Alternating diffusion for common manifold learning with application to sleep stage assessment

In this paper, we address the problem of multimodal signal processing and present a manifold learning method to extract the common source of variability from multiple measurements. This method is based on alternating-diffusion and is particularly adapted to time series. We show that the common source of variability is extracted from multiple sensors as if it were the only source of variability, extracted by a standard manifold learning method from a single sensor, without the influence of the sensor-specific variables. In addition, we present application to sleep stage assessment. We demonstrate that, indeed, through alternating-diffusion, the sleep information hidden inside multimodal respiratory signals can be better captured compared to single-modal methods.

[1]  Anna M. Bianchi,et al.  Sleep-wake detection based on respiratory signal acquired through a Pressure Bed Sensor , 2012, 2012 Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[2]  H. Hotelling.  Relations Between Two Sets of Variates , 1936 .

[3]  Hau-tieng Wu,et al.  Nonparametric and adaptive modeling of dynamic seasonality and trend with heteroscedastic and dependent errors , 2012, 1210.4672.

[4]  Yong Gyu Lim,et al.  REM Sleep Classification with Respiration Rates , 2007, 2007 6th International Special Topic Conference on Information Technology Applications in Biomedicine.

[5]  A. Chesson,et al.  The AASM Manual for the Scoring of Sleep and Associated Events: Rules, Terminology, and Techinical Specifications , 2007 .

[6]  Teofilo Lee-Chiong.  Sleep Medicine: Essentials and Review , 2008 .

[7]  Manohar Das,et al.  A simple sleep stage identification technique for incorporation in inexpensive electronic sleep screening devices , 2011, Proceedings of the 2011 IEEE National Aerospace and Electronics Conference (NAECON).

[8]  Joshua M. Lewis,et al.  Multi-view kernel construction , 2010, Machine Learning.

[9]  A. Chesson,et al.  The American Academy of Sleep Medicine (AASM) Manual for the Scoring of Sleep and Associated Events: Rules, Terminology and Technical Specifications , 2007 .

[10]  Roy R. Lederman,et al.  Common Manifold Learning Using Alternating-Diffusion , 2015 .

[11]  Stéphane Mallat,et al.  Manifold Learning for Latent Variable Inference in Dynamical Systems , 2015, IEEE Transactions on Signal Processing.

[12]  Bo Wang,et al.  Unsupervised metric fusion by cross diffusion , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.

[13]  Noureddine El Karoui,et al.  Connection graph Laplacian methods can be made robust to noise , 2014, 1405.6231.

[14]  S T Roweis,et al.  Nonlinear dimensionality reduction by locally linear embedding. , 2000, Science.

[15]  Christopher J. C. Burges,et al.  Spectral clustering and transductive learning with multiple views , 2007, ICML '07.

[16]  Byron Boots,et al.  Two Manifold Problems with Applications to Nonlinear System Identification , 2012, ICML.

[17]  R. Coifman,et al.  Non-linear independent component analysis with diffusion maps , 2008 .

[18]  Yung-Yu Chuang,et al.  Affinity aggregation for spectral clustering , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.

[19]  Hau-Tieng Wu,et al.  Assess Sleep Stage by Modern Signal Processing Techniques , 2014, IEEE Transactions on Biomedical Engineering.

[20]  A. Rechtschaffen.  A manual of standardized terminology, techniques and scoring system for sleep of human subjects , 1968 .

[21]  Michael E. Tipping,et al.  Probabilistic Principal Component Analysis , 1999 .

[22]  Stéphane Lafon,et al.  Diffusion maps , 2006 .

[23]  Hau-Tieng Wu,et al.  Non‐parametric and adaptive modelling of dynamic periodicity and trend with heteroscedastic and dependent errors , 2014 .

[24]  E. Wolpert.  A Manual of Standardized Terminology, Techniques and Scoring System for Sleep Stages of Human Subjects. , 1969 .

[25]  Stéphane Mallat,et al.  Group Invariant Scattering , 2011, ArXiv.

[26]  Ronald R. Coifman,et al.  Intrinsic modeling of stochastic dynamical systems using empirical geometry , 2015 .

[27]  Ann B. Lee,et al.  Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[28]  Mikhail Belkin,et al.  Laplacian Eigenmaps for Dimensionality Reduction and Data Representation , 2003, Neural Computation.

[29]  D. Donoho,et al.  Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[30]  Hau-tieng Wu,et al.  Instantaneous frequency and wave shape functions (I) , 2011, 1104.2365.

[31]  D. Donoho,et al.  Hessian Eigenmaps : new locally linear embedding techniques for high-dimensional data , 2003 .

[32]  Ronen Talmon,et al.  Empirical intrinsic geometry for nonlinear modeling and time series filtering , 2013, Proceedings of the National Academy of Sciences.

[33]  Ronald R. Coifman,et al.  Audio-Visual Group Recognition Using Diffusion Maps , 2010, IEEE Transactions on Signal Processing.

[34]  A. Rechtschaffen,et al.  A manual of standardized terminology, technique and scoring system for sleep stages of human subjects , 1968 .

[35]  J. Tenenbaum,et al.  A global geometric framework for nonlinear dimensionality reduction. , 2000, Science.

[36]  Colin Fyfe,et al.  Kernel and Nonlinear Canonical Correlation Analysis , 2000, IJCNN.