(no subject)
Multilinear estimation.
Some applications.
Bilinear models.
R.W.Brockett, D.Dobkin (1978) "On the Optimal
Evaluation of a Set of Bilinear Forms" Linear
Algebra and its Applications, 19(3):207-235.
D.H. Marimont, B.A. Wandell (1992) "Linear
models of surface and illuminant spectra"
J.Opt.Sot.Am. A, 9(11):1905-1913.
Tomasi, G. (2006) "Practical and computational
aspects in chemometric data analysis" PhD Th.,
The Royal Veterinary and Agricultural
University, Frederiksberg, Denmark.
Stensholt, B.K., Tjostheim, D. (1987) "Multiple
bilinear time series models" J.T.Ser.An. 8(2):221-233.
S.Ullman, R.Basri (1989) "Recognition by linear
combinations of models" MIT AI Lab Memo No.1152.
Freeman, W.T., Tenenbaum, J.B. (1997) "Learning
bilinear models for two-factor problems in vision"
Proc. of IEEE Comp. Soc. Conf. on Comp.
Vis. and Pattern Rec., pp.:554 - 560.
J.B. Tenenbaum, W.T. Freeman (2000)
"Separating style and content with bilinear
models" Neural Computat., 12(6):1247-1283.
Y.Dai, L.Billard (1998) "A Space-Time Bilinear Model
and its Identification" J.T.Ser.An. 19(6):657-679.
T.Grahn (1995) "A Conditional Least Squares
approach to bilinear time series estimation."
J. of Time Ser. An., 16(5):509-529.
M.Linder, R.Sundberg (1998) "Second-order
calibration: bilinear least squares
regression and a simple alternative"
Chemometrics and Intelligent
Laboratory Systems, 42:159-178.
D.B. Grimes, R.P.N.Rao (2002) "A Bilinear
Model for Sparse Coding" NIPS.
D.B. Grimes, R.P.N.Rao (2005) "Bilinear Sparse
Coding for Invariant Vision" Neural Comp. 17:47-73.
C.W.J.Granger, A.P.Andersen (1978) "Introduction
to Bilinear Time Series Models" Vandenhoeck &
Ruprect, Goittingen.
T. Subba Rao, M. Gabr "An introduction
to bispectral analysis and bilinear time
series models" Lectures Notes in Stat.,
Springer-Verlag, Berlin, Vol. 24.
T. Subba Rao (1981) "On the Theory of
Bilinear Time Series Models" J. of the
Royal Stat. Soc. Ser.B 43(2):244-255.
See also.
Tucker Model (PARAFAC, etc.).
Bro, R. de Jong, S. (1997) "A fast non-negativity-
constrained least squares algorithm"
J. of Chemometrics, 11(5):393-401.
Bro, R. (1998) "Multi-way Analysis
in the Food Industry" PhD thesis.
C.A. Andersson, R.Bro (1998) "Improving the speed of
multi-way algorithms: Part I. Tucker3" Chemometrics
and Intelligent Laboratory Systems 42,1998. 93-103.
Smilde, A. K., Tauler, R., Saurina, J., Bro, R. (1999)
"Calibration methods for complex second-order data"
Analytica Chimica Acta, 398:237-251.
Bro, R., Andersson, C., Kiers, H. (1999) "Parafac2 -
part II. modeling chromatographic data with retention
time shifts" Journal of Chemometrics, 13(3-4):295-309.
Bro, R. Andersson, C.A. (2000) "The n-way toolbox for Matlab"
Chemometrics and Intelligent Laboratory Systems, 52(1):1-4.
R.Bro, N.D.Sidiropoulos, A.K.Smilde (2002) "Maximum
likeihood fitting using ordinary least squares
algorithms" J. Chemometrics, 16(8-10): 387-400.
R.Bro, A.K.Smilde (2003) "Centering and scaling in
component analysis" J. Chemometrics, 17(1): 16-33.
Bro, R. Kiers, H.A.L. (2003) "A new efficient method
for determining the number of components in parafac
models" Journal of Chemometrics, 17(5):274-286.
A.K.Smilde, J.A.Westerhuis, S. de Jong (2003)
"A framework for sequential multiblock component
methods" J. Chemometrics; 17(6):323-337.
Smilde, A., Bro, R., Geladi, P. (2004) "Multi-way Analysis:
Applications in the Chemical Sciences" Wiley.
Stoica, P., Viberg, M. (1996) "Maximum likelihood
parameter and rank estimation in reduced-rank multivariate
linear regressions" IEEE Trans. on Sign.Proc. 44, 3069-3078.
Lim, L.-H., Comon, P. (2009) "Nonnegative approximations
of nonnegative tensors" J. Chemometrics 2009; 23: 432-441.
A.H.Phan, A.Cichocki (2009) "Analysis of Interactions Among
Hidden Components for Tucker Model" APSIPA Conf., pp.154-158.
A.H.Phan, A.Cichocki (2011) "Extended HALS algorithm for
nonnegative Tucker decomposition and its applications for
multiway analysis and classification" Neurocomp. 74(11):1956ff.
M.Mørup, L.K.Hansen, S.M.Arnfred, L.-H.Lim, K.H.Madsen
(2008) "Shift-invariant multilinear decomposition of
neuroimaging data" NeuroImage 42, 1439-1450.
H.Lu, K.N.Plataniotis, A.N.Venetsanopoulos (2006)
"Multilinear Principal Component Analysis of Tensor
Objects for Recognition" Proc. of the Int. Conf.
on Pattern Recognition (ICPR’06).
M.A.O.Vasilescu (2002) "Human Motion Signatures:
Analysis, Synthesis, Recognition" Proc. of the Int.
Conf. on Pattern Recognition (ICPR’02), 3:456-460.
M.A.O.Vasilescu, D.Terzopoulos (2005) "Multilinear
Independent Components Analysis" (CVPR 2005).
N.D. Sidiropoulos (2004) "Low-rank decomposition of
multi-way arrays: a signal processing perspective."
Some applications.
Bilinear models.
R.W.Brockett, D.Dobkin (1978) "On the Optimal
Evaluation of a Set of Bilinear Forms" Linear
Algebra and its Applications, 19(3):207-235.
D.H. Marimont, B.A. Wandell (1992) "Linear
models of surface and illuminant spectra"
J.Opt.Sot.Am. A, 9(11):1905-1913.
Tomasi, G. (2006) "Practical and computational
aspects in chemometric data analysis" PhD Th.,
The Royal Veterinary and Agricultural
University, Frederiksberg, Denmark.
Stensholt, B.K., Tjostheim, D. (1987) "Multiple
bilinear time series models" J.T.Ser.An. 8(2):221-233.
S.Ullman, R.Basri (1989) "Recognition by linear
combinations of models" MIT AI Lab Memo No.1152.
Freeman, W.T., Tenenbaum, J.B. (1997) "Learning
bilinear models for two-factor problems in vision"
Proc. of IEEE Comp. Soc. Conf. on Comp.
Vis. and Pattern Rec., pp.:554 - 560.
J.B. Tenenbaum, W.T. Freeman (2000)
"Separating style and content with bilinear
models" Neural Computat., 12(6):1247-1283.
Y.Dai, L.Billard (1998) "A Space-Time Bilinear Model
and its Identification" J.T.Ser.An. 19(6):657-679.
T.Grahn (1995) "A Conditional Least Squares
approach to bilinear time series estimation."
J. of Time Ser. An., 16(5):509-529.
M.Linder, R.Sundberg (1998) "Second-order
calibration: bilinear least squares
regression and a simple alternative"
Chemometrics and Intelligent
Laboratory Systems, 42:159-178.
D.B. Grimes, R.P.N.Rao (2002) "A Bilinear
Model for Sparse Coding" NIPS.
D.B. Grimes, R.P.N.Rao (2005) "Bilinear Sparse
Coding for Invariant Vision" Neural Comp. 17:47-73.
C.W.J.Granger, A.P.Andersen (1978) "Introduction
to Bilinear Time Series Models" Vandenhoeck &
Ruprect, Goittingen.
T. Subba Rao, M. Gabr "An introduction
to bispectral analysis and bilinear time
series models" Lectures Notes in Stat.,
Springer-Verlag, Berlin, Vol. 24.
T. Subba Rao (1981) "On the Theory of
Bilinear Time Series Models" J. of the
Royal Stat. Soc. Ser.B 43(2):244-255.
See also.
Tucker Model (PARAFAC, etc.).
Bro, R. de Jong, S. (1997) "A fast non-negativity-
constrained least squares algorithm"
J. of Chemometrics, 11(5):393-401.
Bro, R. (1998) "Multi-way Analysis
in the Food Industry" PhD thesis.
C.A. Andersson, R.Bro (1998) "Improving the speed of
multi-way algorithms: Part I. Tucker3" Chemometrics
and Intelligent Laboratory Systems 42,1998. 93-103.
Smilde, A. K., Tauler, R., Saurina, J., Bro, R. (1999)
"Calibration methods for complex second-order data"
Analytica Chimica Acta, 398:237-251.
Bro, R., Andersson, C., Kiers, H. (1999) "Parafac2 -
part II. modeling chromatographic data with retention
time shifts" Journal of Chemometrics, 13(3-4):295-309.
Bro, R. Andersson, C.A. (2000) "The n-way toolbox for Matlab"
Chemometrics and Intelligent Laboratory Systems, 52(1):1-4.
R.Bro, N.D.Sidiropoulos, A.K.Smilde (2002) "Maximum
likeihood fitting using ordinary least squares
algorithms" J. Chemometrics, 16(8-10): 387-400.
R.Bro, A.K.Smilde (2003) "Centering and scaling in
component analysis" J. Chemometrics, 17(1): 16-33.
Bro, R. Kiers, H.A.L. (2003) "A new efficient method
for determining the number of components in parafac
models" Journal of Chemometrics, 17(5):274-286.
A.K.Smilde, J.A.Westerhuis, S. de Jong (2003)
"A framework for sequential multiblock component
methods" J. Chemometrics; 17(6):323-337.
Smilde, A., Bro, R., Geladi, P. (2004) "Multi-way Analysis:
Applications in the Chemical Sciences" Wiley.
Stoica, P., Viberg, M. (1996) "Maximum likelihood
parameter and rank estimation in reduced-rank multivariate
linear regressions" IEEE Trans. on Sign.Proc. 44, 3069-3078.
Lim, L.-H., Comon, P. (2009) "Nonnegative approximations
of nonnegative tensors" J. Chemometrics 2009; 23: 432-441.
A.H.Phan, A.Cichocki (2009) "Analysis of Interactions Among
Hidden Components for Tucker Model" APSIPA Conf., pp.154-158.
A.H.Phan, A.Cichocki (2011) "Extended HALS algorithm for
nonnegative Tucker decomposition and its applications for
multiway analysis and classification" Neurocomp. 74(11):1956ff.
M.Mørup, L.K.Hansen, S.M.Arnfred, L.-H.Lim, K.H.Madsen
(2008) "Shift-invariant multilinear decomposition of
neuroimaging data" NeuroImage 42, 1439-1450.
H.Lu, K.N.Plataniotis, A.N.Venetsanopoulos (2006)
"Multilinear Principal Component Analysis of Tensor
Objects for Recognition" Proc. of the Int. Conf.
on Pattern Recognition (ICPR’06).
M.A.O.Vasilescu (2002) "Human Motion Signatures:
Analysis, Synthesis, Recognition" Proc. of the Int.
Conf. on Pattern Recognition (ICPR’02), 3:456-460.
M.A.O.Vasilescu, D.Terzopoulos (2005) "Multilinear
Independent Components Analysis" (CVPR 2005).
N.D. Sidiropoulos (2004) "Low-rank decomposition of
multi-way arrays: a signal processing perspective."