Abstract
In this study we present the model-based clustering in order to overcome the problem of mixed pixels for satellite imagery. The mixed pixel problem is one of the major reasons that affect the classification accuracy in the classification of remotely sensed images. Mixed pixels are usually the prime reason for degrading the success in image classification and object recognition. A modified model-based clustering algorithm is developed by modifying membership function and compared with the traditional model-based clustering algorithm in terms of classification error and brier score. Results on classification of satellite images reveal that the suggestive algorithms are robust and effective.
REFERENCES
J. Banfield and A. E. Raftery, ‘‘Model-based Gaussian and non-Gaussian clustering,’’ Biometrics 49, 803–821 (1993).
J. Campbell, C. Fraley, D. Stanford, F. Murtagh, and A. E. Raftery, ‘‘Model-based methods for textile fault detection,’’ Int. J. Imaging Syst. Technol. 10, 339–346 (1999).
J. Campbell, C. Fraley, D. Stanford, F. Murtagh, and A. E. Raftery, ‘‘Linear flaw detection in woven textiles using model-based clustering,’’ Pattern Recogn. Lett. 18, 1539–1548 (1997).
A. Dasgupta and A. E. Raftery, ‘‘Detecting features in spatial point processes with clutter via model-based clustering,’’ J. Am. Stat. Assoc. 93, 294–302 (1998).
A. Dempster, N. Laird, and D. Rubin, ‘‘Maximum likelihood from incomplete data via the EM algorithm,’’ J. R. Stat. Soc., Ser. B 39, 1–38 (1977).
C. Fraley and A. E. Raftery, ‘‘How many clusters? Which clustering method? Answers via model based analysis,’’ Comput. J. 41, 578–588 (1998).
C. Fraley and A. E. Raftery, ‘‘MCLUST: Software for model-based cluster analysis,’’ J. Classific. 16, 297–306 (1999).
C. Fraley and A. E. Raftery, ‘‘Model-based clustering, discriminant analysis, and density estimation,’’ J. Am. Stat. Assoc. 97 (458), 611–631 (2002).
H. P. Friedman and J. Rubin, ‘‘On some invariant criteria for group ing data,’’ J. Am. Stat. Assoc. 62, 1159–1178 (1967).
T. Hastie and R. Tibshirani, ‘‘Discriminant analysis by Gaussian mixtures,’’ J. R. Stat. Soc., Ser. B 58, 155–176 (1996).
A. K. Jain and R. C. Dubes, Algorithms for Clustering Data (Prentice Hall, New Jersey, 1988).
R. A. Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis, 6th ed. (Pearson Prentice Hall, Upper Saddle River, NJ, 2007).
L. Kaufman and P. Rousseeuw, Finding Groups in Data – An Introduction to Cluster Analysis (Wiley, New York, 1989).
G. J. McLachlan, Discriminant Analysis and Statistical Pattern Recognition (Wiley, New York, 1992).
G. J. Mclachlan and K. E. Basford, Mixture Models: Inference and Applications to Clustering (Marcel Dekker, New York, 1988).
G. J. Mclachlan and T. Krishnan, The EM Algorithm and Extensions (Wiley, New York, 1997).
G. J. Mclachlan, S. Ng, G. Galloway, and D. Wang, ‘‘Clustering of magnetic resonance images,’’ in Proceedings of the American Statistical Association, Statistical Computing Section, Alexandria, Virginia (1996), pp. 12–17.
G. J. Mclachlan and D. Peel, Finite Mixture Models (Wiley, New York, 2000).
G. J. Mclachlan, D. Peel, K. Basford, and P. Adams, ‘‘The EMMIX software for the fitting of mixtures of normal and T-components,’’ J. Stat. Software 4 (2), 1–14 (1999)
P. D. McNicholas and T. B. Murphy, ‘‘Model-based clustering of microarray expression data via latent Gaussian mixture models,’’ Bioinformatics 26, 2705–2712 (2010).
S. Mukherjee, E. Feigelson, G. Babu, F. Murtagh, C. Fraley, and A. E. Raftery, ‘‘Three types of gamma ray bursts,’’ Astrophys. J. 508, 314–327 (1998).
A. J. Scott and M. J. Symons, ‘‘Clustering methods based on like lihood ratio criteria,’’ Biometrics 27, 387–397 (1971).
D. Stanford and A. E. Raftery, ‘‘Approximate Bayes factors for image segmentation: The Pseudo Likelihood Information Criterion (PLIC),’’ IEEE Trans. Pattern Anal. Machine Intell. 24, 1517–1520 (2002).
N. Wang and A. E. Raftery, ‘‘Nearest Neighbor Variance Estimation (NNVE): Robust covariance estimation via nearest neighbor cleaning (with discussion),’’ J. Am. Stat. Assoc. 97, 994–1019 (2002).
R. Wehrens, A. Simonetti, and L. M. C. Buydens, ‘‘Mixture modelling of medical magnetic resonance data,’’ J. Chemometrics 16, 1–10 (2002).
K. Yeung, C. Fraley, A. Murua, A. E. Raftery, and W. Ruzzo, ‘‘Model based clustering and data transformations for gene expression data,’’ Bioinformatics 17, 977–987 (2001).
Funding
The research of the last listed author was performed under the development program of Volga Region Mathematical Center (agreement no. 075-02-2023-944).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors of this work declare that they have no conflicts of interest.
Additional information
Publisher’s Note.
Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
(Submitted by A. M. Elizarov)
Rights and permissions
About this article
Cite this article
Sherwani, A.R., Ali, Q.M., Ali, I. et al. A Modified Mixture Model-Based Clustering Algorithm for Resolving the Problem of Mixed Pixels Available in Satellite Imagery. Lobachevskii J Math 44, 4824–4838 (2023). https://doi.org/10.1134/S199508022311029X
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S199508022311029X