Fetching the paper…
Reading the bibliography…
Euclidean distance matrices (EDM) are matrices of squared distances between points.
K. Menger, “Untersuchungen Über Allgemeine Metrik,” Math. Ann. , vol. 100, no. 1, pp. 75–163, Dec. 1928
1928
Earlier work this paper cites.
I. J. Schoenberg, “Remarks to Maurice Frechet’s Article “Sur La Définition Axiomatique D’Une Classe D’Espace Distancés Vectoriellement Applicable Sur L’Espace De Hilbert,” Ann. Math. , vol. 36, no. 3, p. 724, Jul. 1935
1935
Earlier work this paper cites.
G. Young and A. Householder, “Discussion of a Set of Points in Terms of Their Mutual Distances,” Psychometrika , vol. 3, no. 1, pp. 19–22, 1938
1938
Earlier work this paper cites.
W. S. Torgerson, “Multidimensional Scaling: I. Theory and Method,” Psychometrika , vol. 17, pp. 401–419, 1952
1952
Earlier work this paper cites.
L. M. Blumenthal, Theory and Applications of Distance Geometry . Clarendon Press, 1953
1953
Earlier work this paper cites.
J. B. Kruskal, “Multidimensional Scaling by Optimizing Goodness of Fit to a Nonmetric Hypothesis,” Psychometrika , vol. 29, no. 1, pp. 1–27, 1964
1964
Earlier work this paper cites.
P. H. Schönemann, “A Solution of the Orthogonal Procrustes Problem With Applications to Orthogonal and Oblique Rotation,” Ph.D. dissertation, University of Illinois at Urbana-Champaign, 1964
1964
Earlier work this paper cites.
J. B. Kruskal, “Nonmetric Multidimensional Scaling: A Numerical Method,” Psychometrika , vol. 29, no. 2, pp. 115–129, 1964
1964
Earlier work this paper cites.
L. Guttman, “A General Nonmetric Technique for Finding the Smallest Coordinate Space for a Configuration of Points,” Psychometrika , vol. 33, no. 4, pp. 469–506, 1968
1968
Earlier work this paper cites.
P. H. Schönemann, “On Metric Multidimensional Unfolding,” Psychometrika , vol. 35, no. 3, pp. 349–366, 1970
1970
Earlier work this paper cites.
J. De Leeuw, “Applications of Convex Analysis to Multidimensional Scaling,” in Recent Developments in Statistics , J. Barra, F. Brodeau, G. Romier, and B. V. Cutsem, Eds. North Holland Publishing Company, 1977, pp. 133–146
1977
Earlier work this paper cites.
Y. Takane, F. Young, and J. De Leeuw, “Nonmetric Individual Differences Multidimensional Scaling: An Alternating Least Squares Method with Optimal Scaling Features,” Psychometrika , vol. 42, no. 1, pp. 7–67, 1977
1977
Earlier work this paper cites.
J. B. Allen and D. A. Berkley, “Image Method for Efficiently Simulating Small-room Acoustics,” J. Acoust. Soc. Am. , vol. 65, no. 4, pp. 943–950, 1979
1979
Earlier work this paper cites.
J. C. Gower, “Euclidean Distance Geometry,” Math. Sci. , vol. 7, pp. 1–14, 1982
1982
Earlier work this paper cites.
T. F. Havel and K. Wüthrich, “An Evaluation of the Combined Use of Nuclear Magnetic Resonance and Distance Geometry for the Determination of Protein Conformations in Solution,” J. Mol. Biol. , vol. 182, no. 2, pp. 281–294, 1985
1985
Earlier work this paper cites.
——, “Properties of Euclidean and non-Euclidean Distance Matrices,” Linear Algebra Appl. , vol. 67, pp. 81–97, 1985
1985
Earlier work this paper cites.
M. Browne, “The Young-Householder Algorithm and the Least Squares Multidimensional Scaling of Squared Distances,” J. Classif. , vol. 4, no. 2, pp. 175–190, 1987
1987
Earlier work this paper cites.
N. Gaffke and R. Mathar, “A Cyclic Projection Algorithm via Duality,” Metrika , vol. 36, no. 1, pp. 29–54, 1989
1989
Earlier work this paper cites.
W. Beavers, D. E. Dudgeon, J. W. Beletic, and M. T. Lane, “Speckle Imaging Through the Atmosphere,” Linconln Lab. J. , vol. 2, pp. 207–228, 1989
1989
Earlier work this paper cites.
W. Glunt, T. L. Hayden, S. Hong, and J. Wells, “An Alternating Projection Algorithm for Computing the Nearest Euclidean Distance Matrix,” SIAM J. Matrix Anal. Appl. , vol. 11, no. 4, pp. 589–600, 1990
1990
Cited alongside, same era.
T. L. Hayden, J. Wells, W.-M. Liu, and P. Tarazaga, “The Cone of Distance Matrices,” Linear Algebra Appl. , vol. 144, no. 0, pp. 153–169, 1990
1990
Cited alongside, same era.
R. P. Millane, “Phase Retrieval in Crystallography and Optics,” J. Opt. Soc. Am. A , vol. 7, no. 3, pp. 394–411, Mar. 1990
1990
Cited alongside, same era.
S. S. Skiena, W. D. Smith, and P. Lemke, “Reconstructing Sets from Interpoint Distances,” in ACM SCG . 1990, pp. 332–339
1990
Cited alongside, same era.
R. Mathar and P. J. F. Groenen, “Algorithms in Convex Analysis Applied to Multidimensional Scaling,” in Symbolic-numeric data analysis and learning , E. Diday and Y. Lechevallier, Eds. Nova Science, 1991, pp. 45–56
N. Duric, P. Littrup, L. Poulo, A. Babkin, R. Pevzner, E. Holsapple, O. Rama, and C. Glide, “Detection of Breast Cancer with Ultrasound Tomography: First Results with the Computed Ultrasound Risk Evaluation (CURE) Prototype,” J. Med. Phys. , vol. 34, no. 2, pp. 773–785, 2007
2007
Later among the works it cites.
M. Pollefeys and D. Nister, “Direct Computation of Sound and Microphone Locations from Time-Difference-of-Arrival Data,” in Proc. Intl. Workshop on HSC . Las Vegas, 2008, pp. 2445–2448
2008
Later among the works it cites.
——, “Graph Implementations for Nonsmooth Convex Programs,” in Recent Advances in Learning and Control , ser. Lecture Notes in Control and Information Sciences, V. Blondel, S. Boyd, and H. Kimura, Eds. Springer-Verlag Limited, 2008, pp. 95–110, http://stanford.edu/~boyd/graph_dcp.html
2008
Later among the works it cites.
E. D. Demaine, F. Gomez-Martin, H. Meijer, D. Rappaport, P. Taslakian, G. T. Toussaint, T. Winograd, and D. R. Wood, “The Distance Geometry of Music,” Comput. Geom. , vol. 42, no. 5, pp. 429–454, Jul. 2009
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
1991
Cited alongside, same era.
W. Glunt, T. L. Hayden, and W.-M. Liu, “The Embedding Problem for Predistance Matrices,” Bull. Math. Biol. , vol. 53, no. 5, pp. 769–796, 1991
1991
Cited alongside, same era.
L. Holm and C. Sander, “Protein Structure Comparison by Alignment of Distance Matrices,” J. Mol. Biol. , vol. 233, no. 1, pp. 123–138, Sep. 1993
1993
Cited alongside, same era.
M. W. Trosset, “Applications of Multidimensional Scaling to Molecular Conformation,” Comp. Sci. Stat. , vol. 29, pp. 148–152, 1998
1998
Cited alongside, same era.
A. Y. Alfakih, A. Khandani, and H. Wolkowicz, “Solving Euclidean Distance Matrix Completion Problems via Semidefinite Programming,” Comput. Optim. Appl. , vol. 12, no. 1-3, pp. 13–30, Jan. 1999
1999
Cited alongside, same era.
J. B. Tenenbaum, V. De Silva, and J. C. Langford, “A Global Geometric Framework for Nonlinear Dimensionality Reduction,” Science , vol. 290, no. 5500, pp. 2319–2323, 2000
2000
Cited alongside, same era.
L. Doherty, K. Pister, and L. El Ghaoui, “Convex Position Estimation in Wireless Sensor Networks,” in Proc. IEEE INFOCOM , vol. 3, 2001, pp. 1655–1663
2001
Cited alongside, same era.
P. Biswas and Y. Ye, “Semidefinite Programming For Ad Hoc Wireless Sensor Network Localization,” in Proc. ACM/IEEE IPSN , 2004, pp. 46–54
2004
Cited alongside, same era.
2009
Later among the works it cites.
R. H. Keshavan, A. Montanari, and S. Oh, “Matrix Completion From a Few Entries,” IEEE Trans. Inf. Theory , vol. 56, no. 6, pp. 2980–2998, Jun. 2010
2010
Later among the works it cites.
J. Dattorro, Convex Optimization & Euclidean Distance Geometry . Meboo, 2011
2011
Later among the works it cites.
M. Crocco, A. D. Bue, and V. Murino, “A Bilinear Approach to the Position Self-Calibration of Multiple Sensors,” IEEE Trans. Signal Process. , vol. 60, no. 2, pp. 660–673, 2012
2012
Later among the works it cites.
N. Krislock and H. Wolkowicz, “Euclidean Distance Matrices and Applications,” in Handbook on Semidefinite, Conic and Polynomial Optimization . Boston, MA: Springer US, Jan. 2012, pp. 879–914
2012
Later among the works it cites.
A. Mucherino, C. Lavor, L. Liberti, and N. Maculan, Distance Geometry: Theory, Methods, and Applications . New York, NY: Springer Science & Business Media, Dec. 2012
2012
Later among the works it cites.
——, “Matrix Completion from Noisy Entries,” arXiv , Apr. 2012
2012
Later among the works it cites.
I. Dokmanić, R. Parhizkar, A. Walther, Y. M. Lu, and M. Vetterli, “Acoustic Echoes Reveal Room Shape,” Proc. Natl. Acad. Sci. , vol. 110, no. 30, Jun. 2013
2013
Later among the works it cites.
J. Ranieri, A. Chebira, Y. M. Lu, and M. Vetterli, “Phase Retrieval for Sparse Signals: Uniqueness Conditions,” submitted to IEEE Trans. Inf. Theory , Jul. 2013
2013
Later among the works it cites.
R. Parhizkar, A. Karbasi, S. Oh, and M. Vetterli, “Calibration Using Matrix Completion with Application to Ultrasound Tomography,” IEEE Trans. Signal Process. , July 2013
2013
Later among the works it cites.
R. Parhizkar, “Euclidean Distance Matrices: Properties, Algorithms and Applications,” Ph.D. dissertation, Ecole Polytechnique Federale de Lausanne (EPFL), 2013
2013
Later among the works it cites.
L. Liberti, C. Lavor, N. Maculan, and A. Mucherino, “Euclidean Distance Geometry and Applications,” SIAM Rev. , vol. 56, no. 1, pp. 3–69, 2014
2014
Later among the works it cites.
I. Dokmanić, L. Daudet, and M. Vetterli, “How to Localize Ten Microphones in One Fingersnap,” Proc. EUSIPCO , 2014
2014
Later among the works it cites.
S. R. Gujarathi, C. L. Farrow, C. Glosser, L. Granlund, and P. M. Duxbury, “Ab-Initio Reconstruction of Complex Euclidean Networks in Two Dimensions,” Physical Review E , vol. 89, no. 5, 2014
2014
Later among the works it cites.
M. Grant and S. Boyd, “CVX: Matlab Software for Disciplined Convex Programming, version 2.1,” http://cvxr.com/cvx , Mar. 2014
2014
Later among the works it cites.
R. Parhizkar, I. Dokmanić, and M. Vetterli, “Single-Channel Indoor Microphone Localization,” Proc. IEEE ICASSP , Florence, 2014
2014
Later among the works it cites.