Bandeira, Afonso S; Chen, Yutong; Lederman, Roy R; Singer, Amit Nonunique games over compact groups and orientation estimation in cryoEM Journal Article Inverse Problems, 36 (6), pp. 064002, 2020, ISSN: 02665611, 13616420. Links  BibTeX  Tags: Algorithms, cryoEM, Nonunique games, Representation Theory @article{bandeira_nonunique_2020,
title = {Nonunique games over compact groups and orientation estimation in cryoEM},
author = {Afonso S Bandeira and Yutong Chen and Roy R Lederman and Amit Singer},
url = {https://iopscience.iop.org/article/10.1088/13616420/ab7d2c},
doi = {10.1088/13616420/ab7d2c},
issn = {02665611, 13616420},
year = {2020},
date = {20200601},
urldate = {20200813},
journal = {Inverse Problems},
volume = {36},
number = {6},
pages = {064002},
keywords = {Algorithms, cryoEM, Nonunique games, Representation Theory},
pubstate = {published},
tppubtype = {article}
}

Lederman, Roy R; Andén, Joakim; Singer, Amit Hypermolecules: on the representation and recovery of dynamical structures for applications in flexible macromolecules in cryoEM Journal Article Inverse Problems, 36 (4), pp. 044005, 2020, ISSN: 02665611, 13616420. Links  BibTeX  Tags: cryoEM, HyperMolecules @article{lederman_hypermolecules_2020,
title = {Hypermolecules: on the representation and recovery of dynamical structures for applications in flexible macromolecules in cryoEM},
author = {Roy R Lederman and Joakim Andén and Amit Singer},
url = {https://iopscience.iop.org/article/10.1088/13616420/ab5ede},
doi = {10.1088/13616420/ab5ede},
issn = {02665611, 13616420},
year = {2020},
date = {20200401},
urldate = {20200813},
journal = {Inverse Problems},
volume = {36},
number = {4},
pages = {044005},
keywords = {cryoEM, HyperMolecules},
pubstate = {published},
tppubtype = {article}
}

Lederman, Roy R; Steinerberger, S Extreme Values of the Fiedler Vector on Trees Technical Report 2019, (arXiv: 1912.08327). Abstract  Links  BibTeX  Tags: Computer Science  Discrete Mathematics, Graph Theory, Mathematics  Combinatorics, Mathematics  Spectral Theory @techreport{lederman_extreme_2019,
title = {Extreme Values of the Fiedler Vector on Trees},
author = {Roy R Lederman and S Steinerberger},
url = {http://arxiv.org/abs/1912.08327},
year = {2019},
date = {20191201},
urldate = {20200813},
abstract = {Let $G$ be a connected tree on $n$ vertices and let $L = DA$ denote the Laplacian matrix on $G$. The secondsmallest eigenvalue $textbackslashlambda_2(G) textgreater 0$, also known as the algebraic connectivity, as well as the associated eigenvector $textbackslashphi_2$ have been of substantial interest. We investigate the question of when the maxima and minima of $textbackslashphi_2$ are assumed at the endpoints of the longest path in $G$. Our results also apply to more general graphs that `behave globally' like a tree but can exhibit more complicated local structure. The crucial new ingredient is a reproducing formula for the eigenvector $textbackslashphi_k$.},
note = {arXiv: 1912.08327},
keywords = {Computer Science  Discrete Mathematics, Graph Theory, Mathematics  Combinatorics, Mathematics  Spectral Theory},
pubstate = {published},
tppubtype = {techreport}
}
Let $G$ be a connected tree on $n$ vertices and let $L = DA$ denote the Laplacian matrix on $G$. The secondsmallest eigenvalue $textbackslashlambda_2(G) textgreater 0$, also known as the algebraic connectivity, as well as the associated eigenvector $textbackslashphi_2$ have been of substantial interest. We investigate the question of when the maxima and minima of $textbackslashphi_2$ are assumed at the endpoints of the longest path in $G$. Our results also apply to more general graphs that `behave globally' like a tree but can exhibit more complicated local structure. The crucial new ingredient is a reproducing formula for the eigenvector $textbackslashphi_k$. 
Lederman, Roy R; Singer, Amit A representation theory perspective on simultaneous alignment and classification Journal Article Applied and Computational Harmonic Analysis, pp. S1063520319301034, 2019, ISSN: 10635203. Links  BibTeX  Tags: Algorithms, cryoEM, Nonunique games, Representation Theory @article{lederman_representation_2019,
title = {A representation theory perspective on simultaneous alignment and classification},
author = {Roy R Lederman and Amit Singer},
url = {https://linkinghub.elsevier.com/retrieve/pii/S1063520319301034},
doi = {10.1016/j.acha.2019.05.005},
issn = {10635203},
year = {2019},
date = {20190101},
urldate = {20200813},
journal = {Applied and Computational Harmonic Analysis},
pages = {S1063520319301034},
keywords = {Algorithms, cryoEM, Nonunique games, Representation Theory},
pubstate = {published},
tppubtype = {article}
}

Shnitzer, Tal; Lederman, Roy R; Liu, GiRen; Talmon, Ronen; Wu, HauTieng Diffusion operators for multimodal data analysis Incollection Handbook of Numerical Analysis, 20 , pp. 1–39, Elsevier, 2019, ISBN: 9780444641403. Links  BibTeX  Tags: Alternating Diffusion, BookChapter, Common variable, diffusion maps, Manifold Learning, Multiview, multimodal, Multimodal data, Sensor fusion, Shape differences @incollection{shnitzer_diffusion_2019,
title = {Diffusion operators for multimodal data analysis},
author = {Tal Shnitzer and Roy R Lederman and GiRen Liu and Ronen Talmon and HauTieng Wu},
url = {https://linkinghub.elsevier.com/retrieve/pii/S1570865919300213},
doi = {10.1016/bs.hna.2019.07.008},
isbn = {9780444641403},
year = {2019},
date = {20190101},
urldate = {20200813},
booktitle = {Handbook of Numerical Analysis},
volume = {20},
pages = {139},
publisher = {Elsevier},
keywords = {Alternating Diffusion, BookChapter, Common variable, diffusion maps, Manifold Learning, Multiview, multimodal, Multimodal data, Sensor fusion, Shape differences},
pubstate = {published},
tppubtype = {incollection}
}

Lederman, Roy R; Talmon, Ronen Learning the geometry of common latent variables using alternatingdiffusion Journal Article Applied and Computational Harmonic Analysis, 44 (3), pp. 509–536, 2018, ISSN: 10635203. Abstract  Links  BibTeX  Tags: Algorithms, Alternating Diffusion, Alternatingdiffusion, Common variable, diffusion maps, Diffusionmaps, Multiview, multimodal, Multimodal analysis, test @article{lederman_learning_2018,
title = {Learning the geometry of common latent variables using alternatingdiffusion},
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 = {10635203},
year = {2018},
date = {20180101},
urldate = {20200813},
journal = {Applied and Computational Harmonic Analysis},
volume = {44},
number = {3},
pages = {509536},
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 sensorspecific effects (hidden variables which we would like to suppress); the relations between the measurements and the hidden variables are unknown. We present a datadriven 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 multisensor experiment as if it were a standard manifold learning algorithm used to analyze a simple singlesensor experiment, in which the common source of variability is the only source of variability.},
keywords = {Algorithms, Alternating Diffusion, Alternatingdiffusion, Common variable, diffusion maps, Diffusionmaps, Multiview, multimodal, Multimodal analysis, test},
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 sensorspecific effects (hidden variables which we would like to suppress); the relations between the measurements and the hidden variables are unknown. We present a datadriven 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 multisensor experiment as if it were a standard manifold learning algorithm used to analyze a simple singlesensor experiment, in which the common source of variability is the only source of variability. 
Shaham, Uri; Lederman, Roy R Learning by coincidence: Siamese networks and common variable learning Journal Article Pattern Recognition, 74 , pp. 52–63, 2018, ISSN: 00313203. Links  BibTeX  Tags: Common variable, Deep Learning, Multiview, multimodal, Siamese networks @article{shaham_learning_2018,
title = {Learning by coincidence: Siamese networks and common variable learning},
author = {Uri Shaham and Roy R Lederman},
url = {https://linkinghub.elsevier.com/retrieve/pii/S0031320317303588},
doi = {10.1016/j.patcog.2017.09.015},
issn = {00313203},
year = {2018},
date = {20180101},
urldate = {20200813},
journal = {Pattern Recognition},
volume = {74},
pages = {5263},
keywords = {Common variable, Deep Learning, Multiview, multimodal, Siamese networks},
pubstate = {published},
tppubtype = {article}
}

Aldroubi, Akram; Huang, Longxiu; Krishtal, Ilya; Ledeczi, Akos; Lederman, Roy R; Volgyesi, Peter Dynamical sampling with additive random noise Journal Article arXiv:1807.10866 [math], 2018, (arXiv: 1807.10866). Abstract  Links  BibTeX  Tags: Mathematics  Numerical Analysis @article{aldroubi_dynamical_2018,
title = {Dynamical sampling with additive random noise},
author = {Akram Aldroubi and Longxiu Huang and Ilya Krishtal and Akos Ledeczi and Roy R Lederman and Peter Volgyesi},
url = {http://arxiv.org/abs/1807.10866},
year = {2018},
date = {20180101},
urldate = {20200813},
journal = {arXiv:1807.10866 [math]},
abstract = {Dynamical sampling deals with signals that evolve in time under the action of a linear operator. The purpose of the present paper is to analyze the performance of the basic dynamical sampling algorithms in the finite dimensional case and study the impact of additive noise. The algorithms are implemented and tested on synthetic and real data sets, and denoising techniques are integrated to mitigate the effect of the noise. We also develop theoretical and numerical results that validate the algorithm for recovering the driving operators, which are defined via a real symmetric convolution.},
note = {arXiv: 1807.10866},
keywords = {Mathematics  Numerical Analysis},
pubstate = {published},
tppubtype = {article}
}
Dynamical sampling deals with signals that evolve in time under the action of a linear operator. The purpose of the present paper is to analyze the performance of the basic dynamical sampling algorithms in the finite dimensional case and study the impact of additive noise. The algorithms are implemented and tested on synthetic and real data sets, and denoising techniques are integrated to mitigate the effect of the noise. We also develop theoretical and numerical results that validate the algorithm for recovering the driving operators, which are defined via a real symmetric convolution. 
Lederman, Roy R Numerical Algorithms for the Computation of Generalized Prolate Spheroidal Functions Technical Report 2017. Abstract  Links  BibTeX  Tags: Algorithms, cryoEM, Fourier Transform, Numerical Analysis, Prolate, Slepian, Software @techreport{lederman_numerical_2017,
title = {Numerical Algorithms for the Computation of Generalized Prolate Spheroidal Functions},
author = {Roy R Lederman},
url = {https://arxiv.org/abs/1710.02874v1},
year = {2017},
date = {20171001},
urldate = {20200813},
abstract = {Generalized Prolate Spheroidal Functions (GPSF) are the eigenfunctions of the
truncated Fourier transform, restricted to Ddimensional balls in the spatial
domain and frequency domain. Despite their useful properties in many
applications, GPSFs are often replaced by crude approximations. The purpose of
this paper is to review the elements of computing GPSFs and associated
eigenvalues. This paper is accompanied by opensource code.},
keywords = {Algorithms, cryoEM, Fourier Transform, Numerical Analysis, Prolate, Slepian, Software},
pubstate = {published},
tppubtype = {techreport}
}
Generalized Prolate Spheroidal Functions (GPSF) are the eigenfunctions of the
truncated Fourier transform, restricted to Ddimensional balls in the spatial
domain and frequency domain. Despite their useful properties in many
applications, GPSFs are often replaced by crude approximations. The purpose of
this paper is to review the elements of computing GPSFs and associated
eigenvalues. This paper is accompanied by opensource code. 
Lederman, Roy R; Singer, Amit Continuously heterogeneous hyperobjects in cryoEM and 3Đ movies of many temporal dimensions Journal Article arXiv:1704.02899 [cs], 2017, (arXiv: 1704.02899). Abstract  Links  BibTeX  Tags: Computer Science  Computer Vision and Pattern Recognition, cryoEM, heterogeneity, HyperMolecules @article{lederman_continuously_2017,
title = {Continuously heterogeneous hyperobjects in cryoEM and 3Đ movies of many temporal dimensions},
author = {Roy R Lederman and Amit Singer},
url = {http://arxiv.org/abs/1704.02899},
year = {2017},
date = {20170401},
urldate = {20200813},
journal = {arXiv:1704.02899 [cs]},
abstract = {Single particle cryoelectron microscopy (EM) is an increasingly popular method for determining the 3D structure of macromolecules from noisy 2D images of single macromolecules whose orientations and positions are random and unknown. One of the great opportunities in cryoEM is to recover the structure of macromolecules in heterogeneous samples, where multiple types or multiple conformations are mixed together. Indeed, in recent years, many tools have been introduced for the analysis of multiple discrete classes of molecules mixed together in a cryoEM experiment. However, many interesting structures have a continuum of conformations which do not fit discrete models nicely; the analysis of such continuously heterogeneous models has remained a more elusive goal. In this manuscript, we propose to represent heterogeneous molecules and similar structures as higher dimensional objects. We generalize the basic operations used in many existing reconstruction algorithms, making our approach generic in the sense that, in principle, existing algorithms can be adapted to reconstruct those higher dimensional objects. As proof of concept, we present a prototype of a new algorithm which we use to solve simulated reconstruction problems.},
note = {arXiv: 1704.02899},
keywords = {Computer Science  Computer Vision and Pattern Recognition, cryoEM, heterogeneity, HyperMolecules},
pubstate = {published},
tppubtype = {article}
}
Single particle cryoelectron microscopy (EM) is an increasingly popular method for determining the 3D structure of macromolecules from noisy 2D images of single macromolecules whose orientations and positions are random and unknown. One of the great opportunities in cryoEM is to recover the structure of macromolecules in heterogeneous samples, where multiple types or multiple conformations are mixed together. Indeed, in recent years, many tools have been introduced for the analysis of multiple discrete classes of molecules mixed together in a cryoEM experiment. However, many interesting structures have a continuum of conformations which do not fit discrete models nicely; the analysis of such continuously heterogeneous models has remained a more elusive goal. In this manuscript, we propose to represent heterogeneous molecules and similar structures as higher dimensional objects. We generalize the basic operations used in many existing reconstruction algorithms, making our approach generic in the sense that, in principle, existing algorithms can be adapted to reconstruct those higher dimensional objects. As proof of concept, we present a prototype of a new algorithm which we use to solve simulated reconstruction problems. 
Lederman, Roy R; Steinerberger, Stefan Lower Bounds for Truncated Fourier and Laplace Transforms Journal Article Integral Equations and Operator Theory, 87 (4), pp. 529–543, 2017, ISSN: 0378620X, 14208989. Links  BibTeX  Tags: Fourier Transform, Laplace Transform @article{lederman_lower_2017,
title = {Lower Bounds for Truncated Fourier and Laplace Transforms},
author = {Roy R Lederman and Stefan Steinerberger},
url = {http://link.springer.com/10.1007/s000200172364z},
doi = {10.1007/s000200172364z},
issn = {0378620X, 14208989},
year = {2017},
date = {20170401},
urldate = {20200813},
journal = {Integral Equations and Operator Theory},
volume = {87},
number = {4},
pages = {529543},
keywords = {Fourier Transform, Laplace Transform},
pubstate = {published},
tppubtype = {article}
}

Stanton, Kelly P; Jin, Jiaqi; Lederman, Roy R; Weissman, Sherman M; Kluger, Yuval Ritornello: high fidelity controlfree chromatin immunoprecipitation peak calling Journal Article Nucleic Acids Research, 45 (21), pp. e173–e173, 2017, ISSN: 03051048, (Publisher: Oxford Academic). Abstract  Links  BibTeX  Tags: DNA sequencing, Sequencing, Software @article{stanton_ritornello_2017,
title = {Ritornello: high fidelity controlfree chromatin immunoprecipitation peak calling},
author = {Kelly P Stanton and Jiaqi Jin and Roy R Lederman and Sherman M Weissman and Yuval Kluger},
url = {https://academic.oup.com/nar/article/45/21/e173/4157402},
doi = {10.1093/nar/gkx799},
issn = {03051048},
year = {2017},
date = {20170101},
urldate = {20200813},
journal = {Nucleic Acids Research},
volume = {45},
number = {21},
pages = {e173e173},
abstract = {Abstract. With the advent of next generation highthroughput DNA sequencing technologies, omics experiments have become the mainstay for studying diverse biolo},
note = {Publisher: Oxford Academic},
keywords = {DNA sequencing, Sequencing, Software},
pubstate = {published},
tppubtype = {article}
}
Abstract. With the advent of next generation highthroughput DNA sequencing technologies, omics experiments have become the mainstay for studying diverse biolo 
Aldroubi, Akram; Huang, Longxiu; Krishtal, Ilya; Lederman, Roy R Dynamical sampling with random noise Inproceedings 2017 International Conference on Sampling Theory and Applications (SampTA), pp. 409–412, IEEE, Tallin, Estonia, 2017, ISBN: 9781538615652. Links  BibTeX  Tags: Dynamical Sampling @inproceedings{aldroubi_dynamical_2017,
title = {Dynamical sampling with random noise},
author = {Akram Aldroubi and Longxiu Huang and Ilya Krishtal and Roy R Lederman},
url = {http://ieeexplore.ieee.org/document/8024372/},
doi = {10.1109/SAMPTA.2017.8024372},
isbn = {9781538615652},
year = {2017},
date = {20170101},
urldate = {20200813},
booktitle = {2017 International Conference on Sampling Theory and Applications (SampTA)},
pages = {409412},
publisher = {IEEE},
address = {Tallin, Estonia},
keywords = {Dynamical Sampling},
pubstate = {published},
tppubtype = {inproceedings}
}

Lederman, Roy R; Steinerberger, Stefan Stability Estimates for Truncated Fourier and Laplace Transforms Journal Article 2016. Abstract  Links  BibTeX  Tags: Laplace Transform @article{lederman_stability_2016,
title = {Stability Estimates for Truncated Fourier and Laplace Transforms},
author = {Roy R Lederman and Stefan Steinerberger},
url = {https://arxiv.org/abs/1605.03866v1},
year = {2016},
date = {20160501},
urldate = {20200813},
abstract = {We prove sharp stability estimates for the Truncated Laplace Transform and
Truncated Fourier Transform. The argument combines an approach recently
introduced by Alaifari, Pierce and the second author for the truncated Hilbert
transform with classical results of Bertero, Grünbaum, Landau, Pollak and
Slepian. In particular, we prove there is a universal constant $c textgreater0$ such that
for all $f textbackslashin Ltextasciicircum2(textbackslashmathbbR)$ with compact support in $[1,1]$ normalized to $textbackslashtextbarftextbackslashtextbar_Ltextasciicircum2[1,1] = 1$ $$ textbackslashint_1textasciicircum1textbartextbackslashwidehatf(ξ)textbartextasciicircum2dξ textbackslashgtrsim
textbackslashleft(ctextbackslashlefttextbackslashtextbarf_x textbackslashrighttextbackslashtextbar_Ltextasciicircum2[1,1] textbackslashright)textasciicircumvphantom ctextbackslashlefttextbackslashtextbarf_x
textbackslashrighttextbackslashtextbar_Ltextasciicircum2[1,1]vphantom$$ The inequality is sharp in the sense that there is an
infinite sequence of orthonormal counterexamples if $c$ is chosen too small.
The question whether and to which extent similar inequalities hold for generic
families of integral operators remains open.},
keywords = {Laplace Transform},
pubstate = {published},
tppubtype = {article}
}
We prove sharp stability estimates for the Truncated Laplace Transform and
Truncated Fourier Transform. The argument combines an approach recently
introduced by Alaifari, Pierce and the second author for the truncated Hilbert
transform with classical results of Bertero, Grünbaum, Landau, Pollak and
Slepian. In particular, we prove there is a universal constant $c textgreater0$ such that
for all $f textbackslashin Ltextasciicircum2(textbackslashmathbbR)$ with compact support in $[1,1]$ normalized to $textbackslashtextbarftextbackslashtextbar_Ltextasciicircum2[1,1] = 1$ $$ textbackslashint_1textasciicircum1textbartextbackslashwidehatf(ξ)textbartextasciicircum2dξ textbackslashgtrsim
textbackslashleft(ctextbackslashlefttextbackslashtextbarf_x textbackslashrighttextbackslashtextbar_Ltextasciicircum2[1,1] textbackslashright)textasciicircumvphantom ctextbackslashlefttextbackslashtextbarf_x
textbackslashrighttextbackslashtextbar_Ltextasciicircum2[1,1]vphantom$$ The inequality is sharp in the sense that there is an
infinite sequence of orthonormal counterexamples if $c$ is chosen too small.
The question whether and to which extent similar inequalities hold for generic
families of integral operators remains open. 
Lederman, Roy R; Rokhlin, V On the Analytical and Numerical Properties of the Truncated Laplace Transform. Part II Journal Article SIAM Journal on Numerical Analysis, 54 (2), pp. 665–687, 2016, ISSN: 00361429, 10957170. Links  BibTeX  Tags: Algorithms, Laplace Transform, Numerical Analysis @article{lederman_analytical_2016,
title = {On the Analytical and Numerical Properties of the Truncated Laplace Transform. Part II},
author = {Roy R Lederman and V Rokhlin},
url = {http://epubs.siam.org/doi/10.1137/15M1028583},
doi = {10.1137/15M1028583},
issn = {00361429, 10957170},
year = {2016},
date = {20160101},
urldate = {20200813},
journal = {SIAM Journal on Numerical Analysis},
volume = {54},
number = {2},
pages = {665687},
keywords = {Algorithms, Laplace Transform, Numerical Analysis},
pubstate = {published},
tppubtype = {article}
}

Shaham, Uri; Lederman, Roy R Common Variable Learning and Invariant Representation Learning using Siamese Neural Networks Technical Report 2015. Abstract  Links  BibTeX  Tags: Common variable, Deep Learning, Multiview @techreport{shaham_common_2015,
title = {Common Variable Learning and Invariant Representation Learning using Siamese Neural Networks},
author = {Uri Shaham and Roy R Lederman},
url = {https://arxiv.org/abs/1512.08806v3},
year = {2015},
date = {20151201},
urldate = {20200813},
abstract = {We consider the statistical problem of learning common source of variability
in data which are synchronously captured by multiple sensors, and demonstrate
that Siamese neural networks can be naturally applied to this problem. This
approach is useful in particular in exploratory, datadriven applications,
where neither a model nor label information is available. In recent years, many
researchers have successfully applied Siamese neural networks to obtain an
embedding of data which corresponds to a "semantic similarity". We present an
interpretation of this "semantic similarity" as learning of equivalence
classes. We discuss properties of the embedding obtained by Siamese networks
and provide empirical results that demonstrate the ability of Siamese networks
to learn common variability.},
keywords = {Common variable, Deep Learning, Multiview},
pubstate = {published},
tppubtype = {techreport}
}
We consider the statistical problem of learning common source of variability
in data which are synchronously captured by multiple sensors, and demonstrate
that Siamese neural networks can be naturally applied to this problem. This
approach is useful in particular in exploratory, datadriven applications,
where neither a model nor label information is available. In recent years, many
researchers have successfully applied Siamese neural networks to obtain an
embedding of data which corresponds to a "semantic similarity". We present an
interpretation of this "semantic similarity" as learning of equivalence
classes. We discuss properties of the embedding obtained by Siamese networks
and provide empirical results that demonstrate the ability of Siamese networks
to learn common variability. 
Lederman, Roy R; Talmon, Ronen; Wu, Hautieng; Lo, YuLun; Coifman, Ronald R Alternating diffusion for common manifold learning with application to sleep stage assessment Inproceedings 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 5758–5762, 2015, (ISSN: 2379190X). Abstract  Links  BibTeX  Tags: Alternating Diffusion, Common variable, diffusion maps, Kernel, learning (artificial intelligence), Manifolds, multimodal, multimodal respiratory signals, multimodal signal processing, Physiology, Sensitivity, Sensor phenomena and characterization, signal processing, sleep, sleep stage assessment, standard manifold learning method, time series @inproceedings{lederman_alternating_2015,
title = {Alternating diffusion for common manifold learning with application to sleep stage assessment},
author = {Roy R Lederman and Ronen Talmon and Hautieng Wu and YuLun Lo and Ronald R Coifman},
doi = {10.1109/ICASSP.2015.7179075},
year = {2015},
date = {20150101},
booktitle = {2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
pages = {57585762},
abstract = {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 alternatingdiffusion 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 sensorspecific variables. In addition, we present application to sleep stage assessment. We demonstrate that, indeed, through alternatingdiffusion, the sleep information hidden inside multimodal respiratory signals can be better captured compared to singlemodal methods.},
note = {ISSN: 2379190X},
keywords = {Alternating Diffusion, Common variable, diffusion maps, Kernel, learning (artificial intelligence), Manifolds, multimodal, multimodal respiratory signals, multimodal signal processing, Physiology, Sensitivity, Sensor phenomena and characterization, signal processing, sleep, sleep stage assessment, standard manifold learning method, time series},
pubstate = {published},
tppubtype = {inproceedings}
}
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 alternatingdiffusion 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 sensorspecific variables. In addition, we present application to sleep stage assessment. We demonstrate that, indeed, through alternatingdiffusion, the sleep information hidden inside multimodal respiratory signals can be better captured compared to singlemodal methods. 
Lederman, Roy R; Rokhlin, V On the Analytical and Numerical Properties of the Truncated Laplace Transform I. Journal Article SIAM Journal on Numerical Analysis, 53 (3), pp. 1214–1235, 2015, ISSN: 00361429, 10957170. Links  BibTeX  Tags: Algorithms, Laplace Transform, Numerical Analysis @article{lederman_analytical_2015,
title = {On the Analytical and Numerical Properties of the Truncated Laplace Transform I.},
author = {Roy R Lederman and V Rokhlin},
url = {http://epubs.siam.org/doi/10.1137/140990681},
doi = {10.1137/140990681},
issn = {00361429, 10957170},
year = {2015},
date = {20150101},
urldate = {20200813},
journal = {SIAM Journal on Numerical Analysis},
volume = {53},
number = {3},
pages = {12141235},
keywords = {Algorithms, Laplace Transform, Numerical Analysis},
pubstate = {published},
tppubtype = {article}
}

Lederman, Roy R; Talmon, Ronen Common Manifold Learning Using AlternatingDiﬀusion Technical Report Yale CS (YALEU/DCS/TR1497), 2014. Links  BibTeX  Tags: AD, Algorithms, Alternating Diffusion, Manifold Learning @techreport{lederman_common_2014,
title = {Common Manifold Learning Using AlternatingDiﬀusion},
author = {Roy R Lederman and Ronen Talmon},
url = {https://cpsc.yale.edu/sites/default/files/files/tr1497.pdf},
year = {2014},
date = {20140101},
number = {YALEU/DCS/TR1497},
pages = {42},
institution = {Yale CS},
keywords = {AD, Algorithms, Alternating Diffusion, Manifold Learning},
pubstate = {published},
tppubtype = {techreport}
}

Lederman, Roy R On the Analytical and Numerical Properties of the Truncated Laplace Transform Technical Report Yale CS (YALEU/DCS/TR1490), 2014. BibTeX  Tags: Algorithms, Laplace Transform, Numerical Analysis @techreport{lederman_analytical_2014,
title = {On the Analytical and Numerical Properties of the Truncated Laplace Transform},
author = {Roy R Lederman},
year = {2014},
date = {20140101},
number = {YALEU/DCS/TR1490},
pages = {82},
institution = {Yale CS},
keywords = {Algorithms, Laplace Transform, Numerical Analysis},
pubstate = {published},
tppubtype = {techreport}
}

Lederman, Roy R A permutationsbased algorithm for fast alignment of long pairedend reads Technical Report Yale CS (YALEU/DCS/TR1474), 2013. BibTeX  Tags: Algorithms, DNA sequencing, Fast algorithms, Randomized algorithms, Sequencing @techreport{lederman_permutationsbased_2013,
title = {A permutationsbased algorithm for fast alignment of long pairedend reads},
author = {Roy R Lederman},
year = {2013},
date = {20130401},
number = {YALEU/DCS/TR1474},
pages = {11},
institution = {Yale CS},
keywords = {Algorithms, DNA sequencing, Fast algorithms, Randomized algorithms, Sequencing},
pubstate = {published},
tppubtype = {techreport}
}

Lederman, Roy R A Note about the ResolutionLength Characteristics of DNA Technical Report Yale CS (YALEU/DCS/TR1473), 2013. BibTeX  Tags: Sequence Alignment, Sequencing @techreport{lederman_note_2013,
title = {A Note about the ResolutionLength Characteristics of DNA},
author = {Roy R Lederman},
year = {2013},
date = {20130401},
number = {YALEU/DCS/TR1473},
pages = {6},
institution = {Yale CS},
keywords = {Sequence Alignment, Sequencing},
pubstate = {published},
tppubtype = {techreport}
}

Lederman, Roy R Building approximate overlap graphs for DNA assembly using randompermutationsbased search Technical Report Yale CS (YALEU/DCS/TR1470), 2012. BibTeX  Tags: DNA sequencing, Sequencing @techreport{lederman_building_2012,
title = {Building approximate overlap graphs for DNA assembly using randompermutationsbased search},
author = {Roy R Lederman},
year = {2012},
date = {20121201},
number = {YALEU/DCS/TR1470},
pages = {10},
institution = {Yale CS},
keywords = {DNA sequencing, Sequencing},
pubstate = {published},
tppubtype = {techreport}
}

Lederman, Roy R Homopolymer Length Filters Technical Report Yale CS (YALEU/DCS/TR1465), 2012. BibTeX  Tags: Algorithms, DNA sequencing, Sequence Alignment, Sequencing @techreport{lederman_homopolymer_2012,
title = {Homopolymer Length Filters},
author = {Roy R Lederman},
year = {2012},
date = {20121001},
number = {YALEU/DCS/TR1465},
pages = {12},
institution = {Yale CS},
keywords = {Algorithms, DNA sequencing, Sequence Alignment, Sequencing},
pubstate = {published},
tppubtype = {techreport}
}
