Pattern Analysis and Applications

, Volume 19, Issue 3, pp 631–645 | Cite as

SWGMM: a semi-wrapped Gaussian mixture model for clustering of circular–linear data

  • Anandarup RoyEmail author
  • Swapan K. Parui
  • Utpal Roy
Theoretical Advances


Finite mixture models are widely used to perform model-based clustering of multivariate data sets. Most of the existing mixture models work with linear data; whereas, real-life applications may involve multivariate data having both circular and linear characteristics. No existing mixture models can accommodate such correlated circular–linear data. In this paper, we consider designing a mixture model for multivariate data having one circular variable. In order to construct a circular–linear joint distribution with proper inclusion of correlation terms, we use the semi-wrapped Gaussian distribution. Further, we construct a mixture model (termed SWGMM) of such joint distributions. This mixture model is capable of approximating the distribution of multi-modal circular–linear data. An unsupervised learning of the mixture parameters is proposed based on expectation maximization method. Clustering is performed using maximum a posteriori criterion. To evaluate the performance of SWGMM, we choose the task of color image segmentation in LCH space. We present comprehensive results and compare SWGMM with existing methods. Our study reveals that the proposed mixture model outperforms the other methods in most cases.


Circular–linear joint distribution Semi-wrapped Gaussian distribution Statistical mixture model Clustering 


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Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.Computer Vision and Pattern Recognition UnitIndian Statistical InstituteKolkataIndia
  2. 2.Department of Computer and System SciencesVisva-Bharati UniversitySantiniketanIndia

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