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Lederman, Roy R; Talmon, Ronen
Learning the geometry of common latent variables using alternating-diffusion Journal Article
In: Applied and Computational Harmonic Analysis, vol. 44, no. 3, pp. 509–536, 2018, ISSN: 1063-5203.
Abstract | Links | BibTeX | Tags: Algorithms, Alternating Diffusion, Alternating-diffusion, Common variable, diffusion maps, Diffusion-maps, Multi-view, multimodal, Multimodal analysis
@article{lederman_learning_2018,
title = {Learning the geometry of common latent variables using alternating-diffusion},
author = {Roy R Lederman and Ronen Talmon},
url = {http://www.sciencedirect.com/science/article/pii/S1063520315001190},
doi = {10.1016/j.acha.2015.09.002},
issn = {1063-5203},
year = {2018},
date = {2018-01-01},
urldate = {2020-08-13},
journal = {Applied and Computational Harmonic Analysis},
volume = {44},
number = {3},
pages = {509--536},
abstract = {One of the challenges in data analysis is to distinguish between different sources of variability manifested in data. In this paper, we consider the case of multiple sensors measuring the same physical phenomenon, such that the properties of the physical phenomenon are manifested as a hidden common source of variability (which we would like to extract), while each sensor has its own sensor-specific effects (hidden variables which we would like to suppress); the relations between the measurements and the hidden variables are unknown. We present a data-driven method based on alternating products of diffusion operators and show that it extracts the common source of variability. Moreover, we show that it extracts the common source of variability in a multi-sensor experiment as if it were a standard manifold learning algorithm used to analyze a simple single-sensor experiment, in which the common source of variability is the only source of variability.},
keywords = {Algorithms, Alternating Diffusion, Alternating-diffusion, Common variable, diffusion maps, Diffusion-maps, Multi-view, multimodal, Multimodal analysis},
pubstate = {published},
tppubtype = {article}
}
One of the challenges in data analysis is to distinguish between different sources of variability manifested in data. In this paper, we consider the case of multiple sensors measuring the same physical phenomenon, such that the properties of the physical phenomenon are manifested as a hidden common source of variability (which we would like to extract), while each sensor has its own sensor-specific effects (hidden variables which we would like to suppress); the relations between the measurements and the hidden variables are unknown. We present a data-driven method based on alternating products of diffusion operators and show that it extracts the common source of variability. Moreover, we show that it extracts the common source of variability in a multi-sensor experiment as if it were a standard manifold learning algorithm used to analyze a simple single-sensor experiment, in which the common source of variability is the only source of variability.