Advertisement

Adaptive Signal Recovery on Graphs via Harmonic Analysis for Experimental Design in Neuroimaging

  • Won Hwa Kim
  • Seong Jae Hwang
  • Nagesh Adluru
  • Sterling C. Johnson
  • Vikas Singh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9910)

Abstract

Consider an experimental design of a neuroimaging study, where we need to obtain p measurements for each participant in a setting where \(p^\prime (< p)\) are cheaper and easier to acquire while the remaining \((p-p^\prime )\) are expensive. For example, the \(p^{\prime }\) measurements may include demographics, cognitive scores or routinely offered imaging scans while the \((p-p^{\prime })\) measurements may correspond to more expensive types of brain image scans with a higher participant burden. In this scenario, it seems reasonable to seek an “adaptive” design for data acquisition so as to minimize the cost of the study without compromising statistical power. We show how this problem can be solved via harmonic analysis of a band-limited graph whose vertices correspond to participants and our goal is to fully recover a multi-variate signal on the nodes, given the full set of cheaper features and a partial set of more expensive measurements. This is accomplished using an adaptive query strategy derived from probing the properties of the graph in the frequency space. To demonstrate the benefits that this framework can provide, we present experimental evaluations on two independent neuroimaging studies and show that our proposed method can reliably recover the true signal with only partial observations directly yielding substantial financial savings.

Keywords

Fractional Anisotropy Mother Wavelet Graph Vertex Full Cohort Matrix Completion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Supplementary material

419981_1_En_12_MOESM1_ESM.pdf (231 kb)
Supplementary material 1 (pdf 231 KB)

References

  1. 1.
    Blum, A.L., Langley, P.: Selection of relevant features and examples in machine learning. Artif. Intell. 97(1), 245–271 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Biswas, A., Parikh, D.: Simultaneous active learning of classifiers & attributes via relative feedback. In: CVPR, pp. 644–651 (2013)Google Scholar
  3. 3.
    Jayaraman, D., Grauman, K.: Zero-shot recognition with unreliable attributes. In: NIPS, pp. 3464–3472 (2014)Google Scholar
  4. 4.
    Lughofer, E.: Hybrid active learning for reducing the annotation effort of operators in classification systems. Pattern Recognit. 45(2), 884–896 (2012)CrossRefGoogle Scholar
  5. 5.
    Hancock, C., Bernal, B., Medina, C., et al.: Cost analysis of diffusion tensor imaging and MR tractography of the brain. Open J. Radiol. 2014 (2014)Google Scholar
  6. 6.
    Saif, M.W., Tzannou, I., Makrilia, N., et al.: Role and cost effectiveness of PET/CT in management of patients with cancer. Yale J. Biol. Med. 83(2), 53–65 (2010)Google Scholar
  7. 7.
    Prasad, A., Jegelka, S., Batra, D.: Submodular meets structured: finding diverse subsets in exponentially-large structured item sets. In: NIPS, pp. 2645–2653 (2014)Google Scholar
  8. 8.
    Deng, J., Dong, W., Socher, R., et al.: Imagenet: a large-scale hierarchical image database. In: CVPR, pp. 248–255 (2009)Google Scholar
  9. 9.
    Vijayanarasimhan, S., Grauman, K.: Large-scale live active learning: training object detectors with crawled data and crowds. IJCV 108(1–2), 97–114 (2014)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Deng, J., Russakovsky, O., Krause, J., et al.: Scalable multi-label annotation. In: SIGCHI, pp. 3099–3102. ACM (2014)Google Scholar
  11. 11.
    Bragg, J., Weld, D.S., et al.: Crowdsourcing multi-label classification for taxonomy creation. In: AAAI (2013)Google Scholar
  12. 12.
    Read, J., Bifet, A., Holmes, G., et al.: Scalable and efficient multi-label classification for evolving data streams. Mach. Learn. 88(1–2), 243–272 (2012)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Settles, B.: Active learning literature survey. University of Wisconsin, Madison vol. 52(55–66), p. 11 (2010)Google Scholar
  14. 14.
    Dasgupta, S.: Analysis of a greedy active learning strategy. In: NIPS, pp. 337–344 (2004)Google Scholar
  15. 15.
    Beygelzimer, A., Dasgupta, S., Langford, J.: Importance weighted active learning. In: ICML, pp. 49–56. ACM (2009)Google Scholar
  16. 16.
    Dasgupta, S., Hsu, D.: Hierarchical sampling for active learning. In: ICML, pp. 208–215. ACM (2008)Google Scholar
  17. 17.
    Winer, B.J., Brown, D.R., Michels, K.M.: Statistical Principles in Experimental Design. McGraw-Hill, New York (1971)Google Scholar
  18. 18.
    Lentner, M.: Generalized least-squares estimation of a subvector of parameters in randomized fractional factorial experiments. Ann. Math. Stat. 40, 1344–1352 (1969)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Myers, J.L.: Fundamentals of Experimental Design. Allyn & Bacon, Boston (1972)Google Scholar
  20. 20.
    Mitchell, T.J.: An algorithm for the construction of D-optimal experimental designs. Technometrics 16(2), 203–210 (1974)MathSciNetzbMATHGoogle Scholar
  21. 21.
    De Aguiar, P.F., Bourguignon, B., Khots, M., et al.: D-optimal designs. Chemometr. Intell. Lab. Syst. 30(2), 199–210 (1995)CrossRefGoogle Scholar
  22. 22.
    Park, J.S.: Optimal Latin-hypercube designs for computer experiments. J. Stat. Plann. Infer. 39(1), 95–111 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Su, X., Khoshgoftaar, T.M.: A survey of collaborative filtering techniques. Adv. Artif. Intell. 2009, 4: 2 (2009)CrossRefGoogle Scholar
  24. 24.
    Dabov, K., Foi, A., Katkovnik, V., et al.: Image denoising by sparse 3-D transform-domain collaborative filtering. Image Process. 16(8), 2080–2095 (2007)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Yu, K., Zhu, S., Lafferty, J., et al.: Fast nonparametric matrix factorization for large-scale collaborative filtering. In: SIGIR, pp. 211–218. ACM (2009)Google Scholar
  26. 26.
    Srebro, N., Salakhutdinov, R.R.: Collaborative filtering in a non-uniform world: learning with the weighted trace norm. In: NIPS, pp. 2056–2064 (2010)Google Scholar
  27. 27.
    Juditsky, A., Nemirovski, A.: On verifiable sufficient conditions for sparse signal recovery via \(\ell \)1 minimization. Math. Program. 127(1), 57–88 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Krahmer, F., Ward, R.: Stable and robust sampling strategies for compressive imaging. Image Process. 23(2), 612–622 (2014)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Rao, N., Yu, H.F., Ravikumar, P.K., et al.: Collaborative filtering with graph information: consistency and scalable methods. In: NIPS (2015)Google Scholar
  30. 30.
    Puy, G., Tremblay, N., Gribonval, R., et al.: Random sampling of bandlimited signals on graphs. Appl. Comput. Harmonic Anal. (2016)Google Scholar
  31. 31.
    Kumar, S., Mohri, M., Talwalkar, A.: Sampling methods for the Nyström method. JMLR 13(1), 981–1006 (2012)MathSciNetzbMATHGoogle Scholar
  32. 32.
    Krishnamurthy, A., Singh, A.: Low-rank matrix and tensor completion via adaptive sampling. In: NIPS, pp. 836–844 (2013)Google Scholar
  33. 33.
    Hammond, D., Vandergheynst, P., Gribonval, R.: Wavelets on graphs via spectral graph theory. Appl. Comput. Harmonic Anal. 30(2), 129–150 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Mallat, S.: A Wavelet Tour of Signal Processing. Academic press, San Diego (1999)zbMATHGoogle Scholar
  35. 35.
    Coifman, R., Maggioni, M.: Diffusion wavelets. Appl. Comput. Harmonic Anal. 21(1), 53–94 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Haykin, S., Veen, B.V.: Signals and Systems. Wiley, New York (2005)zbMATHGoogle Scholar
  37. 37.
    Bronstein, M.M., Kokkinos, I.: Scale-invariant heat kernel signatures for non-rigid shape recognition. In: CVPR, pp. 1704–1711. IEEE (2010)Google Scholar
  38. 38.
    Aubry, M., Schlickewei, U., Cremers, D.: The wave kernel signature: a quantum mechanical approach to shape analysis. In: ICCV Workshops, pp. 1626–1633. IEEE (2011)Google Scholar
  39. 39.
    Rustamov, R.M.: Laplace-Beltrami eigen functions for deformation invariant shape representation. In: Eurographics Symposium on Geometry Processing, Eurographics Association, pp. 225–233 (2007)Google Scholar
  40. 40.
    Kim, W.H., Chung, M.K., Singh, V.: Multi-resolution shape analysis via non-euclidean wavelets: applications to mesh segmentation and surface alignment problems. In: CVPR, pp. 2139–2146. IEEE (2013)Google Scholar
  41. 41.
    Varentsova, A., Zhang, S., Arfanakis, K.: Development of a high angular resolution diffusion imaging human brain template. Neuroimage 91, 177–186 (2014)CrossRefGoogle Scholar
  42. 42.
    Van Essen, D.C., Smith, S.M., Barch, D.M., et al.: The WU-Minn human connectome project: an overview. Neuroimage 80, 62–79 (2013)CrossRefGoogle Scholar
  43. 43.
    Setsompop, K., Cohen-Adad, J., Gagoski, B., et al.: Improving diffusion MRI using simultaneous multi-slice echo planar imaging. Neuroimage 63(1), 569–580 (2012)CrossRefGoogle Scholar
  44. 44.
    Jbabdi, S., Sotiropoulos, S.N., Haber, S.N., et al.: Measuring macroscopic brain connections in vivo. Nature Neurosci. 18(11), 1546–1555 (2015)CrossRefGoogle Scholar
  45. 45.
    Sporns, O., Tononi, G., Kötter, R.: The human connectome: a structural description of the human brain. PLoS Comput. Biol. 1(4), e42 (2005)CrossRefGoogle Scholar
  46. 46.
    Van Essen, D.C., Ugurbil, K.: The future of the human connectome. Neuroimage 62(2), 1299–1310 (2012)CrossRefGoogle Scholar
  47. 47.
    Toga, A.W., Clark, K.A., Thompson, P.M., et al.: Mapping the human connectome. Neurosurgery 71(1), 1 (2012)CrossRefGoogle Scholar
  48. 48.
    Sporns, O.: The human connectome: origins and challenges. Neuroimage 80, 53–61 (2013)CrossRefGoogle Scholar
  49. 49.
    Herrick, R., McKay, M., Olsen, T., et al.: Data dictionary services in XNAT and the human connectome project. Front. Neuroinform. 8, 65 (2014)CrossRefGoogle Scholar
  50. 50.
    Kim, W.H., Kim, H.J., Adluru, N., et al.: Latent variable graphical model selection using harmonic analysis: applications to the human connectome project (HCP). In: CVPR. IEEE (2016)Google Scholar
  51. 51.
    Brier, M.R., Thomas, J.B., Ances, B.M.: Network dysfunction in Alzheimer’s disease: refining the disconnection hypothesis. Brain connectivity 4(5), 299–311 (2014)CrossRefGoogle Scholar
  52. 52.
    Delbeuck, X., Van der Linden, M., Collette, F.: Alzheimer’s disease as a disconnection syndrome? Neuropsychol. Rev. 13(2), 79–92 (2003)CrossRefGoogle Scholar
  53. 53.
    Geschwind, N.: Disconnexion syndromes in animals and man. In: Geschwind, N. (ed.) Selected Papers on Language and the Brain. Boston Studies in the Philosophy of Science, vol. 16, pp. 105–236. Springer, Amsterdam (1974)CrossRefGoogle Scholar
  54. 54.
    Kim, W.H., Adluru, N., Chung, M.K., et al.: Multi-resolution statistical analysis of brain connectivity graphs in preclinical Alzheimer’s disease. Neuroimage 118, 103–117 (2015)CrossRefGoogle Scholar
  55. 55.
    Kim, W.H., Singh, V., Chung, M.K., et al.: Multi-resolutional shape features via non-Euclidean wavelets: applications to statistical analysis of cortical thickness. Neuroimage 93, 107–123 (2014)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Won Hwa Kim
    • 1
  • Seong Jae Hwang
    • 1
  • Nagesh Adluru
    • 4
  • Sterling C. Johnson
    • 3
  • Vikas Singh
    • 1
    • 2
  1. 1.Department of Computer SciencesUniversity of WisconsinMadisonUSA
  2. 2.Department of Biostatistics and Medical InformaticsUniversity of WisconsinMadisonUSA
  3. 3.GRECCWilliam S. Middleton VA HospitalMadisonUSA
  4. 4.Waisman CenterMadisonUSA

Personalised recommendations