Abstract
Component Analysis (CA) consists of a set of statistical techniques that decompose data to appropriate latent components that are relevant to the task-at-hand (e.g., clustering, segmentation, classification). During the past years, an explosion of research in probabilistic CA has been witnessed, with the introduction of several novel methods (e.g., Probabilistic Principal Component Analysis, Probabilistic Linear Discriminant Analysis (PLDA), Probabilistic Canonical Correlation Analysis). A particular subset of CA methods such as PLDA, inspired by the classical Linear Discriminant Analysis, incorporate the knowledge of data labeled in terms of an attribute in order to extract a suitable discriminative subspace. Nevertheless, while many modern datasets incorporate labels with regards to multiple attributes (e.g., age, ethnicity, weight), existing CA methods can exploit at most a single attribute (i.e., one set of labels) per model. That is, in case multiple attributes are available, one needs to train a separate model per attribute, in effect not exploiting knowledge of other attributes for the task-at-hand. In this light, we propose the first, to the best of our knowledge, Multi-Attribute Probabilistic LDA (MAPLDA), that is able to jointly handle data annotated with multiple attributes. We demonstrate the performance of the proposed method on the analysis of 3D facial shapes, a task with increasing value due to the rising popularity of consumer-grade 3D sensors, on problems such as ethnicity, age, and weight identification, as well as 3D facial shape generation.
Supported by an EPSRC DTA studentship from Imperial College London, EPSRC Project EP/N007743/1 (FACER2VM) and a Google Faculty Award.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
For brevity of notation, we denote \( a_1,\dots ,a_N\) as \(a_{1:N}\).
References
Amberg, B., Romdhani, S., Vetter, T.: Optimal step nonrigid ICP algorithms for surface registration. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 1–8. IEEE (2007)
Archambeau, C., Delannay, N., Verleysen, M.: Mixtures of robust probabilistic principal component analyzers. Neurocomputing 71(7), 1274–1282 (2008)
Bach, F.R., Jordan, M.I.: A probabilistic interpretation of canonical correlation analysis (2005)
Belhumeur, P.N., Hespanha, J.P., Kriegman, D.J.: Eigenfaces vs. Fisherfaces: recognition using class specific linear projection. IEEE Trans. Pattern Anal. Mach. Intell. 19(7), 711–720 (1997)
Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, New York (2006)
Booth, J., Roussos, A., Zafeiriou, S., Ponniah, A., Dunaway, D.: A 3D morphable model learnt from 10,000 faces. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 5543–5552 (2016)
Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Stat. Soc. Ser. B (Methodol.) 1–38 (1977)
Hardoon, D.R., Szedmak, S., Shawe-Taylor, J.: Canonical correlation analysis: an overview with application to learning methods. Neural Comput. 16(12), 2639–2664 (2004)
Ioffe, S.: Probabilistic linear discriminant analysis. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3954, pp. 531–542. Springer, Heidelberg (2006). https://doi.org/10.1007/11744085_41
Jolliffe, I.: Principal Component Analysis. Wiley, Hoboken (2002)
Kenny, P., Ouellet, P., Dehak, N., Gupta, V., Dumouchel, P.: A study of interspeaker variability in speaker verification. IEEE Trans. Audio Speech Lang. Process. 16(5), 980–988 (2008)
Klami, A., Virtanen, S., Kaski, S.: Bayesian canonical correlation analysis. J. Mach. Learn. Res. 14(1), 965–1003 (2013)
Lawrence, N.: Probabilistic non-linear principal component analysis with Gaussian process latent variable models. J. Mach. Learn. Res. 6, 1783–1816 (2005)
Li, P., Fu, Y., Mohammed, U., Elder, J.H., Prince, S.J.: Probabilistic models for inference about identity. IEEE Trans. Pattern Anal. Mach. Intell. 34(1), 144–157 (2012)
Loper, M., Mahmood, N., Romero, J., Pons-Moll, G., Black, M.J.: SMPL: a skinned multi-person linear model. ACM Trans. Graph. (TOG) 34(6), 248 (2015)
Lüthi, M., Gerig, T., Jud, C., Vetter, T.: Gaussian process morphable models. IEEE Trans. Pattern Anal. Mach. Intell. 40, 1860–1873 (2017)
Moghaddam, B., Jebara, T., Pentland, A.: Bayesian face recognition. Pattern Recogn. 33(11), 1771–1782 (2000)
Moghaddam, B., Pentland, A.: Probabilistic visual learning for object representation. IEEE Trans. Pattern Anal. Mach. Intell. 19(7), 696–710 (1997)
Nicolaou, M.A., Zafeiriou, S., Pantic, M.: A unified framework for probabilistic component analysis. In: Calders, T., Esposito, F., Hüllermeier, E., Meo, R. (eds.) ECML PKDD 2014. LNCS (LNAI), vol. 8725, pp. 469–484. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44851-9_30
Prince, S.J., Elder, J.H.: Probabilistic linear discriminant analysis for inferences about identity. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 1–8. IEEE (2007)
Romero, J., Tzionas, D., Black, M.J.: Embodied hands: modeling and capturing hands and bodies together. ACM Trans. Graph. (TOG) 36(6), 245 (2017)
Roweis, S.: EM algorithms for PCA and SPCA. In: Advances in Neural Information Processing Systems, pp. 626–632 (1998)
Swets, D.L., Weng, J.J.: Using discriminant eigenfeatures for image retrieval. IEEE Trans. Pattern Anal. Mach. Intell. 8, 831–836 (1996)
Tipping, M.E., Bishop, C.M.: Mixtures of probabilistic principal component analyzers. Neural Comput. 11(2), 443–482 (1999)
Tipping, M.E., Bishop, C.M.: Probabilistic principal component analysis. J. Roy. Stat. Soc.: Ser. B (Stat. Methodol.) 61(3), 611–622 (1999)
Turk, M.A., Pentland, A.P.: Face recognition using eigenfaces. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 586–591. IEEE (1991)
Wang, X., Tang, X.: Dual-space linear discriminant analysis for face recognition. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, vol. 2, pp. II-564–II-569. IEEE (2004)
Wibowo, M.E., Tjondronegoro, D., Zhang, L., Himawan, I.: Heteroscedastic probabilistic linear discriminant analysis for manifold learning in video-based face recognition. In: IEEE Workshop on Applications of Computer Vision (WACV), pp. 46–52. IEEE (2013)
Yu, S., Yu, K., Tresp, V., Kriegel, H.P., Wu, M.: Supervised probabilistic principal component analysis. In: Proceedings of the International Conference on Knowledge Discovery and Data Mining, pp. 464–473. ACM (2006)
Zhang, Y., Yeung, D.-Y.: Heteroscedastic probabilistic linear discriminant analysis with semi-supervised extension. In: Buntine, W., Grobelnik, M., Mladenić, D., Shawe-Taylor, J. (eds.) ECML PKDD 2009. LNCS (LNAI), vol. 5782, pp. 602–616. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-04174-7_39
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
1 Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Moschoglou, S., Ploumpis, S., Nicolaou, M.A., Zafeiriou, S. (2019). Multi-Attribute Probabilistic Linear Discriminant Analysis for 3D Facial Shapes. In: Jawahar, C., Li, H., Mori, G., Schindler, K. (eds) Computer Vision – ACCV 2018. ACCV 2018. Lecture Notes in Computer Science(), vol 11363. Springer, Cham. https://doi.org/10.1007/978-3-030-20893-6_31
Download citation
DOI: https://doi.org/10.1007/978-3-030-20893-6_31
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-20892-9
Online ISBN: 978-3-030-20893-6
eBook Packages: Computer ScienceComputer Science (R0)