International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B3, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
OPTIMISATION OF FUZZY BASED SOFT CLASSIFIERS FOR REMOTE SENSING
DATA
"Rakesh Dwivedi*" ,*Anil Kumar, S. K. Ghosh? , P. S. Roy?
"Indian Institute of Technology Roorkee, India
"Indian Institute of Remote Sensing, Dehradun, India
KEYWORDS: Fuzzy c-Mean (FCM), Possiblistic c-Mean (PCM), Noise clustering (NC), Sub pixel confusion uncertainty
matrix (SCM)
ABSTRACT:
Classification of satellite images are complex process and accuracy of the output is dependent on classifier parameters. This paper
examines the effect of various parameters like weighted exponent *m' for FCM , PCM classifiers and weighted exponent *m' as well
as fixed parameter *?' for NC without entropy based algorithm. The prime focus in this work is to select suitable parameters for
classification of remotely sensed data which improves the accuracy of classification output. The uncertainty criterion has been
estimated from sub-pixel confusion uncertainty matrix (SCM), based on classified and testing outputs. Therefore, these criterions are
dependent on the error of the results and sensitive to error variations. So it has also been tried to estimate entropy, based on outputs
generated by various classifiers like FCM, PCM and NC without entropy based classifier, hence this computed entropy is sensitive to
uncertainty variations. The AWIFS and LISS-III datasets are being used for classification and testing respectively. Soft classified
outputs from FCM, PCM and NC without entropy classifiers for AWiFS and LISS-III have been evaluated using SCM, overall
accuracy, fuzzy kappa coefficient and entropy. The SCM and fuzzy kappa coefficients are used to major relative accuracies, while
entropy is an absolute uncertainty indicator. From resultant aspect, while monitoring entropy of fraction images for different
regularizing parameter values, optimum regularizing parameter has been obtained for ‘m’=2.0 and (2=1, which gives highest
accuracy from sub-pixel confusion uncertainty matrix (SCM) i.e. 96.27% and AWiFS entropy has been 0.71 using noise clustering
without entropy based classifier.
1. INTRODUCTION
A traditional hard classification technique of satellite data does
not take into account gradual spatial variation in land cover
classes. To incorporate the gradual boundary change problem
researchers had proposed the ‘soft’ classification techniques
that decompose the pixel into class proportions (Fisher, 1997).
Fuzzy classification is a soft classification technique (Binaghi
and Rampini 1993), which deals with vagueness in class
definition (Foody et al. 1996). Therefore it can model the
gradual spatial transition between land cover classes. Fuzzy c-
Means (FCM) (Bezdek, et al, 1980; Ehrlich et al, 1984.,
Bezdek et al, 1987) is an unsupervised clustering algorithm
which has been widely used to find fuzzy membership grades
between 0 and 1. The aim of FCM is to find cluster centres in
the feature space such that it minimizes the intra-class variation
and maximizes the inter-class distances using an objective
function. Standard FCM algorithm considers the spectral
characteristics. Fuzzy c-Means supervised classification
algorithm has been widely used to classify satellite images with
ambiguous land cover classes. It is a popular fuzzy set theory
based soft classifier, which handles the vagueness of a pixel at
sub-pixel level. FCM has been successful in assigning the
membership (uj) of a pixel to multiple classes but this
assignment is relative to total number of classes defined and not
absolute (Krishnapuram and Keller, 1993, Foody 2000). This is
due to the constraint imposed on the membership values as
given by the Eq. (1)
Yu-h foralli (1)
The main motivation behind Possibilistic c-Means (PCM)
relates to the relaxaction of the constraint on membership value
in (1) and gives absolute membership value, as stated by Eq. (2)
max, u, >0 forall j (2)
In case of PCM, this membership value represents the “degree
of belongingness or compatibility or typicality", contrary to that
represented by FCM, where it is, “degree of sharing”. An
important aspect in classification is the presence of noise, which
: Corresponding author.
may have been introduced at any stage of data collection and
transmission. This affects the performance of any classification
algorithm. Literature reveals that a good solution to this
problem does not exist. An ideal solution would be one where
the noise points get automatically identified and removed from
the data. A concept of "Noise Cluster" can be introduced such
that noisy data points may be assigned to the noise class. The
approach is developed for an objective functional type (K-
means or fuzzy K-means) algorithm, and its ability to detect
'good' clusters amongst noisy data has been aptly demonstrated
by (Dave, 1991). The approach is applicable to both fuzzy
supervised classification algorithms as well as regression based
methods. In supervised classification, validity plays a pivotal
role in achieving a robust classification because without the
concept of validity, it is neither possible to separate the good
points from the noise points and outliers nor access the quality
of the solution. The solution to the robust clustering problem
requires that the algorithm reject noise data before it computes
the parameter estimates (Dave and Krishnapuram, 1997).
The purpose of study of noise clustering without entropy is not
only to establish a connection between fuzzy set theory and
robust statistics, but also to discuss and compare several
popular clustering methods from the point of view of robustness
(Dave, 1990; Foody et al. 1995). The aim of this paper is to
study the behaviour of associated parameters of FCM, PCM
and noise clustering without entropy with respect to fuzzy
accuracy assessment parameters and entropy as uncertainty
indicator. In the next section, the details of parameters
considered in FCM, PCM and noise clustering without entropy
are provided.
2. CLASSIFIERS AND ACCURACY ASSESSMENT
APPROACHES
2.1 Fuzzy c-Means Approach (FCM)
Fuzzy c-Means (FCM) was originally introduced by Bezdek
(1981). In this supervised classification technique each data
mS NN A.
