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Separating Style and Content with Bilinear Models
Abstract
Perceptual systems routinely separate “content” from “style,” classifying familiar words spoken in an unfamiliar accent, identifying a font or handwriting style across letters, or recognizing a familiar face or object seen under unfamiliar viewing conditions. Yet a general and tractable computational model of this ability to untangle the underlying factors of perceptual observations remains elusive (Hofstadter, 1985). Existing factor models (Mardia, Kent, & Bibby, 1979; Hinton & Zemel, 1994; Ghahramani, 1995; Bell & Sejnowski, 1995; Hinton, Dayan, Frey, & Neal, 1995; Dayan, Hinton, Neal, & Zemel, 1995; Hinton & Ghahramani, 1997) are either insufficiently rich to capture the complex interactions of perceptually meaningful factors such as phoneme and speaker accent or letter and font, or do not allow efficient learning algorithms. We present a general framework for learning to solve two-factor tasks using bilinear models, which provide sufficiently expressive representations of factor interactions but can nonetheless be fit to data using efficient algorithms based on the singular value decomposition and expectation-maximization. We report promising results on three different tasks in three different perceptual domains: spoken vowel classification with a benchmark multi-speaker database, extrapolation of fonts to unseen letters, and translation of faces to novel illuminants.
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“GeAN also uses the bilinear model [29,30] to distil the knowledge interwoven in these representations by allowing each node and edge to collaboratively modulate each other's contributions through a shared learning space.”
From TVGeAN: Tensor Visibility Graph-Enhanced Attention Network for Versatile Multivariant Time Series Learning Tasks (2024) · cites this paper as [29]
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BackgroundDistribution-Based Emotion Recognition in Conversation
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BackgroundWhat Are the Invariant Occlusive Components of Image Patches? A Probabilistic Generative Approach
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MethodEstimating pose and illumination direction for frontal face synthesis
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MethodMosAIc: Finding Artistic Connections across Culture with Conditional Image RetrievalPreprint
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“Generating missing characters is useful when prototyping a new font (Miyazaki et al., 2020, Tenenbaum and Freeman, 2000).”
MethodContent-Aware Multi-task Neural Networks for User Gender Inference Based on Social Media Images
Shigenaka, R., Tsuboshita, Y., & Kato, N. (2016) · IEEE International Symposium on Multimedia (ISM) · doi:10.1109/ism.2016.0040 · Cited by 6
“Furthermore, in order to enhance the feature representation of the output layer, inspired by bilinear models [11]–[13], the representation of the detected concepts is combined with the content-based feature representation.”
MethodAppati, J. K., Adu‐Manu, K. S., & Owusu, E. (2022) · Advances in Multimedia · doi:10.1155/2022/7374550 · Cited by 6
“Finally is the work of [20] which introduced the concept of bilinear generative models to decompose orthogonal factors and further prove that a separable bilinear mapping exists be-tween an input space and the lower-dimensional subspace.”
Multimodal Fusion With Block Term Decomposition for Asynchronous Federated Learning
Gao, M., Zheng, H., Du, M., & Feng, X. (2024) · IEEE Transactions on Industrial Informatics · doi:10.1109/tii.2024.3441634 · Cited by 6
Estimation of Wetness and Color from a Single Multispectral Image
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“(SMM) investigated in [26], and the bilinear model (BM) demonstrated in [27] with the field classification idea.”
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“However, the existing hashing solutions for inter-domain retrieval such as canonical correlational analysis (CCA) [11], bilinear model (BLM) [12] and partial least squares (PLS) [13] merely consider inter-domain similarity measures on common subspace.”
BackgroundKernel-based convolution expansion for facial expression recognition
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“In [7], Tannenbaum and Freeman [7] propose a bilinear model (BLM) to derive a common space for cross-modal face recognition, and Sharma et al.”
BackgroundInfluentialAttentive Action and Context Factorization
Wang, Y., Tran, V., Bertasius, G., Torresani, L., & Nguyen, M. H. (2020) · British Machine Vision Conference (BMVC) · doi:10.5244/c.34.52 · Cited by 6
“Early approaches used bilinear model [34] and encoder-decoder network [19] for separating content and style for images such as faces and text in various fonts.”
MethodImprovement of EMG Pattern Recognition by Eliminating Posture-Dependent Components
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“The main contribution of our model is on its unique structure based on the style–content separation (Tenenbaum and Freeman 2000; Brand and Hertzmann 2000; Wang et al. 2007; Taylor and Hinton 2009; Matsubara et al. 2011, 2012), which allows online automatic adaptation of the parameters of the…”
MethodTDMFS: Tucker decomposition multimodal fusion model for pan-cancer survival prediction
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“Fortunately, bilinear structure [27], [28] have been proposed to model “two-factor” characteristics jointly like “style” and “content” in images, and achieved great success in many computer vision tasks [12], [28], [29], [30].”
Learning the Topology of Object Views
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“Even most techniques which establish the topology of views in a supervised fashion such as [7, 2, 10, 8] require an embedding space in which distances can be measured.”
BackgroundCOFENet: Co-Feature Neural Network Model for Fine-Grained Image Classification
Wang, B.-S., Hsieh, J.-W., Hsieh, Y.-K., et al. (2022) · Proceedings - International Conference on Image Processing · doi:10.1109/icip46576.2022.9897463 · Cited by 5
“Different from the channel-wise bilinear models proposed in [1, 2, 3], our COFENet can explore both distance-wise and direction-wise correlation among feature channels.”
BackgroundMethodReconstruction of Coronary Trees from 3DRA Using a 3D+t Statistical Cardiac Prior
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BackgroundBimode model for face recognition and face representation
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“Bilinear models were introduced by Tenenbaum and Freeman [10] to describe two-factor observations, where concepts like the “content” and “style” of observations should be analyzed and manipulated separately from each other.”
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BackgroundMethodJoint target tracking and recognition using view and identity manifolds
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Estimating Cartesian Compression via Deep Learning
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BackgroundVideo-based face recognition via convolutional neural networks
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MethodFang, Z., Liu, J., Liu, X., Tang, Q., Li, Y., & Lu, H. (2019) · ACM Transactions on Multimedia Computing Communications and Applications · doi:10.1145/3282469 · Cited by 4
“To solve this problem, several fusion methods have been extensively discussed such as concatenation, element-wise addition, element-wise multiplication, and bilinear pooling [55].”
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Style linear k-nearest neighbor classification method
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Multilinear analysis for task recognition and person identification
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BackgroundA Cyclically-Trained Adversarial Network for Invariant Representation Learning
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“In an early study, a bilinear model was proposed to separate content and style for face and text images [38].”
BackgroundLearning a Mahalanobis Metric with Side Information
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Who is doing what? Simultaneous recognition of actions and actors
Cheema, M. S., Eweiwi, A., & Bauckhage, C. (2012) · Proceedings - International Conference on Image Processing · doi:10.1109/icip.2012.6466968 · Cited by 4
“Identifying style and content has been of great interest for the recognition of handwriting, speech, and faces since the idea was pioneered in [3].”
BackgroundMethodInfluentialPerson-specific domain adaptation with applications to heterogeneous face recognition
Tsai, Y.-H. H., Hsu, H.-M., Hou, C.-A., et al. (2014) · Proceedings - International Conference on Image Processing · doi:10.1109/icip.2014.7025067 · Cited by 4
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MethodSynthesis and Control of High Resolution Facial Expressions for Visual Interactions
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“Researchers have used linear models (PCA [6]) and variations such as bilinear models [ 7 , 8] and multilinear tensor models for facial expression analysis”
MethodDiscriminant analysis approach using fuzzy fourfold subspaces model
Song, X., Yang, X., Yang, J., et al. (2010) · Neurocomputing · doi:10.1016/j.neucom.2010.01.007 · Cited by 4
Learning a geometry integrated image appearance manifold from a small training set
Xu, Y., & Roy–Chowdhury, A. K. (2008) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2008.4587365 · Cited by 4
“Active appearance models (AAMs) [4, 10], multilinear models [12, 13, 5, 14], and other low-dimensional manifold representations [9, 7] fall in this genre.”
BackgroundSemantic representation and correspondence for state-based motion transition
Ashraf, G., & Wong, K.-C. (2003) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2003.1260743 · Cited by 4
“The Hidden Markov Model (HMM) [7], [ 23 ], [24] is a popular statistical framework where representative states and transition probabilities are learned from training sequences.”
BackgroundObject Recognition: Physiological and Computational Insights
Tsao, D. Y., Cadieu, C. F., & Livingstone, M. S. (2010) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780195326598.003.0024 · Cited by 4
“In recent work, Tenenbaum and Freeman (2000) describe a bilinear model that separates the ‘‘content’’ and ‘‘style’’ in various data types.”
Dinh, A.-T., & Akagi, M. (2016) · doi:10.1109/icsda.2016.7918985 · Cited by 4
“To improve naturalness without violating intelligibility, an asymmetric bilinear model [6] was introduced to decompose naturalness and intelligibility.”
MethodCoupled feature selection based semi-supervised modality-dependent cross-modal retrieval
Yu, E., Sun, J., Wang, L., et al. (2018) · Multimedia Tools and Applications · doi:10.1007/s11042-018-5958-9 · Cited by 4
“To address this problem, most existing works aim to learn a couple of mapping matrices and project the different modalities features into a common latent space [9, 11, 12, 20, 25], in which the similarity of heterogeneous data can be measured directly.”
BackgroundSufficient dimensionality reduction with irrelevance statistics
Globerson, A., Chechik, G., & Tishby, N. (2002) · Cited by 4
imdpGAN: Generating Private and Specific Data with Generative Adversarial Networks
Gupta, S., Buduru, A. B., & Kumaraguru, P. (2020) · IEEE International Conference on Trust, Privacy and Security in Intelligent Systems and Applications (TPS-ISA) · doi:10.1109/tps-isa50397.2020.00019 · Cited by 5
“Works that use supervision (labeled data): bilinear models [24] to separate style and content; multi-view perceptron [25] to separate face identity from the viewpoint, train a subset of representation to match some supplied label using supervised learning.”
Nurminen, J., Siln, H., Popa, V., Helander, E. E., & Gabbouj, M. (2012) · InTech eBooks · doi:10.5772/37334 · Cited by 4
Style learning with feature-based texture synthesis
Xie, X., Tian, F., & Seah, H. S. (2008) · Computers in entertainment · doi:10.1145/1371216.1371228 · Cited by 4
Stylized synthesis of facial speech motions
Pei, Y., & Zha, H. (2007) · Computer Animation and Virtual Worlds · doi:10.1002/cav.186 · Cited by 4
Keypose and Style Analysis Based on Low-dimensional Representation
Perera, M., Kudoh, S., & Ikeuchi, K. (2009) · Cited by 4
Creature Double Feature: On Style and Subject in the Art of Caricature
Burns, K. J. (2004) · Cited by 4
Visual object recognition using generative models of images
Nair, V. B. (2010) · TSpace (University of Toronto) · Cited by 5
Voice Conversion Using A Two-Factor Gaussian Process Latent Variable Model
Sun, X., Zhang, X., Cao, T., et al. (2012) · PRZEGLĄD ELEKTROTECHNICZNY · Cited by 3
Sternum age estimation with dual channel fusion CNN model
Turk, F. J., Kaya, M., Akhan, B. M., et al. (2022) · Computer Science and Information Systems · doi:10.2298/csis220825054t · Cited by 3
Vision Language Navigation with Knowledge-driven Environmental Dreamer
Zhu, F., Lee, V. C. S., Chang, X., & Liang, X. (2023) · International Joint Conference on Artificial Intelligence · doi:10.24963/ijcai.2023/204 · Cited by 4
“Many classic works of style transfer [Hertz-mann et al. , 2001; Johnson et al. , 2016; Tenenbaum and Freeman, 2000] focus on obtaining human faces of different styles [Hertzmann et al. , 2001; Tenenbaum and Freeman, 2000] as well as art works [Chen et al. , 2017; Gatys et al. , 2016].”
BackgroundBoger, T., & Firestone, C. (2025) · Nature Human Behaviour · doi:10.1038/s41562-025-02249-8 · Cited by 3
“28) and then explore those processes using newly available style-transfer techniques (as well as naturally occurring styled images, such as styled sets of cutlery).”
Flexible editing of human motion by three‐way decomposition
He, Z., Liang, X., Jian, W., et al. (2013) · Computer Animation and Virtual Worlds · doi:10.1002/cav.1534 · Cited by 3
“Bilinear models have been adopted earlier in the work of Tenenbaum and Freeman [18] for the style and content separating in the face images.”
MethodMatsubara, T., Uchikata, A., & Morimoto, J. (2012) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra.2012.6224854 · Cited by 3
“By applying the factorization, we can form a style-content factorial model (referred to as the asymmetric bilinear model in [15]).”
Method
Metadata
- Authors
- Tenenbaum, J. B., & Freeman, W. T.
- Affiliations
- Massachusetts Institute of Technology (US)
- Mitsubishi Electric Research Laboratories (United States) (US)
- Venue
- Neural Computation
- Publisher
- MIT Press
- Published
- 2000-06-01
- Volume
- 12
- Issue
- 6
- Pages
- 1247-1283
- ISSN
- 0899-7667 (ISSN-L)
- 1530-888X
- OpenAlex
- W2170653751
- Semantic Scholar
- 7e85f7d59e37972ec52cbabfef0512588d87f125
- Cited by
- 840
- References
- 61
- Citations by year
- 2026: 2 · 2025: 17 · 2024: 20 · 2023: 31 · 2022: 38 · 2021: 61 · 2020: 58 · 2019: 70 · 2018: 49 · 2017: 39 · 2016: 56 · 2015: 34 · 2014: 27 · 2013: 39 · 2012: 30
- FWCI
- 13.29
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Neural Computation (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Face and Expression Recognition
- Physical Sciences › Computer Science › Artificial Intelligence › Speech Recognition and Synthesis
- Keywords
- bilinear model, factor models, perceptual learning, speaker accent, singular value decomposition, expectation-maximization algorithm, factor interactions
- MeSH terms
- Algorithms, Face, Humans, Learning, Pattern Recognition, Visual, Speech Perception, Linear Models, Neural Networks, Computer
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