Multidimensional Projection for Visual Analytics
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Results        

Quality Measure Name and Reference(s):

Spearman's Correlation
S. Siegel. Nonparametric statistics for the behavioral sciences. McGraw- hill, 1956.


Stress/Strain
A.Buja,D.Swayne,M.Littman,N.Dean,H.Hofmann,andL.Chen. Data visualization with multidimensional scaling. J. Comp. and Graph. Stat., 17(2):444–472, 2008.
J. Kruskal. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29(1):1–27, 1964.
J. Sammon. A nonlinear mapping for data structure analysis. IEEE Trans. on Comp., 18(5):401–409, 1969.


Graph-based Family
R.Motta,R.Minghim,A.Lopes,andM.Oliveira.Graph-basedmeasures to assist user assessment of multidimensional projections. Neurocomput- ing, 150:583–598, 2015.


NIEQA
P. Zhang, Y. Ren, and B. Zhang. A new embedding quality assessment method for manifold learning. Neurocomputing, 97:251–266, 2012.


Correlation Coefficient
X. Geng, D.-C. Zhan, and Z.-H. Zhou. Supervised nonlinear dimen- sionality reduction for visualization and classification. IEEE Trans. Sys., Man, and Cyber., 35(6):1098–1107, 2005.


Topographic Product
H.-U.BauerandK.Pawelzik.Quantifyingtheneighborhoodpreservation of self-organizing feature maps. IEEE Trans. Neural Networks, 3(4):570– 579, 1992.


Mean Rel. Rank Errors
J. Lee and M. Verleysen. Nonlinear dimensionality reduction. Springer Science & Business Media, 2007.


Trustworthiness/Continuity
J.Venna and S.Kaski. Local multidimensional scaling. NeuralNetworks, 19(6):889–899, 2006.


Procrustes Measure
Y. Goldberg and Y. Ritov. Local procrustes for manifold embedding: a measure of embedding quality and embedding algorithms. Mach. Learn., 77(1):1–25, 2009.


LC Meta-criterion
L. Chen and A. Buja. Local multidimensional scaling for nonlinear dimension reduction, graph drawing, and proximity analysis. J. Amer. Stat. Assoc., 104(485):209–219, 2009.


Global Quality Qy
D. Meng, Y. Leung, and Z. Xu. A new quality assessment criterion for nonlinear dimensionality reduction. Neurocomputing, 74(6):941–948, 2011.


KL Diverg.
G. Hinton and S. Roweis. Stochastic neighbor embedding. In NIPS, pp. 833–840, 2002.
J. Venna, J. Peltonen, K. Nybo, H. Aidos, and S. Kaski. Information retrieval perspective to nonlinear dimensionality reduction for data visu- alization. J. Mach. Learn. Res., 11:451–490, 2010.


Persit. Homol.
B. Rieck and H. Leitte. Persistent homology for the evaluation of di- mensionality reduction schemes. Comp. Graph. Forum., 34(3):431–440, 2015.


Smooth. Neigh. Pres.
P. Pagliosa, F. Paulovich, R. Minghim, H. Levkowitz, and L. G. Nonato. Projection inspector: Assessment and synthesis of multidimensional projections. Neurocomputing, 150:599–610, 2015.


Quality Measure Name and Reference(s):

Spearman's Correlation
S. Siegel. Nonparametric statistics for the behavioral sciences. McGraw- hill, 1956.


Stress/Strain
A.Buja,D.Swayne,M.Littman,N.Dean,H.Hofmann,andL.Chen. Data visualization with multidimensional scaling. J. Comp. and Graph. Stat., 17(2):444–472, 2008.
J. Kruskal. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29(1):1–27, 1964.
J. Sammon. A nonlinear mapping for data structure analysis. IEEE Trans. on Comp., 18(5):401–409, 1969.


Graph-based Family
R.Motta,R.Minghim,A.Lopes,andM.Oliveira.Graph-basedmeasures to assist user assessment of multidimensional projections. Neurocomput- ing, 150:583–598, 2015.


NIEQA
P. Zhang, Y. Ren, and B. Zhang. A new embedding quality assessment method for manifold learning. Neurocomputing, 97:251–266, 2012.


Correlation Coefficient
X. Geng, D.-C. Zhan, and Z.-H. Zhou. Supervised nonlinear dimen- sionality reduction for visualization and classification. IEEE Trans. Sys., Man, and Cyber., 35(6):1098–1107, 2005.


Topographic Product
H.-U.BauerandK.Pawelzik.Quantifyingtheneighborhoodpreservation of self-organizing feature maps. IEEE Trans. Neural Networks, 3(4):570– 579, 1992.


Mean Rel. Rank Errors
J. Lee and M. Verleysen. Nonlinear dimensionality reduction. Springer Science & Business Media, 2007.


Trustworthiness/Continuity
J.Venna and S.Kaski. Local multidimensional scaling. NeuralNetworks, 19(6):889–899, 2006.


Procrustes Measure
Y. Goldberg and Y. Ritov. Local procrustes for manifold embedding: a measure of embedding quality and embedding algorithms. Mach. Learn., 77(1):1–25, 2009.


LC Meta-criterion
L. Chen and A. Buja. Local multidimensional scaling for nonlinear dimension reduction, graph drawing, and proximity analysis. J. Amer. Stat. Assoc., 104(485):209–219, 2009.


Global Quality Qy
D. Meng, Y. Leung, and Z. Xu. A new quality assessment criterion for nonlinear dimensionality reduction. Neurocomputing, 74(6):941–948, 2011.


KL Diverg.
G. Hinton and S. Roweis. Stochastic neighbor embedding. In NIPS, pp. 833–840, 2002.
J. Venna, J. Peltonen, K. Nybo, H. Aidos, and S. Kaski. Information retrieval perspective to nonlinear dimensionality reduction for data visu- alization. J. Mach. Learn. Res., 11:451–490, 2010.


Persit. Homol.
B. Rieck and H. Leitte. Persistent homology for the evaluation of di- mensionality reduction schemes. Comp. Graph. Forum., 34(3):431–440, 2015.


Smooth. Neigh. Pres.
P. Pagliosa, F. Paulovich, R. Minghim, H. Levkowitz, and L. G. Nonato. Projection inspector: Assessment and synthesis of multidimensional projections. Neurocomputing, 150:599–610, 2015.


Quality Measure Name and Reference(s):

Spearman's Correlation
S. Siegel. Nonparametric statistics for the behavioral sciences. McGraw- hill, 1956.


Stress/Strain
A.Buja,D.Swayne,M.Littman,N.Dean,H.Hofmann,andL.Chen. Data visualization with multidimensional scaling. J. Comp. and Graph. Stat., 17(2):444–472, 2008.
J. Kruskal. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29(1):1–27, 1964.
J. Sammon. A nonlinear mapping for data structure analysis. IEEE Trans. on Comp., 18(5):401–409, 1969.


Graph-based Family
R.Motta,R.Minghim,A.Lopes,andM.Oliveira.Graph-basedmeasures to assist user assessment of multidimensional projections. Neurocomput- ing, 150:583–598, 2015.


NIEQA
P. Zhang, Y. Ren, and B. Zhang. A new embedding quality assessment method for manifold learning. Neurocomputing, 97:251–266, 2012.


Correlation Coefficient
X. Geng, D.-C. Zhan, and Z.-H. Zhou. Supervised nonlinear dimen- sionality reduction for visualization and classification. IEEE Trans. Sys., Man, and Cyber., 35(6):1098–1107, 2005.


Topographic Product
H.-U.BauerandK.Pawelzik.Quantifyingtheneighborhoodpreservation of self-organizing feature maps. IEEE Trans. Neural Networks, 3(4):570– 579, 1992.


Mean Rel. Rank Errors
J. Lee and M. Verleysen. Nonlinear dimensionality reduction. Springer Science & Business Media, 2007.


Trustworthiness/Continuity
J.Venna and S.Kaski. Local multidimensional scaling. NeuralNetworks, 19(6):889–899, 2006.


Procrustes Measure
Y. Goldberg and Y. Ritov. Local procrustes for manifold embedding: a measure of embedding quality and embedding algorithms. Mach. Learn., 77(1):1–25, 2009.


LC Meta-criterion
L. Chen and A. Buja. Local multidimensional scaling for nonlinear dimension reduction, graph drawing, and proximity analysis. J. Amer. Stat. Assoc., 104(485):209–219, 2009.


Global Quality Qy
D. Meng, Y. Leung, and Z. Xu. A new quality assessment criterion for nonlinear dimensionality reduction. Neurocomputing, 74(6):941–948, 2011.


KL Diverg.
G. Hinton and S. Roweis. Stochastic neighbor embedding. In NIPS, pp. 833–840, 2002.
J. Venna, J. Peltonen, K. Nybo, H. Aidos, and S. Kaski. Information retrieval perspective to nonlinear dimensionality reduction for data visu- alization. J. Mach. Learn. Res., 11:451–490, 2010.


Persit. Homol.
B. Rieck and H. Leitte. Persistent homology for the evaluation of di- mensionality reduction schemes. Comp. Graph. Forum., 34(3):431–440, 2015.


Smooth. Neigh. Pres.
P. Pagliosa, F. Paulovich, R. Minghim, H. Levkowitz, and L. G. Nonato. Projection inspector: Assessment and synthesis of multidimensional projections. Neurocomputing, 150:599–610, 2015.


Quality Measure Name and Reference(s):

Spearman's Correlation
S. Siegel. Nonparametric statistics for the behavioral sciences. McGraw- hill, 1956.


Stress/Strain
A.Buja,D.Swayne,M.Littman,N.Dean,H.Hofmann,andL.Chen. Data visualization with multidimensional scaling. J. Comp. and Graph. Stat., 17(2):444–472, 2008.
J. Kruskal. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29(1):1–27, 1964.
J. Sammon. A nonlinear mapping for data structure analysis. IEEE Trans. on Comp., 18(5):401–409, 1969.


Graph-based Family
R.Motta,R.Minghim,A.Lopes,andM.Oliveira.Graph-basedmeasures to assist user assessment of multidimensional projections. Neurocomput- ing, 150:583–598, 2015.


NIEQA
P. Zhang, Y. Ren, and B. Zhang. A new embedding quality assessment method for manifold learning. Neurocomputing, 97:251–266, 2012.


Correlation Coefficient
X. Geng, D.-C. Zhan, and Z.-H. Zhou. Supervised nonlinear dimen- sionality reduction for visualization and classification. IEEE Trans. Sys., Man, and Cyber., 35(6):1098–1107, 2005.


Topographic Product
H.-U.BauerandK.Pawelzik.Quantifyingtheneighborhoodpreservation of self-organizing feature maps. IEEE Trans. Neural Networks, 3(4):570– 579, 1992.


Mean Rel. Rank Errors
J. Lee and M. Verleysen. Nonlinear dimensionality reduction. Springer Science & Business Media, 2007.


Trustworthiness/Continuity
J.Venna and S.Kaski. Local multidimensional scaling. NeuralNetworks, 19(6):889–899, 2006.


Procrustes Measure
Y. Goldberg and Y. Ritov. Local procrustes for manifold embedding: a measure of embedding quality and embedding algorithms. Mach. Learn., 77(1):1–25, 2009.


LC Meta-criterion
L. Chen and A. Buja. Local multidimensional scaling for nonlinear dimension reduction, graph drawing, and proximity analysis. J. Amer. Stat. Assoc., 104(485):209–219, 2009.


Global Quality Qy
D. Meng, Y. Leung, and Z. Xu. A new quality assessment criterion for nonlinear dimensionality reduction. Neurocomputing, 74(6):941–948, 2011.


KL Diverg.
G. Hinton and S. Roweis. Stochastic neighbor embedding. In NIPS, pp. 833–840, 2002.
J. Venna, J. Peltonen, K. Nybo, H. Aidos, and S. Kaski. Information retrieval perspective to nonlinear dimensionality reduction for data visu- alization. J. Mach. Learn. Res., 11:451–490, 2010.


Persit. Homol.
B. Rieck and H. Leitte. Persistent homology for the evaluation of di- mensionality reduction schemes. Comp. Graph. Forum., 34(3):431–440, 2015.


Smooth. Neigh. Pres.
P. Pagliosa, F. Paulovich, R. Minghim, H. Levkowitz, and L. G. Nonato. Projection inspector: Assessment and synthesis of multidimensional projections. Neurocomputing, 150:599–610, 2015.