H. Akaike, A new look at the statistical model identification, IEEE Transactions on Automatic Control, vol.19, issue.6, pp.716-723, 1974.

T. Ando, Bayesian factor analysis with fat-tailed factors and its exact marginal likelihood, Journal of Multivariate Analysis, vol.100, issue.8, pp.1717-1726, 2009.

C. Archambeau and F. Bach, Sparse probabilistic projections, Advances in neural information processing systems, pp.73-80, 2009.

J. Bai and S. Ng, Determining the number of factors in approximate factor models. Econometrica, vol.70, pp.191-221, 2002.

Z. Bai, K. P. Choi, and Y. Fujikoshi, Consistency of AIC and BIC in estimating the number of significant components in high-dimensional principal component analysis, The Annals of Statistics, vol.46, issue.3, pp.1050-1076, 2018.

C. M. Bishop and P. Bayesian, Advances in Neural Information Processing Systems, pp.382-388, 1999.

C. Bouveyron, S. Girard, and C. Schmid, High-dimensional data clustering, Computational Statistics & Data Analysis, vol.52, issue.1, pp.502-519, 2007.
URL : https://hal.archives-ouvertes.fr/inria-00548573

C. Bouveyron, G. Celeux, and S. Girard, Intrinsic dimension estimation by maximum likelihood in isotropic probabilistic PCA, Pattern Recognition Letters, vol.32, issue.14, pp.1706-1713, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00440372

C. Bouveyron, P. Latouche, and P. Mattei, Bayesian variable selection for globally sparse probabilistic PCA, Electronic Journal of Statistics, vol.12, issue.2, pp.3036-3070, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01310409

R. Bro, K. Kjeldahl, A. K. Smilde, and H. A. Kiers, Cross-validation of component models: a critical look at current methods, Analytical and bioanalytical chemistry, vol.390, issue.5, pp.1241-1251, 2008.

R. B. Cattell, The scree test for the number of factors, Multivariate behavioral research, vol.1, issue.2, pp.245-276, 1966.

T. Chan, K. Jia, S. Gao, J. Lu, Z. Zeng et al., PCANet: A simple deep learning baseline for image classification?, IEEE Transactions on Image Processing, vol.24, issue.12, pp.5017-5032, 2015.

C. Deledalle, J. Salmon, and A. S. Dalalyan, Image denoising with patch based PCA: local versus global, Proceedings of the British Machine Vision Conference, vol.10, pp.25-26, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00654289

P. Ding and J. K. Blitzstein, On the Gaussian mixture representation of the Laplace distribution, The American Statistician, 2017.

M. Drton and M. Plummer, A Bayesian information criterion for singular models (with discussion), Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.79, issue.2, pp.323-380, 2017.

N. Evangelopoulos, X. Zhang, and V. R. Prybutok, Latent semantic analysis: five methodological recommendations, European Journal of Information Systems, vol.21, issue.1, pp.70-86, 2012.

P. Fogel, S. S. Young, D. M. Hawkins, and N. Ledirac, Inferential, robust non-negative matrix factorization analysis of microarray data, Bioinformatics, vol.23, issue.1, p.44, 2007.

N. Friel and J. Wyse, Estimating the evidence-a review, Statistica Neerlandica, vol.66, issue.3, pp.288-308, 2012.

M. Gavish and D. L. Donoho, The optimal hard threshold for singular values is 4/ ? 3, IEEE Transactions on Information Theory, vol.60, issue.8, pp.5040-5053, 2014.

E. I. George and R. E. Mcculloch, Variable selection via gibbs sampling, Journal of the American Statistical Association, vol.88, issue.423, pp.881-889, 1993.

A. Hannachi, I. T. Jolliffe, D. B. Stephenson, and N. Trendafilov, In search of simple structures in climate: simplifying EOFs, International journal of climatology, vol.26, issue.1, pp.7-28, 2006.

J. A. Hoeting, D. Madigan, A. E. Raftery, and C. T. Volinsky, Bayesian model averaging: a tutorial, Statistical Science, pp.382-401, 1999.

P. D. Hoff, Model averaging and dimension selection for the singular value decomposition, Journal of the American Statistical Association, vol.102, issue.478, pp.674-685, 2007.

H. Hotelling, Analysis of a complex of statistical variables into principal components, Journal of educational psychology, vol.24, issue.6, p.417, 1933.

D. C. Hoyle, Automatic PCA dimension selection for high dimensional data and small sample sizes, Journal of Machine Learning Research, vol.9, pp.2733-2759, 2008.

D. A. Jackson, Stopping rules in principal components analysis: a comparison of heuristical and statistical approaches, Ecology, vol.74, issue.8, pp.2204-2214, 1993.

I. T. Jolliffe, Principal component analysis, 2002.

I. T. Jolliffe and J. Cadima, Principal component analysis: a review and recent developments, Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol.374, 2016.

J. Josse and F. Husson, Selecting the number of components in principal component analysis using cross-validation approximations, Computational Statistics & Data Analysis, vol.56, issue.6, pp.1869-1879, 2012.

R. E. Kass and A. E. Raftery, Bayes factors, Journal of the american statistical association, vol.90, issue.430, pp.773-795, 1995.

R. E. Kass and D. Steffey, Approximate Bayesian inference in conditionally independent hierarchical models (parametric empirical Bayes models), Journal of the American Statistical Association, vol.84, issue.407, pp.717-726, 1989.

D. Knowles and Z. Ghahramani, Nonparametric Bayesian sparse factor models with application to gene expression modeling, The Annals of Applied Statistics, pp.1534-1552, 2011.

S. Kotz, T. Kozubowski, and K. Podgórski, The Laplace distribution and generalizations: a revisit with applications to communications, exonomics, engineering, and finance. Number 183, 2001.

T. Kozubowski, K. Podgórski, and I. Rychlik, Multivariate generalized Laplace distribution and related random fields, Journal of Multivariate Analysis, vol.113, pp.59-72, 2013.

D. N. Lawley, A modified method of estimation in factor analysis and some large sample results, Proceedings of the Uppsala Symposium on Psychological Factor Analysis, pp.35-42, 1953.

S. Lin, B. Sturmfels, and Z. Xu, Marginal likelihood integrals for mixtures of independence models, Journal of Machine Learning Research, vol.10, pp.1611-1631, 2009.

M. Mäechler, Bessel: Bessel -Bessel Functions Computations and Approximations, pp.5-5, 2013.

P. Mattei, Multiplying a Gaussian matrix by a Gaussian vector, Statistics & Probability Letters, vol.128, pp.67-70, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01462941

T. P. Minka, Automatic choice of dimensionality for PCA, Advances in Neural Information Processing Systems, vol.13, pp.598-604, 2000.

A. Mnih and R. R. Salakhutdinov, Probabilistic matrix factorization, Advances in Neural Information Processing Systems, pp.1257-1264, 2008.

K. P. Murphy, Conjugate Bayesian analysis of the Gaussian distribution, 2007.

S. Nakajima, R. Tomioka, M. Sugiyama, and S. D. Babacan, Condition for perfect dimensionality recovery by variational Bayesian PCA, Journal of Machine Learning Research, vol.16, pp.3757-3811, 2015.

D. Passemier, Z. Li, and J. Yao, On estimation of the noise variance in high dimensional probabilistic principal component analysis, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.79, issue.1, pp.51-67, 2017.
URL : https://hal.archives-ouvertes.fr/hal-00851783

K. Pearson, On lines and planes of closest fit to systems of point in space, Philosophical Magazine, vol.2, issue.11, pp.559-572, 1901.

M. Ringnér, What is principal component analysis?, Nature biotechnology, vol.26, issue.3, pp.303-304, 2008.

G. Schwarz, Estimating the dimension of a model, The Annals of Statistics, vol.6, issue.2, pp.461-464, 1978.

P. Sobczyk, M. Bogdan, and J. Josse, Bayesian dimensionality reduction with PCA using penalized semi-integrated likelihood, Journal of Computational and Graphical Statistics, vol.26, issue.4, pp.826-839, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01342815

C. M. Theobald, An inequality with application to multivariate analysis, Biometrika, vol.62, issue.2, pp.461-466, 1975.

M. E. Tipping and C. M. Bishop, Probabilistic principal component analysis, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.61, issue.3, pp.611-622, 1999.

M. O. Ulfarsson and V. Solo, Dimension estimation in noisy PCA with SURE and random matrix theory, IEEE Transactions on Signal Processing, vol.56, issue.12, pp.5804-5816, 2008.

S. Wold, Cross-validatory estimation of the number of components in factor and principal components models, Technometrics, vol.20, issue.4, pp.397-405, 1978.

Y. Zhang and L. E. Ghaoui, Large-scale sparse principal component analysis with application to text data, Advances in Neural Information Processing Systems, pp.532-539, 2011.

M. Zhu and A. Ghodsi, Automatic dimensionality selection from the scree plot via the use of profile likelihood, Computational Statistics & Data Analysis, vol.51, issue.2, pp.918-930, 2006.