Dimensionality Reduction for Classification of Stochastic Texture Images

  • C. T. J. DodsonEmail author
  • W. W. Sampson
Part of the Signals and Communication Technology book series (SCT)


Stochastic textures yield images representing density variations of differing degrees of spatial disorder, ranging from mixtures of Poisson point processes to macrostructures of distributed finite objects. They arise in areas such as signal processing, molecular biology, cosmology, agricultural spatial distributions, oceanography, meteorology, tomography, radiography and medicine. The new contribution here is to couple information geometry with multidimensional scaling, also called dimensionality reduction, to identify small numbers of prominent features concerning density fluctuation and clustering in stochastic texture images, for classification of groupings in large datasets. Familiar examples of materials with such textures in one dimension are cotton yarns, audio noise and genomes, and in two dimensions paper and nonwoven fibre networks for which radiographic images are used to assess local variability and intensity of fibre clustering. Information geometry of trivariate Gaussian spatial distributions of mean pixel density with the mean densities of its first and second neighbours illustrate features related to sizes and density of clusters in stochastic texture images. We derive also analytic results for the case of stochastic textures arising from Poisson processes of line segments on a line and rectangles in a plane. Comparing human and yeast genomes, we use 12-variate spatial covariances to capture possible differences relating to secondary structure. For each of our types of stochastic textures: analytic, simulated, and experimental, we obtain dimensionality reduction and hence 3D embeddings of sets of samples to illustrate the various features that are revealed, such as mean density, size and shape of distributed objects, and clustering effects.


Dimensionality reduction Stochastic texture Density array Clustering Spatial covariance Trivariate Gaussian Radiographic images Genome Simulations Poisson process 


  1. 1.
    Arwini, K., Dodson, C.T.J.: Information geometry near randomness and near independence. In: Sampson, W.W. (eds.) Stochasic Fibre Networks (Chapter 9), pp. 161–194. Lecture Notes in Mathematics, Springer-Verlag, New York, Berlin (2008)Google Scholar
  2. 2.
    Atkinson, C., Mitchell, A.F.S.: Rao’s distance measure. Sankhya: Indian J. Stat. Ser. A 48(3), 345–365 (1981)Google Scholar
  3. 3.
    Cai, Y., Dodson, C.T.J .Wolkenhauer, O. Doig, A.J.: Gamma distribution analysis of protein sequences shows that amino acids self cluster. J. Theor. Biol. 218(4), 409–418 (2002)Google Scholar
  4. 4.
    Carter, K.M., Raich, R., Hero, A.O.:. Learning on statistical manifolds for clustering and visualization. In 45th Allerton Conference on Communication, Control, and Computing, Monticello, Illinois. (2007).
  5. 5.
    Carter, K.M.: Dimensionality reduction on statistical manifolds. Ph.D. thesis, University of Michigan (2009).
  6. 6.
    Deng, M., Dodson, C.T.J.: Paper: An Engineered Stochastic Structure. Tappi Press, Atlanta (1994)Google Scholar
  7. 7.
    Dodson, C.T.J.: Spatial variability and the theory of sampling in random fibrous networks. J. Roy. Statist. Soc. B 33(1), 88–94 (1971)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Dodson, C.T.J.: A geometrical representation for departures from randomness of the inter-galactic void probablity function. In: Workshop on Statistics of Cosmological Data Sets NATO-ASI Isaac Newton Institute, 8–13 August 1999.
  9. 9.
    Dodson, C.T.J., Ng, W.K., Singh, R.R.: Paper: stochastic structure analysis archive. Pulp and Paper Centre, University of Toronto (1995) (3 CDs)Google Scholar
  10. 10.
    Dodson, C.T.J., Sampson, W.W.: In Advances in Pulp and Paper Research, Oxford 2009. In: I’Anson, S.J., (ed.) Transactions of the XIVth Fundamental Research Symposium, pp. 665–691. FRC, Manchester (2009)Google Scholar
  11. 11.
    Dodson, C.T.J., Sampson, W.W.: Dimensionality reduction for classification of stochastic fibre radiographs. In Proceedings of GSI2013—Geometric Science of Information, Paris, 28–30: Lecture Notes in Computer Science 8085. Springer-Verlag, Berlin (August 2013)Google Scholar
  12. 12.
    Doroshkevich, A.G., Tucker, D.L., Oemler, A., Kirshner, R.P., Lin, H., Shectman, S.A., Landy, S.D., Fong, R.: Large- and superlarge-scale structure in the las campanas redshift survey. Mon. Not. R. Astr. Soc. 283(4), 1281–1310 (1996)CrossRefGoogle Scholar
  13. 13.
    Ghosh, B.: Random distances within a rectangle and between two rectangles. Calcutta Math. Soc. 43(1), 17–24 (1951)zbMATHGoogle Scholar
  14. 14.
    Mardia, K.V., Kent, J.T., Bibby, J.M.: Multivariate Analysis. Academic Press, London (1980)Google Scholar
  15. 15.
    NCBI Genbank of The National Center for Biotechnology Information. Samples from CCDS\_protein. 20130430.faa.gz.
  16. 16.
    Nielsen, F., Garcia, V., Nock, R.: Simplifying Gaussian mixture models via entropic quantization. In: Proceedings of 17th European Signal Processing Conference, Glasgow, Scotland 24–28 August 2009, pp. 2012–2016Google Scholar
  17. 17.
    Sampson, W.W.: Modelling Stochastic Fibre Materials with Mathematica. Springer-Verlag, Berlin, New York (2009)Google Scholar
  18. 18.
    Sampson, W.W.: Spatial variability of void structure in thin stochastic fibrous materials. Mod. Sim. Mater. Sci. Eng. 20:015008 pp13 (2012). doi: 10.1088/0965-0393/20/1/015008
  19. 19.
    Saccharomyces Cerevisiae Yeast Genome Database.

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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.School of MathematicsUniversity of ManchesterManchesterUK
  2. 2.School of MaterialsUniversity of ManchesterManchesterUK

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