Modeling Cognitive Trends in Preclinical Alzheimer’s Disease (AD) via Distributions over Permutations

  • Gregory PlumbEmail author
  • Lindsay Clark
  • Sterling C. Johnson
  • Vikas Singh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10435)


This paper presents an algorithm to identify subsets of subjects who share similarities in the context of imaging and clinical measurements within a cohort of cognitively healthy individuals at risk for Alzheimer’s disease (AD). In particular, we wish to evaluate how patterns in the subjects’ cognitive scores or PIB-PET image measurements are associated with a clinical assessment of risk of developing AD, image based measures, and future cognitive decline. The challenge here is that all the participants are asymptomatic, our predictors are noisy and heterogeneous, and the disease specific signal, when present, is weak. As a result, off-the-shelf methods do not work well. We develop a model that uses a probability distribution over the set of permutations to represent the data; this yields a distance measure robust to these issues. We then show that our algorithm produces consistent and meaningful groupings of subjects based on their cognitive scores and that it provides a novel and interesting representation of measurements from PIB-PET images.


  1. 1.
    Backman, L., Jones, S., Berger, A.K., et al.: Cognitive impairment in preclinical Alzheimer’s disease: a meta-analysis. Neuropsychology 19(4), 520–531 (2005)CrossRefGoogle Scholar
  2. 2.
    Blacker, D., Lee, H., Muzikansky, A., et al.: Neuropsychological measures in normal individuals that predict subsequent cognitive decline. Arch. Neurol. 64(6), 862–871 (2007)CrossRefGoogle Scholar
  3. 3.
    Clark, L.R., Racine, A.M., Koscik, R.L., et al.: Beta-amyloid and cognitive decline in late middle age: findings from the Wisconsin registry for Alzheimer’s prevention study. Alzheimers Dement. 12, 805–814 (2016)CrossRefGoogle Scholar
  4. 4.
    Clark, L.R., Schiehser, D.M., Weissberger, G.H., et al.: Specific measures of executive function predict cognitive decline in older adults. J. Int. Neuropsychol. Soc. 18(1), 118–127 (2012)CrossRefGoogle Scholar
  5. 5.
    Clausen, M.: Fast generalized fourier transforms. Theor. Comput. Sci. 67(1), 55–63 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Jack, C.R., Knopman, D.S., Jagust, W.J., et al.: Tracking pathophysiological processes in Alzheimer’s disease: an updated hypothetical model of dynamic biomarkers. Lancet Neurol. 12(2), 207–216 (2013)CrossRefGoogle Scholar
  7. 7.
    Kondor, R.: Group theoretical methods in machine learning. Ph.D. thesis, Columbia University (2008)Google Scholar
  8. 8.
    Kondor, R., Howard, A., Jebara, T.: Multi-object tracking with representations of the symmetric group. In: AISTATS (2007)Google Scholar
  9. 9.
    Ng, A.Y., Jordan, M.I., Weiss, Y.: On spectral clustering: analysis and an algorithm. In: NIPS, pp. 849–856 (2002)Google Scholar
  10. 10.
    Plumb, G., Pachauri, D., Kondor, R., Singh, V.: \(\mathbb{S}_n\)FFT: a Julia toolkit for fourier analysis of functions over permutations. J. Mach. Learn. Res. 16, 3469–3473 (2015)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Sperling, R.A., Aisen, P.S., Beckett, L.A., et al.: Toward defining the preclinical stages of Alzheimer’s disease: recommendations from the National Institute on Aging-Alzheimer’s association workgroups on diagnostic guidelines for Alzheimer’s disease. Alzheimers Dement. 7(3), 280–292 (2011)CrossRefGoogle Scholar
  12. 12.
    Young, A.L., Oxtoby, N.P., Huang, J., et al.: Multiple orderings of events in disease progression. Inf. Process. Med. Imaging 24, 711–722 (2015)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Gregory Plumb
    • 1
    Email author
  • Lindsay Clark
    • 1
    • 2
  • Sterling C. Johnson
    • 1
    • 2
  • Vikas Singh
    • 1
  1. 1.University of Wisconsin–MadisonMadisonUSA
  2. 2.William S. Middleton Memorial Veterans HospitalMadisonUSA

Personalised recommendations