an employ-
ment of probabilistic graphical models [Bishop, 2006]. Applica-
tion of probabilistic graphical models becomes more and more
popular and efficient solution for image annotation, classification,
for definition of semantic link between data and a high level la-
id [Lienou et al., 2010], [Bratasanu et al., 2011], [Wang et al.,
009].
Factor graphs (FG) were proposed in 1997 [Kschischang et al.,
2001] and since then the application of FGs for signal/image
processing and recognition is gradually emerging. B. Frey et
al. [Frey and Jojic, 2005] performed a work on a comparison of
learning and inference methods for probabilistic graphical mod-
els (Bayesian networks, Markov random fields, factor graphs).
Factor graph is a convenient tool to define complex systems for
data processing/interpretation, to expand the systems, allow to
model complex interactions among a system parts (e.g. map fea-
tures/properties from low to high level), to perform approximate
inference on data, or use non full data for plausible decision mak-
ing. Nevertheless, application of factor graphs as a more general
137
vised classification using factor graph is proposed. The structure
of the factor graph is defined in order to define prior probabilities
for input data, to map the input data to a latent variable (a mixture
of the input features) and bridge the mixture to a semantic class.
A configuration of the factor graph on training data allows to es-
timate the parameter set of the graph (probabilistic functions in
the factors) and an employment of a fast inference method (Mean
field [Frey and Jojic, 2005]) allows to obtain a competitive accu-
racy of the hyperspectral data classification.
2 FACTOR GRAPH MODEL FOR CLASSIFICATION
Factor graph (undirected probabilistic model) is a more general
graphical model than a Bayesian network or a Markov random
field. An FG possesses properties of Bayesian network and Markov
random field and allows to describe complex relationships among
parts of a modeled system. A factor graph is a bipartite graph
containing two types of nodes: variable nodes (x;, i — 1..n) and
function nodes (factors) (f;(x1,x2,..-,Xn),] = 1..m), where
a variable node x; takes value on a finite domain (alphabet A:)
[Kschischang et al, 2001]. Figure 1 presents an example of
