Data Classification with Modified Density Weighted Distance Measure for Diffusion Maps


Clinical data analysis is of fundamental importance, as classifications and detailed characterizations of diseases help physicians decide suitable management for patients, individually. In our study, we adopt diffusion maps to embed the data into corresponding lower dimensional representation, which integrate the information of potentially nonlinear progressions of the diseases. To deal with nonuniformaity of the data, we also consider an alternative distance measure based on the estimated local density. Performance of this modification is assessed using artificially generated data. Another clinical dataset that comprises metabolite concentrations measured with magnetic resonance spectroscopy was also classified. The algorithm shows improved results compared with conventional Euclidean distance measure.

Share and Cite:

Chen, K. , Hung, C. , Soong, B. , Wu, H. , Wu, Y. and Wang, P. (2014) Data Classification with Modified Density Weighted Distance Measure for Diffusion Maps. Journal of Biosciences and Medicines, 2, 12-18. doi: 10.4236/jbm.2014.24003.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Coifman, R.R. and Lafon, S. (2006) Diffusion Maps. Applied and Computational Harmonic Analysis, 21, 5-30.
[2] Singer, A. and Coifman, R.R. (2008) Non-Linear Independent Component Analysis with Diffusion Maps. Applied and Computational Harmonic Analysis, 25, 226-239.
[3] Lafon, S., Keller, Y. and Coifman, R.R. (2006) Data Fusion and Multicue Data Matching by Diffusion Maps. IEEE Transactions on Pattern Analysis and Machine Intelligence, 28, 1784-1797.
[4] Nadler, B., Lafon, S., Coifman, R.R. and Kevrekidis, I.G. (2005) Diffusion Maps, Spectral Clustering and Eigenfunctions of Fokker-Plank Operators. Neural Information Process. System 18, MIT Press, 955-962.
[5] Singer, A., Shkolnisky, Y. and Nadler, B. (2009) Diffusion Interpretation of Nonlocal Neighborhood Filters for Signal Denosing. SIAM Journal Imaging Science, 2, 118-139.
[6] Silverman, B.W. (1986) Density Estimation for Statistics and Data Analysis. Monographs on Statistics and Applied Probability, Vol. 26, Chapman and Hall, London.
[7] Etyngier, P., S’egonne and Kwriven, R. (2007) Shape Prior Using Manifold Learning Techniques. Proceedings of the IEEE International Conference on Computer Vision, 15, 132-141.
[8] Chandola, V., Banerjee, A. and Kumar, V. (2009) Anomaly Detection: A Survey. ACM Computing Surveys, 41, 1-58.
[9] Liring, J.F., Wang, P.S., Chen, H.C., Soong, B.W. and Guo, W.Y. Differences between Spinocerebellar Ataxias and Multiple System Atrophy-Cerebellar Type on Proton Magnetic Resonance Spectroscopy. PLoS ONE, 7, e47925.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.