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Optimal inventory policy for fast-moving consumer goods under e-commerce environment
Supervised distance preserving projection using alternating direction method of multipliers
School of Mathematics, University of Dhaka, Bangladesh, School of Mathematics, University of Southampton, UK |
Supervised Distance Preserving Projection (SDPP) is a dimension reduction method in supervised setting proposed recently by Zhu et. al in [
References:
[1] |
E. Barshan, A. Ghodsi, Z. Azimifar and M. Z. Jahromi,
Supervised principal component analysis: Visualization, classification and regression on subspaces and submanifolds, Pattern Recognit, 44 (2010), 1357-1371.
doi: 10.1016/j.patcog.2010.12.015. |
[2] |
J. Borwein and A. S. Lewis, Convex Analysis and Non Linear Optimization: Theory and Examples, Springer, New York, 2006.
doi: 10.1007/978-0-387-31256-9. |
[3] |
S. Boyd, N. Parikh, E. Chu, B. Peleato and J. Eckstein, Distributed optimization and statistical learning via the alternating direction method of multipliers, Machine Learning, 3 (2010), 1-122. Google Scholar |
[4] |
S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004.
doi: 10.1017/CBO9780511804441.![]() ![]() |
[5] |
M. R. Brito, E. L. Chávez, A. J. Quiroz and J. E. Yukich,
Connectivity of the mutual k-nearest-neighbor graph in clustering and outlier detection, Stat. Probabil. Lett., 35 (1997), 33-42.
doi: 10.1016/S0167-7152(96)00213-1. |
[6] |
I. Cheng Yeh,
Modeling of strength of high performance concrete using artificial neural networks, Cement and Concrete Research, 28 (1998), 1797-1808.
doi: 10.1016/S0008-8846(98)00165-3. |
[7] |
F. Coronaa, Z. Zhu, A. H. d. Souza Jr, M. Mulasd, E. Muruf, L. Sassuf, G. Barretob and R. Baratti,
Supervised Distance Preserving Projections: Applications in the quantitative analysis of diesel fuels and light cycle oils from NIR spectra, Journal of Process Control, 30 (2015), 10-21.
doi: 10.1016/j.jprocont.2014.11.005. |
[8] |
J. Eckstein and D. P. Bertsekas,
On the douglas-rachford splitting method and the proximal point algorithm for maximal monotone operators, Mathematical Programming, 55 (1992), 293-318.
doi: 10.1007/BF01581204. |
[9] |
J. Eckstein and M. Fukushima, Some reformulations and applications of the alternating direction method of multipliers, Large Scale Optimization: State of the Art, (1993), 115–134. |
[10] |
J. Eckstein and W. Yao, Understanding the convergence of Alternating Direction Method of Multipliers, Theoritical and Computational Perspectives, RUTCOR Research Report, 2014. Google Scholar |
[11] |
R. A. Fisher,
The use of multiple measurements in taxonomic problems, Annals of Eugenics, 7 (1936), 179-188.
doi: 10.1111/j.1469-1809.1936.tb02137.x. |
[12] |
M. Fortin and R. Glowinski, Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems, North-Holland Publishing Co., Amsterdam, 1983. |
[13] |
M. Fortin and R. Glowinski, On Decomposition-Coordination Methods Using an Augmented Lagrangian, Augmented Lagrangian Methods: Applications to the Solution of Boundary-Value Problems, North-Holland: Amsterdam, 1983. |
[14] |
K. Fukumizu, F. R. Bach and M. Jordan,
Kernel dimension reduction in regression, Annals of Statistics, 37 (2009), 1871-1905.
doi: 10.1214/08-AOS637. |
[15] |
D. Gabay, Applications of the method of multipliers to variational inequalities, in Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems, studies in Mathematics, 15 (1983), 299-331. Google Scholar |
[16] |
D. Gabay and B. Mercier, A dual algorithm for the solution of nonlinearvariational problems via Finite element approximation, Computers and Mathematics with Applications, 2 (1976), 17-40. Google Scholar |
[17] |
R. Glowinski, Lectures on Numerical Methods for Nonlinear Variational Problem, Tata Institute of Fundamental Research Lectures on Mathematics and Physics, Tata Institute of Fundamental Research, Bombay, Notes by M. G. Vijayasundaram and M. Adimurthi, 1980. |
[18] |
R. Glowinski and A. Marrocco, Sur l'approximation, par $\acute{e}l\acute{e}ments$ finis d'ordre un, et la $r\acute{e}$solution, par $p\acute{e}$nalisation-dualit$\acute{e}$, d'une classe de probl$\grave{e}$mes de dirichlet non lin$\acute{e}$ares, Revue Francaise d'Automatique, Informatique et Recherche Op$\acute{e}$rationelle, 9 (1975), 41–76. |
[19] |
R. Glowinski and P. L. Tallec, Augmented Lagrangian Methods for the Solution of Variational Problems, Studies in Applied and Numerical Mathematics, 1989.
doi: 10.1137/1.9781611970838.ch3. |
[20] |
J. Han, M. Kamber and J. Pei, Data Mining: Concepts and Techniques, Springer-Verlag, Berlin, 2011.
doi: 10.1007/978-3-642-19721-5. |
[21] |
B. He, H. Yang and S. Wang, Alternating direction method with self-adaptive penalty parameters for monotone variational inequalities, Journal of Optimization Theory and Applications, 106 (2000), 337–356.
doi: 10.1023/A:1004603514434. |
[22] |
S. Jahan and H. D. Qi,
Regularized Multidimensional Scaling with Radial Basis Functions, Journal of Industrial and Management Optimization, 12 (2016), 543-563.
doi: 10.3934/jimo.2016.12.543. |
[23] |
K. Jiang, D. Sun and K.-C. Toh,
Solving nuclear norm regularized and semidefinite matrix least square problems with linear equality constraints, Discrete Geometry and Optimization, 69 (2013), 133-162.
doi: 10.1007/978-3-319-00200-2_9. |
[24] |
J. Lee and M. Verleysen, Nonlinear Dimensionality Reduction, Springer, New York, 2007.
doi: 10.1007/978-0-387-39351-3. |
[25] |
K. Li,
Sliced inverse regression for dimension reduction, J Am Stat Assoc, 86 (1991), 316-342.
doi: 10.1080/01621459.1991.10475035. |
[26] |
X. Li, D. Sun and K.-C. Toh, A Schur complement based semi-proximal ADMM for convex quadratic conic programming and extensions,, Math. Program., 155 (2016), Ser. A, 333–373.
doi: 10.1007/s10107-014-0850-5. |
[27] |
L. J. P. Maaten, E. Postma and H. V. D. Herik, Dimensionality Reduction: A Comparative Review, Technical Report TiCC-TR 2009–005, Tilburg University Technical, Tilburg, 2009. Google Scholar |
[28] |
S. Mika, G. Ratsch, J. Weston, B. Scholkopf and K. Mullers, Fisher discriminant analysis with kernels, Neural Networks for Signal Processing IX, Proceedings of the IEEE Signal Processing Society Workshop, IEEE, Piscataway, (2002), 41–48.
doi: 10.1109/NNSP.1999.788121. |
[29] |
H.-D. Qi and D. Sun,
An augmented Lagrangian dual approach for the H-weighted nearest correlation matrix problem, IMA Journal of Numerical Analysis, 31 (2011), 491-511.
doi: 10.1093/imanum/drp031. |
[30] |
H.-D. Qi, N. H. Xiu and X. M. Yuan,
A Lagrangian dual approach to the single source localization problem, IEEE Transactions on Signal Processing, 61 (2013), 3815-3826.
doi: 10.1109/TSP.2013.2264814. |
[31] |
R. T. Rockafellar,
Augmented lagrangians and applications of the proximal point algorithm in convex programming, Mathematics of Operations Research, 1 (1976), 97-116.
doi: 10.1287/moor.1.2.97. |
[32] |
S. Roweis and L. Saul, Nonlinear dimensionality reduction by locally linear embedding, Science, 290 (2000), 2323-2326. Google Scholar |
[33] |
B. Schölkopf, A. Smola and K. Müller, Nonlinear component analysis as a kernel eigenvalue problem, Neural Computation, 10 (1998), 1299-1319. Google Scholar |
[34] |
D. Sun, K.-C. Toh and L. Yang,
A convergent 3-block semi-proximal alternating direction method of multipliers for conic programming with 4-type of constraints, SIAM Journal on Optimization, 25 (2015), 882-915.
doi: 10.1137/140964357. |
[35] |
J. Tenenbaum, V. Silva and J. Langford, A global geometric framework for nonlinear dimensionality reduction, Science, 290 (2000), 2319-2323. Google Scholar |
[36] |
S. Theodoridis and K. Koutroumbas, An Introduction to Pattern Recognition, A MATLAB approach, Elsevier Inc., 2010. Google Scholar |
[37] |
S. Theodoridis and K. Koutroumbas, Pattern Recognition, Elsevier Inc., 2009. Google Scholar |
[38] |
A. Tsanas, M. A. Little, P. E. McSharry and L. O. Ramig,
Accurate telemonitoring of Parkinson.s disease progression by non-invasive speech tests, IEEE Transactions on Biomedical Engineering, 57 (2010), 884-893.
doi: 10.1109/TBME.2009.2036000. |
[39] |
J. Venna and S. Kaski,
Comparison of visualization methods for an atlas of gene expression data sets, Inf Vis, 6 (2007), 139-154.
doi: 10.1057/palgrave.ivs.9500153. |
[40] |
H. Wold, Soft modeling by latent variables: The nonlinear iterative partial least squares approach, Perspectives in Probability and Statistics, Papers in Honour of MS Bartlett, 1975,117–142.
doi: 10.1017/s0021900200047604. |
[41] |
H. Wold, Partial Least Squares, Encyclopedia of Statistical Sciences, 2009. Google Scholar |
[42] |
Y. Yeh Y, S. Huang and Y. Lee, Nonlinear dimension reduction with kernel sliced inverse regression, IEEE Trans Knowl Data Eng, 21 (2009), 1590-1603. Google Scholar |
[43] |
Z. Zhu, T. Simil$\ddot{a}$ and F. Corona,
Supervised distance preserving projection, Neural Processing Letters, 38 (2013), 445-463.
doi: 10.1007/s11063-013-9285-x. |
show all references
References:
[1] |
E. Barshan, A. Ghodsi, Z. Azimifar and M. Z. Jahromi,
Supervised principal component analysis: Visualization, classification and regression on subspaces and submanifolds, Pattern Recognit, 44 (2010), 1357-1371.
doi: 10.1016/j.patcog.2010.12.015. |
[2] |
J. Borwein and A. S. Lewis, Convex Analysis and Non Linear Optimization: Theory and Examples, Springer, New York, 2006.
doi: 10.1007/978-0-387-31256-9. |
[3] |
S. Boyd, N. Parikh, E. Chu, B. Peleato and J. Eckstein, Distributed optimization and statistical learning via the alternating direction method of multipliers, Machine Learning, 3 (2010), 1-122. Google Scholar |
[4] |
S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004.
doi: 10.1017/CBO9780511804441.![]() ![]() |
[5] |
M. R. Brito, E. L. Chávez, A. J. Quiroz and J. E. Yukich,
Connectivity of the mutual k-nearest-neighbor graph in clustering and outlier detection, Stat. Probabil. Lett., 35 (1997), 33-42.
doi: 10.1016/S0167-7152(96)00213-1. |
[6] |
I. Cheng Yeh,
Modeling of strength of high performance concrete using artificial neural networks, Cement and Concrete Research, 28 (1998), 1797-1808.
doi: 10.1016/S0008-8846(98)00165-3. |
[7] |
F. Coronaa, Z. Zhu, A. H. d. Souza Jr, M. Mulasd, E. Muruf, L. Sassuf, G. Barretob and R. Baratti,
Supervised Distance Preserving Projections: Applications in the quantitative analysis of diesel fuels and light cycle oils from NIR spectra, Journal of Process Control, 30 (2015), 10-21.
doi: 10.1016/j.jprocont.2014.11.005. |
[8] |
J. Eckstein and D. P. Bertsekas,
On the douglas-rachford splitting method and the proximal point algorithm for maximal monotone operators, Mathematical Programming, 55 (1992), 293-318.
doi: 10.1007/BF01581204. |
[9] |
J. Eckstein and M. Fukushima, Some reformulations and applications of the alternating direction method of multipliers, Large Scale Optimization: State of the Art, (1993), 115–134. |
[10] |
J. Eckstein and W. Yao, Understanding the convergence of Alternating Direction Method of Multipliers, Theoritical and Computational Perspectives, RUTCOR Research Report, 2014. Google Scholar |
[11] |
R. A. Fisher,
The use of multiple measurements in taxonomic problems, Annals of Eugenics, 7 (1936), 179-188.
doi: 10.1111/j.1469-1809.1936.tb02137.x. |
[12] |
M. Fortin and R. Glowinski, Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems, North-Holland Publishing Co., Amsterdam, 1983. |
[13] |
M. Fortin and R. Glowinski, On Decomposition-Coordination Methods Using an Augmented Lagrangian, Augmented Lagrangian Methods: Applications to the Solution of Boundary-Value Problems, North-Holland: Amsterdam, 1983. |
[14] |
K. Fukumizu, F. R. Bach and M. Jordan,
Kernel dimension reduction in regression, Annals of Statistics, 37 (2009), 1871-1905.
doi: 10.1214/08-AOS637. |
[15] |
D. Gabay, Applications of the method of multipliers to variational inequalities, in Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems, studies in Mathematics, 15 (1983), 299-331. Google Scholar |
[16] |
D. Gabay and B. Mercier, A dual algorithm for the solution of nonlinearvariational problems via Finite element approximation, Computers and Mathematics with Applications, 2 (1976), 17-40. Google Scholar |
[17] |
R. Glowinski, Lectures on Numerical Methods for Nonlinear Variational Problem, Tata Institute of Fundamental Research Lectures on Mathematics and Physics, Tata Institute of Fundamental Research, Bombay, Notes by M. G. Vijayasundaram and M. Adimurthi, 1980. |
[18] |
R. Glowinski and A. Marrocco, Sur l'approximation, par $\acute{e}l\acute{e}ments$ finis d'ordre un, et la $r\acute{e}$solution, par $p\acute{e}$nalisation-dualit$\acute{e}$, d'une classe de probl$\grave{e}$mes de dirichlet non lin$\acute{e}$ares, Revue Francaise d'Automatique, Informatique et Recherche Op$\acute{e}$rationelle, 9 (1975), 41–76. |
[19] |
R. Glowinski and P. L. Tallec, Augmented Lagrangian Methods for the Solution of Variational Problems, Studies in Applied and Numerical Mathematics, 1989.
doi: 10.1137/1.9781611970838.ch3. |
[20] |
J. Han, M. Kamber and J. Pei, Data Mining: Concepts and Techniques, Springer-Verlag, Berlin, 2011.
doi: 10.1007/978-3-642-19721-5. |
[21] |
B. He, H. Yang and S. Wang, Alternating direction method with self-adaptive penalty parameters for monotone variational inequalities, Journal of Optimization Theory and Applications, 106 (2000), 337–356.
doi: 10.1023/A:1004603514434. |
[22] |
S. Jahan and H. D. Qi,
Regularized Multidimensional Scaling with Radial Basis Functions, Journal of Industrial and Management Optimization, 12 (2016), 543-563.
doi: 10.3934/jimo.2016.12.543. |
[23] |
K. Jiang, D. Sun and K.-C. Toh,
Solving nuclear norm regularized and semidefinite matrix least square problems with linear equality constraints, Discrete Geometry and Optimization, 69 (2013), 133-162.
doi: 10.1007/978-3-319-00200-2_9. |
[24] |
J. Lee and M. Verleysen, Nonlinear Dimensionality Reduction, Springer, New York, 2007.
doi: 10.1007/978-0-387-39351-3. |
[25] |
K. Li,
Sliced inverse regression for dimension reduction, J Am Stat Assoc, 86 (1991), 316-342.
doi: 10.1080/01621459.1991.10475035. |
[26] |
X. Li, D. Sun and K.-C. Toh, A Schur complement based semi-proximal ADMM for convex quadratic conic programming and extensions,, Math. Program., 155 (2016), Ser. A, 333–373.
doi: 10.1007/s10107-014-0850-5. |
[27] |
L. J. P. Maaten, E. Postma and H. V. D. Herik, Dimensionality Reduction: A Comparative Review, Technical Report TiCC-TR 2009–005, Tilburg University Technical, Tilburg, 2009. Google Scholar |
[28] |
S. Mika, G. Ratsch, J. Weston, B. Scholkopf and K. Mullers, Fisher discriminant analysis with kernels, Neural Networks for Signal Processing IX, Proceedings of the IEEE Signal Processing Society Workshop, IEEE, Piscataway, (2002), 41–48.
doi: 10.1109/NNSP.1999.788121. |
[29] |
H.-D. Qi and D. Sun,
An augmented Lagrangian dual approach for the H-weighted nearest correlation matrix problem, IMA Journal of Numerical Analysis, 31 (2011), 491-511.
doi: 10.1093/imanum/drp031. |
[30] |
H.-D. Qi, N. H. Xiu and X. M. Yuan,
A Lagrangian dual approach to the single source localization problem, IEEE Transactions on Signal Processing, 61 (2013), 3815-3826.
doi: 10.1109/TSP.2013.2264814. |
[31] |
R. T. Rockafellar,
Augmented lagrangians and applications of the proximal point algorithm in convex programming, Mathematics of Operations Research, 1 (1976), 97-116.
doi: 10.1287/moor.1.2.97. |
[32] |
S. Roweis and L. Saul, Nonlinear dimensionality reduction by locally linear embedding, Science, 290 (2000), 2323-2326. Google Scholar |
[33] |
B. Schölkopf, A. Smola and K. Müller, Nonlinear component analysis as a kernel eigenvalue problem, Neural Computation, 10 (1998), 1299-1319. Google Scholar |
[34] |
D. Sun, K.-C. Toh and L. Yang,
A convergent 3-block semi-proximal alternating direction method of multipliers for conic programming with 4-type of constraints, SIAM Journal on Optimization, 25 (2015), 882-915.
doi: 10.1137/140964357. |
[35] |
J. Tenenbaum, V. Silva and J. Langford, A global geometric framework for nonlinear dimensionality reduction, Science, 290 (2000), 2319-2323. Google Scholar |
[36] |
S. Theodoridis and K. Koutroumbas, An Introduction to Pattern Recognition, A MATLAB approach, Elsevier Inc., 2010. Google Scholar |
[37] |
S. Theodoridis and K. Koutroumbas, Pattern Recognition, Elsevier Inc., 2009. Google Scholar |
[38] |
A. Tsanas, M. A. Little, P. E. McSharry and L. O. Ramig,
Accurate telemonitoring of Parkinson.s disease progression by non-invasive speech tests, IEEE Transactions on Biomedical Engineering, 57 (2010), 884-893.
doi: 10.1109/TBME.2009.2036000. |
[39] |
J. Venna and S. Kaski,
Comparison of visualization methods for an atlas of gene expression data sets, Inf Vis, 6 (2007), 139-154.
doi: 10.1057/palgrave.ivs.9500153. |
[40] |
H. Wold, Soft modeling by latent variables: The nonlinear iterative partial least squares approach, Perspectives in Probability and Statistics, Papers in Honour of MS Bartlett, 1975,117–142.
doi: 10.1017/s0021900200047604. |
[41] |
H. Wold, Partial Least Squares, Encyclopedia of Statistical Sciences, 2009. Google Scholar |
[42] |
Y. Yeh Y, S. Huang and Y. Lee, Nonlinear dimension reduction with kernel sliced inverse regression, IEEE Trans Knowl Data Eng, 21 (2009), 1590-1603. Google Scholar |
[43] |
Z. Zhu, T. Simil$\ddot{a}$ and F. Corona,
Supervised distance preserving projection, Neural Processing Letters, 38 (2013), 445-463.
doi: 10.1007/s11063-013-9285-x. |





Dataset | Dim | Class | no. of ins. | Source | |
Classification | Seismic bump | 19 | 2 | 2584 | UCI Repository |
Cardiotocography | 21 | 3 | 2126 | UCI Repository | |
Diabetic Retinopathy | 19 | 2 | 1115 | UCI Repository | |
Mushroom | 22 | 2 | 8124 | UCI Repository | |
Regression | Parkinson's Telemonitoring | 16 | - | 5875 | UCI Repository |
Concrete Compressive Strength | 8 | - | 1030 | UCI Repository |
Dataset | Dim | Class | no. of ins. | Source | |
Classification | Seismic bump | 19 | 2 | 2584 | UCI Repository |
Cardiotocography | 21 | 3 | 2126 | UCI Repository | |
Diabetic Retinopathy | 19 | 2 | 1115 | UCI Repository | |
Mushroom | 22 | 2 | 8124 | UCI Repository | |
Regression | Parkinson's Telemonitoring | 16 | - | 5875 | UCI Repository |
Concrete Compressive Strength | 8 | - | 1030 | UCI Repository |
Method | RMSE (mean |
MAE (mean |
SLS-SDPP | 10.6781 |
8.3503 |
SDPP | 10.7934 |
8.7459 |
PLS | 10.8133 |
8.7822 |
SPCA | 10.8006 |
8.7714 |
KDR | 10.8478 |
8.8008 |
Method | RMSE (mean |
MAE (mean |
SLS-SDPP | 10.6781 |
8.3503 |
SDPP | 10.7934 |
8.7459 |
PLS | 10.8133 |
8.7822 |
SPCA | 10.8006 |
8.7714 |
KDR | 10.8478 |
8.8008 |
Error | Dim | SLS-SDPP | SDPP | PLS | SPCA | KDR |
RMSE | 1 | 10.4649 |
10.5241 |
12.7666 |
12.8090 |
13.7423 |
2 | 10.4540 |
10.4075 |
11.8629 |
12.8712 |
11.6399 |
|
3 | 10.4629 |
10.4079 |
10.9379 |
12.8370 |
11.5163 |
|
4 | 10.4450 |
10.5890 |
10.5108 |
12.8674 |
11.0320 |
|
5 | 10.2932 |
10.7247 |
10.4432 |
12.9647 |
10.2933 |
|
6 | 10.9910 |
10.4893 |
10.4359 |
10.4770 |
10.4473 |
|
7 | 10.4495 |
10.5313 |
10.4480 |
10.4520 |
10.4514 |
|
8 | 10.4349 |
10.4342 |
10.4342 |
10.4342 |
16.3019 |
|
MAE | 1 | 8.3879 |
8.3687 |
10.3995 |
10.4451 |
10.8884 |
2 | 8.2339 |
8.2338 |
9.3977 |
10.4484 |
9.2285 |
|
3 | 8.2288 |
8.2342 |
8.3771 |
10.4125 |
8.9818 |
|
4 | 8.5898 |
8.3935 |
8.2199 |
10.4553 |
8.6622 |
|
5 | 8.0177 |
8.5133 |
8.1563 |
10.5221 |
8.0167 |
|
6 | 8.3434 |
8.2713 |
8.1612 |
8.1860 |
8.1659 |
|
7 | 8.2747 |
8.2820 |
8.1869 |
8.1872 |
8.1868 |
|
8 | 8.1852 |
8.1842 |
8.1842 |
8.1842 |
13.1814 |
Error | Dim | SLS-SDPP | SDPP | PLS | SPCA | KDR |
RMSE | 1 | 10.4649 |
10.5241 |
12.7666 |
12.8090 |
13.7423 |
2 | 10.4540 |
10.4075 |
11.8629 |
12.8712 |
11.6399 |
|
3 | 10.4629 |
10.4079 |
10.9379 |
12.8370 |
11.5163 |
|
4 | 10.4450 |
10.5890 |
10.5108 |
12.8674 |
11.0320 |
|
5 | 10.2932 |
10.7247 |
10.4432 |
12.9647 |
10.2933 |
|
6 | 10.9910 |
10.4893 |
10.4359 |
10.4770 |
10.4473 |
|
7 | 10.4495 |
10.5313 |
10.4480 |
10.4520 |
10.4514 |
|
8 | 10.4349 |
10.4342 |
10.4342 |
10.4342 |
16.3019 |
|
MAE | 1 | 8.3879 |
8.3687 |
10.3995 |
10.4451 |
10.8884 |
2 | 8.2339 |
8.2338 |
9.3977 |
10.4484 |
9.2285 |
|
3 | 8.2288 |
8.2342 |
8.3771 |
10.4125 |
8.9818 |
|
4 | 8.5898 |
8.3935 |
8.2199 |
10.4553 |
8.6622 |
|
5 | 8.0177 |
8.5133 |
8.1563 |
10.5221 |
8.0167 |
|
6 | 8.3434 |
8.2713 |
8.1612 |
8.1860 |
8.1659 |
|
7 | 8.2747 |
8.2820 |
8.1869 |
8.1872 |
8.1868 |
|
8 | 8.1852 |
8.1842 |
8.1842 |
8.1842 |
13.1814 |
Error | Dim | SLS-SDPP | SDPP | SPCA | KDR | FDA |
Error Rate | 2 | 0.2251 | 0.2865 | 0.2739 | 0.2593 | 0.208 |
3 | 0.1940 | 0.2827 | 0.2661 | 0.2992 | 0.208 | |
4 | 0.1949 | 0.2943 | 0.3314 | 0.2427 | 0.208 | |
5 | 0.1969 | 0.2661 | 0.3372 | 0.2437 | 0.208 | |
6 | 0.1969 | 0.2749 | 0.2710 | 0.2115 | 0.208 | |
7 | 0.1988 | 0.2827 | 0.2768 | 0.2193 | 0.208 | |
8 | 0.1979 | 0.2768 | 0.2817 | 0.2300 | 0.208 | |
9 | 0.1988 | 0.2700 | 0.2612 | 0.2315 | 0.208 | |
10 | 0.1949 | 0.2690 | 0.2515 | 0.2412 | 0.208 |
Error | Dim | SLS-SDPP | SDPP | SPCA | KDR | FDA |
Error Rate | 2 | 0.2251 | 0.2865 | 0.2739 | 0.2593 | 0.208 |
3 | 0.1940 | 0.2827 | 0.2661 | 0.2992 | 0.208 | |
4 | 0.1949 | 0.2943 | 0.3314 | 0.2427 | 0.208 | |
5 | 0.1969 | 0.2661 | 0.3372 | 0.2437 | 0.208 | |
6 | 0.1969 | 0.2749 | 0.2710 | 0.2115 | 0.208 | |
7 | 0.1988 | 0.2827 | 0.2768 | 0.2193 | 0.208 | |
8 | 0.1979 | 0.2768 | 0.2817 | 0.2300 | 0.208 | |
9 | 0.1988 | 0.2700 | 0.2612 | 0.2315 | 0.208 | |
10 | 0.1949 | 0.2690 | 0.2515 | 0.2412 | 0.208 |
Error | Dim | SLS-SDPP | SDPP | SPCA | KDR | FDA |
Error Rate | 1 | 0.0328 | 0.0328 | 0.0328 | 0.0328 | 0.0328 |
2 | 0.0701 | 0.0707 | 0.1004 | 0.0688 | 0.0328 | |
3 | 0.0701 | 0.0669 | 0.0694 | 0.0669 | 0.0328 | |
4 | 0.0701 | 0.0720 | 0.0676 | 0.0720 | 0.032 | |
5 | 0.0701 | 0.0720 | 0.0732 | 0.0726 | 0.0328 | |
6 | 0.0701 | 0.0713 | 0.0789 | 0.0728 | 0.0328 | |
7 | 0.0701 | 0.0713 | 0.0789 | 0.0727 | 0.0328 | |
8 | 0.0701 | 0.0713 | 0.0795 | 0.0729 | 0.0328 | |
9 | 0.0701 | 0.0713 | 0.0795 | 0.0730 | 0.0328 | |
10 | 0.0701 | 0.0713 | 0.0795 | 0.0730 | 0.0328 |
Error | Dim | SLS-SDPP | SDPP | SPCA | KDR | FDA |
Error Rate | 1 | 0.0328 | 0.0328 | 0.0328 | 0.0328 | 0.0328 |
2 | 0.0701 | 0.0707 | 0.1004 | 0.0688 | 0.0328 | |
3 | 0.0701 | 0.0669 | 0.0694 | 0.0669 | 0.0328 | |
4 | 0.0701 | 0.0720 | 0.0676 | 0.0720 | 0.032 | |
5 | 0.0701 | 0.0720 | 0.0732 | 0.0726 | 0.0328 | |
6 | 0.0701 | 0.0713 | 0.0789 | 0.0728 | 0.0328 | |
7 | 0.0701 | 0.0713 | 0.0789 | 0.0727 | 0.0328 | |
8 | 0.0701 | 0.0713 | 0.0795 | 0.0729 | 0.0328 | |
9 | 0.0701 | 0.0713 | 0.0795 | 0.0730 | 0.0328 | |
10 | 0.0701 | 0.0713 | 0.0795 | 0.0730 | 0.0328 |
Error | Dim | SLS-SDPP | SDPP | SPCA | KDR | FDA |
Error Rate | 1 | 0.6382 | 0.6382 | 0.6382 | 0.6382 | 0.6382 |
2 | 0.2678 | 0.3390 | 0.2963 | 0.2934 | 0.6382 | |
3 | 0.2678 | 0.3105 | 0.3618 | 0.2963 | 0.6382 | |
4 | 0.2678 | 0.3191 | 0.2877 | 0.3048 | 0.6382 | |
5 | 0.2678 | 0.2934 | 0.2906 | 0.3134 | 0.6382 | |
6 | 0.2678 | 0.2849 | 0.2877 | 0.3048 | 0.6382 | |
7 | 0.2735 | 0.3191 | 0.2963 | 0.3048 | 0.6382 | |
8 | 0.2707 | 0.3191 | 0.2934 | 0.3134 | 0.6382 | |
9 | 0.2707 | 0.2906 | 0.2906 | 0.3134 | 0.6382 | |
10 | 0.2678 | 0.3020 | 0.3077 | 0.3048 | 0.6382 |
Error | Dim | SLS-SDPP | SDPP | SPCA | KDR | FDA |
Error Rate | 1 | 0.6382 | 0.6382 | 0.6382 | 0.6382 | 0.6382 |
2 | 0.2678 | 0.3390 | 0.2963 | 0.2934 | 0.6382 | |
3 | 0.2678 | 0.3105 | 0.3618 | 0.2963 | 0.6382 | |
4 | 0.2678 | 0.3191 | 0.2877 | 0.3048 | 0.6382 | |
5 | 0.2678 | 0.2934 | 0.2906 | 0.3134 | 0.6382 | |
6 | 0.2678 | 0.2849 | 0.2877 | 0.3048 | 0.6382 | |
7 | 0.2735 | 0.3191 | 0.2963 | 0.3048 | 0.6382 | |
8 | 0.2707 | 0.3191 | 0.2934 | 0.3134 | 0.6382 | |
9 | 0.2707 | 0.2906 | 0.2906 | 0.3134 | 0.6382 | |
10 | 0.2678 | 0.3020 | 0.3077 | 0.3048 | 0.6382 |
Error | Dim | SLS-SDPP | SDPP | SPCA | KDR | FDA |
Error Rate | 1 | 0.2486 | 0.2486 | 0.2486 | 0.2486 | 0.2486 |
2 | 0.3555 | 0.1318 | 0.2735 | 0.3037 | 0.2486 | |
3 | 0.2891 | 0.1266 | 0.1836 | 0.2741 | 0.2486 | |
4 | 0.1516 | 0.2076 | 0.2020 | 0.2018 | 0.2486 | |
5 | 0.1648 | 0.2524 | 0.1911 | 0.2311 | 0.2486 | |
6 | 0.1667 | 0.2524 | 0.3785 | 0.3815 | 0.2486 | |
7 | 0.1723 | 0.2693 | 0.3653 | 0.3544 | 0.2486 | |
8 | 0.1728 | 0.2255 | 0.3630 | 0.2587 | 0.2486 | |
9 | 0.1186 | 0.2655 | 0.1756 | 0.1615 | 0.2486 | |
10 | 0.1427 | 0.2665 | 0.3545 | 0.2812 | 0.2486 |
Error | Dim | SLS-SDPP | SDPP | SPCA | KDR | FDA |
Error Rate | 1 | 0.2486 | 0.2486 | 0.2486 | 0.2486 | 0.2486 |
2 | 0.3555 | 0.1318 | 0.2735 | 0.3037 | 0.2486 | |
3 | 0.2891 | 0.1266 | 0.1836 | 0.2741 | 0.2486 | |
4 | 0.1516 | 0.2076 | 0.2020 | 0.2018 | 0.2486 | |
5 | 0.1648 | 0.2524 | 0.1911 | 0.2311 | 0.2486 | |
6 | 0.1667 | 0.2524 | 0.3785 | 0.3815 | 0.2486 | |
7 | 0.1723 | 0.2693 | 0.3653 | 0.3544 | 0.2486 | |
8 | 0.1728 | 0.2255 | 0.3630 | 0.2587 | 0.2486 | |
9 | 0.1186 | 0.2655 | 0.1756 | 0.1615 | 0.2486 | |
10 | 0.1427 | 0.2665 | 0.3545 | 0.2812 | 0.2486 |
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