@comment{{This file has been generated by bib2bib 1.97}}
@comment{{Command line: bib2bib ../bibli.bib -c 'subject:"dimred" or keywords:"dimred"' -ob tmp.bib}}
@article{Balasubramanian2002isomap,
author = {Balasubramanian, M. and Schwartz, E. L.},
title = {The isomap algorithm and topological stability},
journal = {Science},
year = {2002},
volume = {295},
pages = {7},
number = {5552},
month = {Jan},
doi = {10.1126/science.295.5552.7a},
pdf = {../local/Balasubramanian2002isomap.pdf},
file = {Balasubramanian2002isomap.pdf:local/Balasubramanian2002isomap.pdf:PDF},
keywords = {dimred},
pii = {295/5552/7a},
url = {http://dx.doi.org/10.1126/science.295.5552.7a}
}
@article{Belkin2003Laplacian,
author = {Belkin, M. and Niyogi, P.},
title = {Laplacian {E}igenmaps for {D}imensionality {R}eduction and {D}ata
{R}epresentation},
journal = {Neural {C}omput.},
year = {2003},
volume = {15},
pages = {1373-1396},
number = {6},
abstract = {One of the central problems in machine learning and pattern recognition
is to develop appropriate representations for complex data. {W}e
consider the problem of constructing a representation for data lying
on a low-dimensional manifold embedded in a high-dimensional space.
{D}rawing on the correspondence between the graph {L}aplacian, the
{L}aplace {B}eltrami operator on the manifold, and the connections
to the heat equation, we propose a geometrically motivated algorithm
for representing the high-dimensional data. {T}he algorithm provides
a computationally efficient approach to nonlinear dimensionality
reduction that has locality-preserving properties and a natural connection
to clustering. {S}ome potential applications and illustrative examples
are discussed.},
pdf = {../local/1373.pdf:http\},
file = {1373.pdf:http\://neco.mitpress.org/cgi/reprint/15/6/1373.pdf:PDF},
keywords = {dimred},
url = {http://neco.mitpress.org/cgi/content/abstract/15/6/1373}
}
@article{Bengio2004Learning,
author = {Bengio, Y. and Delalleau, O. and Le Roux, N. and Paiement, J.-F.
and Vincent, P. and Ouimet, M.},
title = {Learning eigenfunctions links spectral embedding and kernel {PCA}.},
journal = {Neural {C}omput.},
year = {2004},
volume = {16},
pages = {2197-219},
number = {10},
month = {Oct},
abstract = {In this letter, we show a direct relation between spectral embedding
methods and kernel principal components analysis and how both are
special cases of a more general learning problem: learning the principal
eigenfunctions of an operator defined from a kernel and the unknown
data-generating density. {W}hereas spectral embedding methods provided
only coordinates for the training points, the analysis justifies
a simple extension to out-of-sample examples (the {N}yström formula)
for multidimensional scaling ({MDS}), spectral clustering, {L}aplacian
eigenmaps, locally linear embedding ({LLE}), and {I}somap. {T}he
analysis provides, for all such spectral embedding methods, the definition
of a loss function, whose empirical average is minimized by the traditional
algorithms. {T}he asymptotic expected value of that loss defines
a generalization performance and clarifies what these algorithms
are trying to learn. {E}xperiments with {LLE}, {I}somap, spectral
clustering, and {MDS} show that this out-of-sample embedding formula
generalizes well, with a level of error comparable to the effect
of small perturbations of the training set on the embedding.},
doi = {10.1162/0899766041732396},
pdf = {../local/Bengio2004Learning.pdf},
file = {Bengio2004Learning.pdf:local/Bengio2004Learning.pdf:PDF},
keywords = {dimred},
url = {http://dx.doi.org/10.1162/0899766041732396}
}
@article{Donoho2003Hessian,
author = {Donoho, D. L. and Grimes, C.},
title = {Hessian eigenmaps: {L}ocally linear embedding techniques for high-dimensional
data},
journal = {Proc. {N}atl. {A}cad. {S}ci. {USA}},
year = {2003},
volume = {100},
pages = {5591-5596},
number = {10},
doi = {10.1073/pnas.1031596100},
pdf = {../local/5591.pdf:http\},
file = {5591.pdf:http\://www.pnas.org/cgi/reprint/100/10/5591.pdf:PDF},
keywords = {dimred},
url = {http://www.pnas.org/cgi/content/abstract/100/10/5591}
}
@article{LHeureux2004Locally,
author = {L'Heureux, P. J. and Carreau, J. and Bengio, Y. and Delalleau, O.
and Yue, S. Y.},
title = {Locally linear embedding for dimensionality reduction in {QSAR}.},
journal = {J. {C}omput. {A}ided {M}ol. {D}es.},
year = {2004},
volume = {18},
pages = {475-82},
number = {7-9},
abstract = {Current practice in {Q}uantitative {S}tructure {A}ctivity {R}elationship
({QSAR}) methods usually involves generating a great number of chemical
descriptors and then cutting them back with variable selection techniques.
{V}ariable selection is an effective method to reduce the dimensionality
but may discard some valuable information. {T}his paper introduces
{L}ocally {L}inear {E}mbedding ({LLE}), a local non-linear dimensionality
reduction technique, that can statistically discover a low-dimensional
representation of the chemical data. {LLE} is shown to create more
stable representations than other non-linear dimensionality reduction
algorithms, and to be capable of capturing non-linearity in chemical
data.},
doi = {10.1007/s10822-004-5319-9},
pdf = {../local/LHeureux2004Locally.pdf},
file = {LHeureux2004Locally.pdf:local/LHeureux2004Locally.pdf:PDF},
keywords = {dimred},
url = {http://dx.doi.org/10.1007/s10822-004-5319-9}
}
@article{Nilsson2004Approximate,
author = {Nilsson, J. and Fioretos, T. and Höglund, M. and Fontes, M.},
title = {Approximate geodesic distances reveal biologically relevant structures
in microarray data.},
journal = {Bioinformatics},
year = {2004},
volume = {20},
pages = {874-80},
number = {6},
month = {Apr},
abstract = {M{OTIVATION}: {G}enome-wide gene expression measurements, as currently
determined by the microarray technology, can be represented mathematically
as points in a high-dimensional gene expression space. {G}enes interact
with each other in regulatory networks, restricting the cellular
gene expression profiles to a certain manifold, or surface, in gene
expression space. {T}o obtain knowledge about this manifold, various
dimensionality reduction methods and distance metrics are used. {F}or
data points distributed on curved manifolds, a sensible distance
measure would be the geodesic distance along the manifold. {I}n this
work, we examine whether an approximate geodesic distance measure
captures biological similarities better than the traditionally used
{E}uclidean distance. {RESULTS}: {W}e computed approximate geodesic
distances, determined by the {I}somap algorithm, for one set of lymphoma
and one set of lung cancer microarray samples. {C}ompared with the
ordinary {E}uclidean distance metric, this distance measure produced
more instructive, biologically relevant, visualizations when applying
multidimensional scaling. {T}his suggests the {I}somap algorithm
as a promising tool for the interpretation of microarray data. {F}urthermore,
the results demonstrate the benefit and importance of taking nonlinearities
in gene expression data into account.},
doi = {10.1093/bioinformatics/btg496},
pdf = {../local/Nilsson2004Approximate.pdf},
file = {Nilsson2004Approximate.pdf:local/Nilsson2004Approximate.pdf:PDF},
keywords = {dimred},
pii = {btg496},
url = {http://dx.doi.org/10.1093/bioinformatics/btg496}
}
@article{Roweis2000Nonlinear,
author = {Roweis, S. T. and Saul, L. K.},
title = {Nonlinear dimensionality reduction by locally linear embedding.},
journal = {Science},
year = {2000},
volume = {290},
pages = {2323-6},
number = {5500},
month = {Dec},
abstract = {Many areas of science depend on exploratory data analysis and visualization.
{T}he need to analyze large amounts of multivariate data raises the
fundamental problem of dimensionality reduction: how to discover
compact representations of high-dimensional data. {H}ere, we introduce
locally linear embedding ({LLE}), an unsupervised learning algorithm
that computes low-dimensional, neighborhood-preserving embeddings
of high-dimensional inputs. {U}nlike clustering methods for local
dimensionality reduction, {LLE} maps its inputs into a single global
coordinate system of lower dimensionality, and its optimizations
do not involve local minima. {B}y exploiting the local symmetries
of linear reconstructions, {LLE} is able to learn the global structure
of nonlinear manifolds, such as those generated by images of faces
or documents of text.},
doi = {10.1126/science.290.5500.2323},
pdf = {../local/Roweis2000Nonlinear.pdf},
file = {Roweis2000Nonlinear.pdf:local/Roweis2000Nonlinear.pdf:PDF},
keywords = {dimred},
pii = {290/5500/2323},
url = {http://dx.doi.org/10.1126/science.290.5500.2323}
}
@article{Saul2003Think,
author = {Saul, L. K. and Roweis, S. T.},
title = {Think {G}lobally, {F}it {L}ocally: {U}nsupervised {L}earning of {L}ow
{D}imensional {M}anifolds},
journal = {J. {M}ach. {L}earn. {R}es.},
year = {2003},
volume = {4},
pages = {119-155},
abstract = {The problem of dimensionality reduction arises in many fields of information
processing, including machine learning, data compression, scientific
visualization, pattern recognition, and neural computation. {H}ere
we describe locally linear embedding ({LLE}), an unsupervised learning
algorithm that computes low dimensional, neighborhood preserving
embeddings of high dimensional data. {T}he data, assumed to be sampled
from an underlying manifold, are mapped into a single global coordinate
system of lower dimensionality. {T}he mapping is derived from the
symmetries of locally linear reconstructions, and the actual computation
of the embedding reduces to a sparse eigenvalue problem. {N}otably,
the optimizations in {LLE}---though capable of generating highly
nonlinear embeddings---are simple to implement, and they do not involve
local minima. {I}n this paper, we describe the implementation of
the algorithm in detail and discuss several extensions that enhance
its performance. {W}e present results of the algorithm applied to
data sampled from known manifolds, as well as to collections of images
of faces, lips, and handwritten digits. {T}hese examples are used
to provide extensive illustrations of the algorithm's performance---both
successes and failures---and to relate the algorithm to previous
and ongoing work in nonlinear dimensionality reduction.},
pdf = {../local/saul03a.pdf:http\},
file = {saul03a.pdf:http\://www.jmlr.org/papers/volume4/saul03a/saul03a.pdf:PDF},
keywords = {dimred},
url = {http://www.jmlr.org/papers/v4/saul03a.html}
}
@article{Tenenbaum2000global,
author = {Tenenbaum, J. B. and de Silva, V. and Langford, J. C.},
title = {A global geometric framework for nonlinear dimensionality reduction},
journal = {Science},
year = {2000},
volume = {290},
pages = {2319-23},
number = {5500},
month = {Dec},
abstract = {Scientists working with large volumes of high-dimensional data, such
as global climate patterns, stellar spectra, or human gene distributions,
regularly confront the problem of dimensionality reduction: finding
meaningful low-dimensional structures hidden in their high-dimensional
observations. {T}he human brain confronts the same problem in everyday
perception, extracting from its high-dimensional sensory inputs-30,000
auditory nerve fibers or 10(6) optic nerve fibers-a manageably small
number of perceptually relevant features. {H}ere we describe an approach
to solving dimensionality reduction problems that uses easily measured
local metric information to learn the underlying global geometry
of a data set. {U}nlike classical techniques such as principal component
analysis ({PCA}) and multidimensional scaling ({MDS}), our approach
is capable of discovering the nonlinear degrees of freedom that underlie
complex natural observations, such as human handwriting or images
of a face under different viewing conditions. {I}n contrast to previous
algorithms for nonlinear dimensionality reduction, ours efficiently
computes a globally optimal solution, and, for an important class
of data manifolds, is guaranteed to converge asymptotically to the
true structure.},
doi = {10.1126/science.290.5500.2319},
pdf = {../local/Tenenbaum2000global.pdf},
file = {Tenenbaum2000global.pdf:local/Tenenbaum2000global.pdf:PDF},
keywords = {dimred},
pii = {290/5500/2319},
url = {http://dx.doi.org/10.1126/science.290.5500.2319}
}
@inproceedings{Weinberger2005Nonlinear,
author = {Weinberger, K. and Packer, B. and Saul, L.},
title = {Nonlinear {D}imensionality {R}eduction by {S}emidefinite {P}rogramming
and {K}ernel {M}atrix {F}actorization},
booktitle = {Proceedings of the {T}enth {I}nternational {W}orkshop on {A}rtificial
{I}ntelligence and {S}tatistics, {J}an 6-8, 2005, {S}avannah {H}otel,
{B}arbados},
year = {2005},
editor = {Cowell, R. G. and Ghahramani, Z.},
pages = {381-388},
publisher = {Society for Artificial Intelligence and Statistics},
abstract = {We describe an algorithm for nonlinear dimensionality reduction based
on semidefinite programming and kernel matrix factorization. {T}he
algorithm learns a kernel matrix for high dimensional data that lies
on or near a low dimensional manifold. {I}n earlier work, the kernel
matrix was learned by maximizing the variance in feature space while
preserving the distances and angles between nearest neighbors. {I}n
this paper, adapting recent ideas from semi-supervised learning on
graphs, we show that the full kernel matrix can be very well approximated
by a product of smaller matrices. {R}epresenting the kernel matrix
in this way, we can reformulate the semidefinite program in terms
of a much smaller submatrix of inner products between randomly chosen
landmarks. {T}he new framework leads to order-of-magnitude reductions
in computation time and makes it possible to study much larger problems
in manifold learning.},
pdf = {../local/We describe an algorithm for nonlinear dimensionality reduction based on semidefinite programming and kernel matrix factorization. The algorithm learns a kernel matrix for high dimensional data that lies on or near a low dimensional manifold. In earlier work, the kernel matrix was learned by maximizing the variance in feature space while preserving the distances and angles between nearest neighbors. In this paper, adapting recent ideas from semi-supervised learning on graphs, we show that the full kernel matrix can be very well approximated by a product of smaller matrices. Representing the kernel matrix in this way, we can reformulate the semidefinite program in terms of a much smaller submatrix of inner products between randomly chosen landmarks. The new framework leads to order-of-magnitude reductions in computation time and makes it possible to study much larger problems in manifold learning.},
file = {We describe an algorithm for nonlinear dimensionality reduction based on semidefinite programming and kernel matrix factorization. The algorithm learns a kernel matrix for high dimensional data that lies on or near a low dimensional manifold. In earlier work, the kernel matrix was learned by maximizing the variance in feature space while preserving the distances and angles between nearest neighbors. In this paper, adapting recent ideas from semi-supervised learning on graphs, we show that the full kernel matrix can be very well approximated by a product of smaller matrices. Representing the kernel matrix in this way, we can reformulate the semidefinite program in terms of a much smaller submatrix of inner products between randomly chosen landmarks. The new framework leads to order-of-magnitude reductions in computation time and makes it possible to study much larger problems in manifold learning.:We describe an algorithm for nonlinear dimensionality reduction based on semidefinite programming and kernel matrix factorization. The algorithm learns a kernel matrix for high dimensional data that lies on or near a low dimensional manifold. In earlier work, the kernel matrix was learned by maximizing the variance in feature space while preserving the distances and angles between nearest neighbors. In this paper, adapting recent ideas from semi-supervised learning on graphs, we show that the full kernel matrix can be very well approximated by a product of smaller matrices. Representing the kernel matrix in this way, we can reformulate the semidefinite program in terms of a much smaller submatrix of inner products between randomly chosen landmarks. The new framework leads to order-of-magnitude reductions in computation time and makes it possible to study much larger problems in manifold learning.:PDF},
keywords = {dimred}
}
@inproceedings{Weinberger2004Unsupervised,
author = {Weinberger, K. Q. and Saul, L. K.},
title = {Unsupervised {L}earning of {I}mage {M}anifolds by {S}emidefinite
{P}rogramming},
booktitle = {2004 {IEEE} {C}omputer {S}ociety {C}onference on {C}omputer {V}ision
and {P}attern {R}ecognition ({CVPR}'04)},
year = {2004},
volume = {2},
number = {2},
pages = {988-995},
abstract = {Can we detect low dimensional structure in high dimensional data sets
of images and video? {T}he problem of dimensionality reduction arises
often in computer vision and pattern recognition. {I}n this paper,
we propose a new solution to this problem based on semidefinite programming.
{O}ur algorithm can be used to analyze high dimensional data that
lies on or near a low dimensional manifold. {I}t overcomes certain
limitations of previous work in manifold learning, such as {I}somap
and locally linear embedding. {W}e illustrate the algorithm on easily
visualized examples of curves and surfaces, as well as on actual
images of faces, handwritten digits, and solid objects.},
doi = {doi.ieeecomputersociety.org/10.1109/CVPR.2004.256},
pdf = {../local/sdeFinal_cvpr04.pdf:http\://www.seas.upenn.edu/~kilianw/publications/PDFs/sdeFinal_cvpr04.pdf:PDF;sdeFinal_cvpr04.pdf:http\},
file = {sdeFinal_cvpr04.pdf:http\://www.seas.upenn.edu/~kilianw/publications/PDFs/sdeFinal_cvpr04.pdf:PDF;sdeFinal_cvpr04.pdf:http\://www.seas.upenn.edu/~kilianw/publications/PDFs/sdeFinal_cvpr04.pdf:PDF},
keywords = {dimred}
}
@inproceedings{Weinberger2004Learning,
author = {Weinberger, K. Q. and Sha, F. and Saul, L. K.},
title = {Learning a kernel matrix for nonlinear dimensionality reduction},
booktitle = {I{CML} '04: {T}wenty-first international conference on {M}achine
learning},
year = {2004},
address = {New York, NY, USA},
publisher = {ACM Press},
abstract = {We investigate how to learn a kernel matrix for high dimensional data
that lies on or near a low dimensional manifold. {N}oting that the
kernel matrix implicitly maps the data into a nonlinear feature space,
we show how to discover a mapping that "unfolds" the underlying manifold
from which the data was sampled. {T}he kernel matrix is constructed
by maximizing the variance in feature space subject to local constraints
that preserve the angles and distances between nearest neighbors.
{T}he main optimization involves an instance of semidefinite programming---a
fundamentally different computation than previous algorithms for
manifold learning, such as {I}somap and locally linear embedding.
{T}he optimized kernels perform better than polynomial and {G}aussian
kernels for problems in manifold learning, but worse for problems
in large margin classification. {W}e explain these results in terms
of the geometric properties of different kernels and comment on various
interpretations of other manifold learning algorithms as kernel methods.},
doi = {http://doi.acm.org/10.1145/1015330.1015345},
pdf = {../local/kernel_icml04.pdf:http\://www.seas.upenn.edu/~kilianw/publications/PDFs/kernel_icml04.pdf:PDF;kernel_icml04.pdf:http\},
file = {kernel_icml04.pdf:http\://www.seas.upenn.edu/~kilianw/publications/PDFs/kernel_icml04.pdf:PDF;kernel_icml04.pdf:http\://www.seas.upenn.edu/~kilianw/publications/PDFs/kernel_icml04.pdf:PDF},
keywords = {dimred}
}
@comment{{jabref-meta: selector_author:}}
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ochim. Biophys. Acta;Bioinformatics;Biometrika;BMC Bioinformatics;Br.
J. Pharmacol.;Breast Cancer Res.;Cell;Cell. Signal.;Chem. Res. Toxicol
.;Clin. Cancer Res.;Combinator. Probab. Comput.;Comm. Pure Appl. Math.
;Comput. Chem.;Comput. Comm. Rev.;Comput. Stat. Data An.;Curr. Genom.;
Curr. Opin. Chem. Biol.;Curr. Opin. Drug Discov. Devel.;Data Min. Know
l. Discov.;Electron. J. Statist.;Eur. J. Hum. Genet.;FEBS Lett.;Found.
Comput. Math.;Genome Biol.;IEEE T. Neural Networ.;IEEE T. Pattern. An
al.;IEEE T. Signal. Proces.;IEEE Trans. Inform. Theory;IEEE Trans. Kno
wl. Data Eng.;IEEE/ACM Trans. Comput. Biol. Bioinf.;Int. J. Comput. Vi
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ACM;J. Am. Soc. Inf. Sci. Technol.;J. Am. Stat. Assoc.;J. Bioinform. C
omput. Biol.;J. Biol. Chem.;J. Biomed. Inform.;J. Cell. Biochem.;J. Ch
em. Inf. Comput. Sci.;J. Chem. Inf. Model.;J. Clin. Oncol.;J. Comput.
Biol.;J. Comput. Graph. Stat.;J. Eur. Math. Soc.;J. Intell. Inform. Sy
st.;J. Mach. Learn. Res.;J. Med. Chem.;J. Mol. BIol.;J. R. Stat. Soc.
Ser. B;Journal of Statistical Planning and Inference;Mach. Learn.;Math
. Program.;Meth. Enzymol.;Mol. Biol. Cell;Mol. Biol. Evol.;Mol. Cell.
Biol.;Mol. Syst. Biol.;N. Engl. J. Med.;Nat. Biotechnol.;Nat. Genet.;N
at. Med.;Nat. Methods;Nat. Rev. Cancer;Nat. Rev. Drug Discov.;Nat. Rev
. Genet.;Nature;Neural Comput.;Neural Network.;Neurocomputing;Nucleic
Acids Res.;Pattern Anal. Appl.;Pattern Recognit.;Phys. Rev. E;Phys. Re
v. Lett.;PLoS Biology;PLoS Comput. Biol.;Probab. Theory Relat. Fields;
Proc. IEEE;Proc. Natl. Acad. Sci. USA;Protein Eng.;Protein Eng. Des. S
el.;Protein Sci.;Protein. Struct. Funct. Genet.;Random Struct. Algorit
hm.;Rev. Mod. Phys.;Science;Stat. Probab. Lett.;Statistica Sinica;Theo
r. Comput. Sci.;Trans. Am. Math. Soc.;Trends Genet.;}}
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