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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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Items 301–400 of 839
Local Temporal Bilinear Pooling for Fine-Grained Action Parsing
Zhang, Y., Tang, S., Muandet, K., Jarvers, C., & Heiko Neumann, B. (2019) · 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.2019.01228 · Cited by 26
“Bilinear pooling (or second-order pooling) is widely used in fine-grained visual classification [2, 30, 22, 26, 27, 24, 25, 9, 42, 16, 21, 47, 48, 49, 45, 13, 38], visual questioning answering [8, 15, 50], feature fusion and disentangling [26, 27, 43, 4, 7, 14], action recognition [51, 46, 11, 14, 7] and other tasks.”
BackgroundPattern Field Classification with Style Normalized Transformation
Zhang, X.-Y., Huang, K., & Liu, C. (2012) · Cited by 26
Cross-modal subspace learning for sketch-based image retrieval: A comparative study
Xu, P., Li, K., Ma, Z., et al. (2016) · IEEE International Conference on Network Infrastructure and Digital Content (IC-NIDC) · doi:10.1109/icnidc.2016.7974625 · Cited by 25
“LCFS, GMLDA, and GMMFA are supervised methods while CCA, PLS, and BLM are unsupervised.”
MethodInfluentialCross-Modal Retrieval: A Review of Methodologies, Datasets, and Future Perspectives
Han, Z., Azman, A., Mustaffa, M. R., & Khalid, F. (2024) · IEEE Access · doi:10.1109/access.2024.3444817 · Cited by 29
“Similar to CCA, methods such as Partial Least Squares (PLS) [19] and Bilinear Models [20] also attempt to perform cross-modal retrieval by learning subspaces; however, these methods rely on explicit pairing between two modalities to establish corresponding relationships.”
MethodSelf-Attentive Moving Average for Time Series Prediction
Su, Y., Cui, C., & Qu, H. (2022) · Applied Sciences · doi:10.3390/app12073602 · Cited by 32
Explicit Disentanglement of Appearance and Perspective in Generative ModelsPreprint
Detlefsen, N. S., & Hauberg, S. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1906.11881 · Cited by 31
“Early work on non-negative matrix factorization [Lee and Seung, 1999] and bilinear models [Tenenbaum and Freeman, 2000] showed how images can be composed into semantic “parts” that can be glued together to form the final image.”
BackgroundShapes as Product Differentiation: Neural Network Embedding in the Analysis of Markets for FontsPreprint
Han, S., Schulman, E. H., Grauman, K. L., & Ramakrishnan, S. K. (2021) · RePEc: Research Papers in Economics · doi:10.48550/arxiv.2107.02739 · Cited by 25
“Tenenbaum and Freeman (2000) propose bilinear models that separate style and content with fonts as one of the examples.”
BackgroundPeng, L., Mao, J., Huang, G., Han, G.-S., Liu, X., Liao, W., Tian, G., & Yang, J. (2025) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.4c02088 · Cited by 25
Domain Adaptive Self-Taught Learning for Heterogeneous Face Recognition
Hou, C.-A., Yang, M.-C., & Wang, Y.-C. F. (2014) · Proceedings - International Conference on Pattern Recognition/Proceedings/International Conference on Pattern Recognition · doi:10.1109/icpr.2014.529 · Cited by 24
“To compare our proposed method with other HFR approaches (especially those aiming at determining common feature spaces), we consider Canonical Correlational Analysis (CCA) [26], Bilinear Model (BLM) [27], Partial Least Square (PLS) [11], and the method of Huang et al.”
MethodInfluentialRegion Ranking SVM for Image Classification
Wei, Z., & Hoai, M. (2016) · 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.2016.326 · Cited by 24
“RRSVM bares some similarities to bilinear models [26, 36].”
BackgroundFixed point iteration in identifying bilinear models
Li, G., Wen, C., & Zhang, A. (2015) · Systems & Control Letters · doi:10.1016/j.sysconle.2015.06.008 · Cited by 24
Manifold Learning for Biomarker Discovery in MR Imaging
Wolz, R., Aljabar, P., Hajnal, J. V., et al. (2010) · Lecture notes in computer science · doi:10.1007/978-3-642-15948-0_15 · Cited by 24
Shivaswamy, P. K., & Jebara, T. (2006) · International Conference on Machine Learning · doi:10.1145/1143844.1143947 · Cited by 24
“•Images - when going from vector to a bag of set representation ( Tenenbaum & Freeman, 2000 )”
BackgroundCross-media retrieval with collective deep semantic learning
Zhang, B., Zhu, L., Sun, J., & Zhang, H. (2018) · Multimedia Tools and Applications · doi:10.1007/s11042-018-5896-6 · Cited by 23
“Other similar methods of this kind include Bilinear Model (BLM) [28] and Partial Least Squares (PLS) [25].”
InfluentialXiong, J., Wang, G., Zhang, P., Huang, W., Zha, Y., & Zhai, G. (2023) · 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/cvpr52729.2023.00623 · Cited by 24
“Moreover, the Bilinear fusion operation [38] is also introduced to compare with the designed AVIM, the obtained observations are listed below: (i) The combination of AVIM and CPC can continuously improve the performance of the model, which achieves the best performance, (ii) The linear version of AVIM has roughly the…”
MethodUsing matrices to model symbolic relationship
Sutskever, I., & Hinton, G. E. (2008) · Cited by 23
Cross-Paced Representation Learning With Partial Curricula for Sketch-Based Image Retrieval
Xu, D., Alameda-Pineda, X., Song, J., et al. (2018) · IEEE Transactions on Image Processing · doi:10.1109/tip.2018.2837381 · Cited by 23
“We compared the proposed approach with several baseline methods including: canonical correlation analysis (CCA), partial least squares (PLS) [55], bilinear model [56], semi-coupled dictionary learning (SCDL) [8], joint dictionary learning (JDL) [7] and coupled dictionary learning (CDL) [9].”
MethodResultInfluentialSertolli, B., Ren, Z. X., Schuller, B. W., & Cummins, N. (2021) · Computer Speech & Language · doi:10.1016/j.csl.2021.101204 · Cited by 22
Few-Shot Font Generation With Weakly Supervised Localized Representations
Park, S., Chun, S., Cha, J., Lee, B., & Shim, H. (2022) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2022.3196675 · Cited by 23
“Notably, [10], [48] also uses a factorization strategy for font generation; however, they directly apply factorization to the complex glyph space (i.e., each element is an image), while LF-Font factorizes the localized style features into the style and the content factors.”
MethodChen, J., Zhan, Y., Xu, Y., & Pan, X. (2022) · IET Image Processing · doi:10.1049/ipr2.12614 · Cited by 22
“For the alignment of high-level and low-level features, most existing neural networks use the bilinear interpolation method for feature upsampling[32].”
Neuromorphic visual scene understanding with resonator networks
Renner, A., Supic, L., Danielescu, A., Indiveri, G., Olshausen, B. A., Sandamirskaya, Y., Sommer, F. T., & Frady, E. P. (2024) · Nature Machine Intelligence · doi:10.1038/s42256-024-00848-0 · Cited by 29
“Decorrelated hypervectors for overlapping shape templates can be produced by learning whitened versions of the generative factors by using singular value decomposition [49].”
BackgroundA Deep Factorization of Style and Structure in Fonts
Srivatsan, A., Barron, J. T., Klein, D., et al. (2019) · Conference on Empirical Methods in Natural Language Processing (EMNLP) · doi:10.18653/v1/d19-1225 · Cited by 22
“work has tackled this problem through the use of bilinear factorization models (Freeman and Tenenbaum, 1997; Tenenbaum and Freeman, 2000), while others have used discriminative neural models (Zhang et al.”
MethodCNN2GNN: How to Bridge CNN With GNN
Jiao, Z., Zhang, H., & Li, X. (2025) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2025.3583357 · Cited by 23
“Different from the linear projections in CNN, GNN is a bilinear model according to [9].”
Co-occurrence of deep convolutional features for image search
Forcen, J. I., Pagola, M., Barrenechea, E., & Bustince, H. (2020) · Image and Vision Computing · doi:10.1016/j.imavis.2020.103909 · Cited by 21
Generative AI Model for Artistic Style Transfer Using Convolutional Neural Networks
Miah, J., Cao, D. M., Sayed, M. A., et al. (2023) · Journal of Computer Science and Technology Studies · doi:10.32996/jcsts.2023.5.4.9 · Cited by 21
Wang, L., Sun, W., Zhao, Z., et al. (2016) · Signal Processing · doi:10.1016/j.sigpro.2016.08.012 · Cited by 21
“Other algorithms are also proposed to deal with cross-modal problems, such as partial least square (PLS) [6], Bilinear Model (BLM) [7,8], etc.”
BackgroundCoarse-to-Fine Grained Classification
Huo, Y., Lu, Y., Niu, Y., et al. (2019) · International ACM SIGIR Conference on Research and Development in Information Retrieval (SIGIR) · doi:10.1145/3331184.3331336 · Cited by 21
“In fine-grained classification, bilinear models were initially proposed by [12] to model two-factor variations, such as “style” and “content” for images.”
MethodBilinear elastically deformable models with application to 3D face and facial expression recognition
Mpiperis, I., Malassiotis, S., & Strintzis, M. G. (2008) · International Conference on Automatic Face and Gesture Recognition · doi:10.1109/afgr.2008.4813333 · Cited by 21
“In this paper, we present a technique for joint recognition based on decoupling identity and expression components of face appearance by means of bilinear models [13].”
BackgroundMethodInfluentialHuman activity recognition by separating style and content
Cheema, M. S., Eweiwi, A., & Bauckhage, C. (2013) · Pattern Recognition Letters · doi:10.1016/j.patrec.2013.09.024 · Cited by 20
“Further, the vector transpose VT operation is employed to determine a ðBKÞ A matrix transpose of an ðAKÞ B stacked matrix, See details in Tanenbaum and Freeman (2000).”
BackgroundMethodInfluentialRiemannian Similarity Learning
Cheng, L. (2013) · Cited by 20
Feature Guided Texture Synthesis (FGTS) for artistic style transfer
Xie, X., Tian, F., & Seah, H. S. (2007) · Digital Interactive Media in Entertainment and Arts · doi:10.1145/1306813.1306830 · Cited by 20
“T o incorporate the content of the source image during the process of artistic style transfer, example-based image synthesis techniques [ 13 ] [3] [8] [6] [5] [12] are developed based on constrained texture synthesis methods.”
MethodVenkataraman, V., Fan, G., Yu, L., et al. (2011) · EURASIP Journal on Advances in Signal Processing · doi:10.1186/1687-6180-2011-124 · Cited by 20
“The bilinear models [32] and tensor analysis [33] provide a more systematic multi-factor representation by decomposing HD data into several independent factors.”
MethodStyle-based exploration of illustration datasets
Garcés, E., Agarwala, A., Hertzmann, A., et al. (2016) · Multimedia Tools and Applications · doi:10.1007/s11042-016-3702-x · Cited by 20
“A common way to algorithmically capture the style elements is to learn a generative model; that is, a model that learns to create new examples of a style from scratch, such as generating new typefaces [3, 32], and learning 3D hatching styles from examples [13].”
BackgroundZaki, H. F. M., Faisal Shafait, B., & Mian, A. S. (2017) · Robotics and Autonomous Systems · doi:10.1016/j.robot.2017.02.008 · Cited by 20
Multispectral Periocular Classification With Multimodal Compact Multi-Linear Pooling
Algashaam, F. M. A., Nguyen, K., Alkanhal, M. I., Chandran, V., Boles, W., & Banks, J. (2017) · IEEE Access · doi:10.1109/access.2017.2731118 · Cited by 19
“Bilinear pooling calculates the outer product of two feature vectors, f 1 ∈ n 1 and f 2 ∈ n 2 , and learns a model W (here linear), i.e. , where ⊗ denotes the outer product ( f 1 f T 2 ) and [.] denotes linearizing the matrix in a vector [39].”
BackgroundHuman motion recognition using an eigenspace
Rahman, M. M., & Ishikawa, S. (2004) · Pattern Recognition Letters · doi:10.1016/j.patrec.2004.09.019 · Cited by 20
“Tenenbaum and Freeman (2000) have proposed a bilinear model with separating style and content in order to recognize a human face.”
BackgroundGINA-3D: Learning to Generate Implicit Neural Assets in the Wild
Shen, B., Yan, X., Qi, C. R., Najibi, M., Deng, B., Guibas, L. J., Zhou, Y., & Anguelov, D. (2023) · 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/cvpr52729.2023.00476 · Cited by 23
“Given a collection of images containing 3D objects captured in the wild X = { x } ( x is an image data sample), 3D-aware image synthesis [51,52,63–79 , 81 The probabilistic formulation is shown in Fig.”
BackgroundDiffSal: Joint Audio and Video Learning for Diffusion Saliency Prediction
Xiong, J., Zhang, P., You, T., Li, C., Huang, W., & Zha, Y. (2024) · 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/cvpr52733.2024.02575 · Cited by 21
“The effects of using different multi-modal interaction meth-ods, such as Bilinear [49], Addition, and Concatenation, are compared in Table 3.”
MethodLearning transport operators for image manifolds
Culpepper, B. J., & Olshausen, B. A. (2009) · neural information processing systems · Cited by 19
Kim, D., & Sung, J. (2009) · IGI Global eBooks · doi:10.4018/978-1-60566-216-9.ch006 · Cited by 42
Coupled locality preserving projections for cross-view gait recognition
Xu, W., Luo, C., Ji, A., & Zhu, C. (2016) · Neurocomputing · doi:10.1016/j.neucom.2016.10.054 · Cited by 19
On the Impact of Machine Learning: Architecture without Architects?
Belém, C., Santos, L., & Leitão, A. (2019) · Cited by 19
Efficient Optimization for Low-Rank Integrated Bilinear Classifiers
Kobayashi, T., & Otsu, N. (2012) · Lecture notes in computer science · doi:10.1007/978-3-642-33709-3_34 · Cited by 19
“The dimensionality of the concatenated feature vector is the product of two-way’s dimensions, resulting in high dimensionality, and the inherent structure of the two-way features is unfortunately collapsed [5].”
BackgroundFacial expressional image synthesis controlled by emotional parameters
Zhou, C., & Lin, X. (2005) · Pattern Recognition Letters · doi:10.1016/j.patrec.2005.06.007 · Cited by 19
Sparse Bilinear Logistic RegressionPreprint
Shi, J. V., Xu, Y., & Baraniuk, R. G. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1404.4104 · Cited by 24
“Bilinear logistic regression has also found application in style and content separation, which can improve the performance of object recognition tasks under various nuisance variables such as orientation, scale, and viewpoint [36].”
BackgroundWeakly-supervised Compositional FeatureAggregation for Few-shot RecognitionPreprint
Hu, P., Sun, X., Saenko, K., & Sclaroff, S. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1906.04833 · Cited by 24
“Bilinear models were propose in [43] to model two-factor variations like “style” and “content” for images.”
MethodDai, W., Sun, X., Zhang, W., Wang, D., Tang, D., & Peng, Y. (2025) · Journal of Manufacturing Processes · doi:10.1016/j.jmapro.2025.01.033 · Cited by 19
DISP6D: Disentangled Implicit Shape and Pose Learning for Scalable 6D Pose Estimation
Wen, Y., Li, X., Pan, H., et al. (2022) · Lecture notes in computer science · doi:10.1007/978-3-031-20077-9_24 · Cited by 18
“Entanglement is a recurring topic in machine learning, with implementation techniques like parameter generation [46,54,13] that boil down to a tensor product structure [52,38].”
BackgroundSrinivasan, R., Rudolph, C., & Roy–Chowdhury, A. K. (2015) · IEEE Signal Processing Magazine · doi:10.1109/msp.2015.2410783 · Cited by 18
A stochastic algorithm for probabilistic independent component analysis
Allassonnière, S., & Laurent Younes, B. (2012) · The Annals of Applied Statistics · doi:10.1214/11-aoas499 · Cited by 18
Learning from Few Samples with Memory Network
Zhang, S., Huang, K., Zhang, R., & Hussain, A. (2017) · Cognitive Computation · doi:10.1007/s12559-017-9507-z · Cited by 18
ISNN: Impact Sound Neural Network for Audio-Visual Object Classification
Sterling, A., Wilson, J., Lowe, S., & Lin, M. C. (2018) · Lecture notes in computer science · doi:10.1007/978-3-030-01267-0_34 · Cited by 18
Semi-Supervised Semantic-Preserving Hashing for Efficient Cross-Modal Retrieval
Wang, X., Liu, X., Hu, Z., et al. (2019) · IEEE International Conference on Multimedia and Expo (ICME) · doi:10.1109/icme.2019.00177 · Cited by 18
“, Canonical Correlation Analysis (CCA) [1], Bilinear model (BLM) [2] , and Partial Least Square (PLS) [3].”
MethodAnalyzing Liquid Pouring Sequences via Audio-Visual Neural Networks
Wilson, J., Sterling, A., & Lin, M. C. (2019) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros40897.2019.8968118 · Cited by 23
Weighted bilinear coding over salient body parts for person re-identification
Chang, Z., Zhou, Q., Fan, H., et al. (2020) · Neurocomputing · doi:10.1016/j.neucom.2020.05.009 · Cited by 18
“Bilinear models are designed to separate style and content by [48].”
BackgroundCombination of deep speaker embeddings for diarisation
Sun, G., Zhang, C., & Woodland, P. C. (2021) · Neural Networks · doi:10.1016/j.neunet.2021.04.020 · Cited by 19
“Bilinear pooling (Tenenbaum and Freeman, 2000) is a commonly used approach for fusing multimodal representations (Zhang et al., 2020), which combines two vectors using the bilinear form on their vector space by where 1 and 2 are the 𝑀 -dimensional (-dim) and 𝑁 -dim vectors to combine, and and are…”
BackgroundMethodMohammed, U., Prince, S. J. D., & Kautz, J. (2009) · ACM SIGGRAPH Conference (SIGGRAPH) · doi:10.1145/1576246.1531363 · Cited by 18
“We employ an asymmetric bilinear model [Tenenbaum and Freeman 2000] which describes the generative process as: xij = µj + Fj hi + eij, (7) where xij represents the i th face in the j th style.”
MethodIlluminant Estimation: Beyond the Bases
DiCarlo, J. M., & Wandell, B. A. (2000) · Color and Imaging Conference · doi:10.2352/cic.2000.8.1.art00018 · Cited by 18
Appearance factorization for facial expression analysis
Abboud, B., & Davoine, F. (2004) · British Machine Vision Conference (BMVC) · doi:10.5244/c.18.53 · Cited by 18
Homeomorphic Manifold Analysis (HMA): Generalized separation of style and content on manifolds
Elgammal, A., & Lee, C.-S. (2013) · Image and Vision Computing · doi:10.1016/j.imavis.2012.12.003 · Cited by 17
“Such subspace analysis can be further extended to decompose multiple orthogonal factors using bilinear models and multilinear tensor analysis [11] [12].”
3D Object Representation Learning: A Set-to-Set Matching Perspective
Yu, T., Meng, J., Yang, M., et al. (2021) · IEEE Transactions on Image Processing · doi:10.1109/tip.2021.3049968 · Cited by 17
“Bilinear pooling was firstly proposed by Tenenbaum and Freeman [22] to separate style and content.”
Method3D shape creation by style transfer
Han, Z., Liu, Z., Han, J., & Bu, S. (2014) · The Visual Computer · doi:10.1007/s00371-014-0999-1 · Cited by 17
“Nowadays, the two terms of shapes, style and content, are used to synthesize shapes for novel shape creation [17,26,28].”
BackgroundMethodInfluentialCross-modal Retrieval by Real Label Partial Least Squares
He, J., Ma, B., Wang, S., et al. (2016) · ACM International Conference on Multimedia (ACM MM) · doi:10.1145/2964284.2967216 · Cited by 17
“To solve the retrieval problem of the different feature spaces, recent works are devoted to the common subspace learning [8] [9] [13] [19].”
MethodMulti-Modal Knowledge Representation Learning via Webly-Supervised Relationships Mining
Nian, F., Bao, B., Li, T., & Xu, C. (2017) · ACM International Conference on Multimedia (ACM MM) · doi:10.1145/3123266.3123443 · Cited by 17
“The most widely used feature subspace methods on multiple modalities are canonical correlation analysis (CCA) [33], Partial Least Squares (PLS) [8] and Bilinear Model (BLM) [28] [32].”
MethodLópez-Sánchez, D., Arrieta, A. G., & Corchado, J. M. (2019) · Neurocomputing · doi:10.1016/j.neucom.2019.05.104 · Cited by 17
“Bilinear models were originally proposed in [21] , where the authors used them to separately model the style and content of images.”
MethodReconstruction regularized low-rank subspace learning for cross-modal retrieval
Wu, J., Xie, X., Nie, L., et al. (2021) · Pattern Recognition · doi:10.1016/j.patcog.2020.107813 · Cited by 17
“For unsupervised cross-modal retrieval, we compare the unsupervised RRLSL (URRLSL) with five unsupervised algorithms, including the CCA [5] , PLS [7] , BLM [7] , self-paced cross-modal subspace matching (SCSM) [10] , and simultaneous pairwise and groupwise correspondences maximization (SPGCM) [11] .”
BackgroundMethodExploiting parameter domain knowledge for learning in bayesian networks
Mitchell, T. M., & Niculescu, R. S. (2005) · Cited by 17
Locating Nose-Tips and Estimating Head Poses in Images by Tensorposes
Tu, J., Fu, Y., & Huang, T. S. (2008) · IEEE Transactions on Circuits and Systems for Video Technology · doi:10.1109/tcsvt.2008.2005806 · Cited by 17
“This idea of separation of style and content was originally proposed by Tenenbaum in [26].”
BackgroundAdaptive Deep Kernel LearningPreprint
Tossou, P., Dura, B., Laviolette, F., Marchand, M., & Lacoste, A. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1905.12131 · Cited by 19
“Alternatively, different architectures such as Feature-wise Linear Modulation (FiLM) [24], Hypernetwork [25], or Bilinear transformation [26] could be used to compute φ θ ( x ; z ) , though we found that a simple concatenation was sufficient for our applications.”
MethodCapturing Label Characteristics in VAEsPreprint
Joy, T., Schmon, S. M., Torr, P. H. S., Siddharth, N., & Rainforth, T. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2006.10102 · Cited by 17
“…learn meaningful factors—capturing human-understandable characteristics from data—has been of interest from the perspective of human-like learning (Tenenbaum & Freeman, 2000; Lake et al., 2015) and improving decision making and generalization across tasks (Bengio et al., 2013; Tenenbaum &…”
Efficient Compact Bilinear Pooling via Kronecker Product
Yu, T., Cai, Y., & Li, P. (2022) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v36i3.20225 · Cited by 16
“Compared with widely-used sum-pooling and max-pooling (Krizhevsky, Sutskever, and Hinton 2012; He et al. 2016), bilinear pooling (Tenenbaum and Freeman 2000) has achieved competitive performance in fine-grained recognition (Lin, RoyChowdhury, and Maji 2015; Gao et al. 2016; Wang et al. 2016; Li et…”
MethodRG-Flow: a hierarchical and explainable flow model based on renormalization group and sparse prior
Hu, H.-Y., Wu, D., You, Y., Olshausen, B. A., & Chen, Y. (2022) · Machine Learning Science and Technology · doi:10.1088/2632-2153/ac8393 · Cited by 16
Alignment Enhancement Network for Fine-grained Visual Categorization
Hu, Y., Liu, X., Zhang, B., Han, J., & Cao, X. (2021) · ACM Transactions on Multimedia Computing Communications and Applications · doi:10.1145/3446208 · Cited by 15
“As far as we know, bilinear pooling is one of the earliest encoding-based methods in FGVC, which is first proposed by Tanenbaum et al. [54] to model interaction relationship between features.”
MethodRobust Tensor Classifiers for Color Object Recognition
Bauckhage, C. (2007) · Lecture notes in computer science · doi:10.1007/978-3-540-74260-9_32 · Cited by 16
“Tenenbaum and Freeman [8] devise bi-linear functions for a shape classification task where the input is formed by two independent factors.”
BackgroundImproving Style Transfer with Calibrated Metrics
Yeh, M.-C., Tang, S., Bhattad, A., Zou, C., & Forsyth, D. A. (2020) · IEEE Winter Conference on Applications of Computer Vision · doi:10.1109/wacv45572.2020.9093351 · Cited by 17
“Style transfer : bilinear models [26] , non-parametric methods [8], image analogies [13] and adjusting filter statistics [2, 25] are capable of image style transfer and yield texture synthesis.”
MethodZhuang, L., Wang, H., Zhao, J. M., & Sun, Y. (2023) · Information Sciences · doi:10.1016/j.ins.2023.119139 · Cited by 15
Representation Disentanglement for Multi-task Learning with Application to Fetal Ultrasound
Meng, Q., Pawlowski, N., Rueckert, D., et al. (2019) · Lecture notes in computer science · doi:10.1007/978-3-030-32875-7_6 · Cited by 15
Xiao, F., Liu, H., & Lee, Y. J. (2019) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2019.00711 · Cited by 15
“Early works like Tenenbaum and Freeman [51] operate in a fully-supervised setting in which the factors of interest (e.g., content and style) are annotated for each training image.”
BackgroundBourached, A., Cann, G., Griffths, R.-R., et al. (2021) · Electronic Imaging · doi:10.2352/issn.2470-1173.2021.14.cvaa-042 · Cited by 15
Fast and Compact Bilinear Pooling by Shifted Random Maclaurin
Yu, T., Li, X., & Li, P. (2021) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v35i4.16435 · Cited by 15
“Bilinear model was proposed by Tenenbaum and Freeman (2000) to disentangle style from content.”
MethodA novel technique for voice conversion based on style and content decomposition with bilinear models
Popa, V., Nurminen, J., & Gabbouj, M. (2009) · Interspeech (USB) · doi:10.21437/interspeech.2009-498 · Cited by 15
“One of the tasks that fall under the framework proposed in [1] and which is of particular interest in voice conversion is the extrapolation which is illustrated in Table 1.”
BackgroundMethodInfluentialEfficient illumination independent appearance-based face tracking
Buenaposada, J. M., Muñoz, E., & Baumela, L. (2008) · Image and Vision Computing · doi:10.1016/j.imavis.2008.04.015 · Cited by 15
A new image classification model based on brain parallel interaction mechanism
Yu, Y., Hao, K., & Ding, Y. (2018) · Neurocomputing · doi:10.1016/j.neucom.2018.07.016 · Cited by 15
A theoretical framework for learning Bayesian networks with parameter inequality constraints
Niculescu, R. S., Mitchell, T. M., & Rao, R. B. (2007) · International Joint Conference on Artificial Intelligence · Cited by 15
A support vector approach for cross-modal search of images and texts
Verma, Y., & Jawahar, C. V. (2016) · Computer Vision and Image Understanding · doi:10.1016/j.cviu.2016.10.001 · Cited by 15
“Other than the CCA, methods such as Partial Least Squares (PLS) [42] and Bilinear Model (BLM) [43] have been proposed for cross-modal problems.”
MethodNon-linear latent factor models for revealing structure in high-dimensional data
Memisevic, R. (2008) · TSpace (University of Toronto) · Cited by 12
Neuron Interaction Based Representation Composition for Neural Machine Translation
Li, J., Wang, X., Yang, B., Shi, S., Lyu, M. R.-T., & Tu, Z. (2020) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v34i05.6334 · Cited by 15
“Rank Constraint for Bilinear Pooling Bilinear Pooling Bilinear pooling has been well-studied in the computer vision community, which is first introduced by Tenenbaum and Freeman (2000) to separate style and content.”
BackgroundAcademic Coupled Dictionary Learning for Sketch-based Image Retrieval
Xu, D., Alameda-Pineda, X., Song, J., et al. (2016) · ACM International Conference on Multimedia (ACM MM) · doi:10.1145/2964284.2964329 · Cited by 14
“We compare the proposed ACDL method to seven baseline methods: canonical correlation analysis (CCA), partial least squares (PLS) [30], bilinear model (Bil) [35], semi-coupled dictionary learning (SCDL) [36], joint dictionary learning (JDL) [42] and coupled dictionary learn-1330 ing (CDL) [13].”
MethodFine-Grained Driving Behavior Prediction via Context-Aware Multi-Task Inverse Reinforcement Learning
Nishi, K., & Shimosaka, M. (2020) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra40945.2020.9197126 · Cited by 14
“Multilinear model also employed in our model, in which the weight parameter is represented as a tensor, have recently gained attention in the machine learning field as a way to introduce external factors explicitly into the model [25], [22].”
MethodPredictive Statistical Model of Early Cranial Development
PorrasPerez, A. R., Keating, R., Lee, J., et al. (2021) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.2021.3100745 · Cited by 14
Exploring Graph-Structured Semantics for Cross-Modal Retrieval
Zhang, L., Chen, L., Zhou, C., et al. (2021) · ACM International Conference on Multimedia (ACM MM) · doi:10.1145/3474085.3475567 · Cited by 14
“Traditional approaches for CMR mainly based on linear model to generate a lower-dimensional common space with handcrafted or learnable features [4, 6, 10, 12, 14, 28, 30, 31, 33] for multimedia data.”
MethodA Continuous Technique for the Weighted Low-Rank Approximation Problem
Buono, N. D., & Politi, T. (2004) · Lecture notes in computer science · doi:10.1007/978-3-540-24709-8_104 · Cited by 14
“In other cases, entries in the target matrix represents aggregates of many samples so that while the unweighted low rank approximation considers a uniform number of samples for each entry, the incorporation of weights allows to account for varying numbers of samples ([ 13 ]).”
BackgroundMethodUnsupervised learning of a steerable basis for invariant image representations
Bethge, M., Gerwinn, S., & Macke, J. H. (2007) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.711119 · Cited by 14
Intelligent Expression Blending for Performance Driven Facial Animation
Khanum, A., & Mufti, M. (2007) · IEEE Transactions on Consumer Electronics · doi:10.1109/tce.2007.381732 · Cited by 14
“Tenenbaum and Freeman [43] propose a general bilinear model that can express the relationship between style and content, and can generate any one of these given the values of the other.”
BackgroundSelf-Organization of Topographic Bilinear Networks for Invariant Recognition
Bergmann, U., & von der Malsburg, C. (2011) · Neural Computation · doi:10.1162/neco_a_00195 · Cited by 14
Gait Tracking and Recognition Using Person-Dependent Dynamic Shape Model
Lee, C.-S., & Elgammal, A. (2006) · International Conference on Automatic Face and Gesture Recognition · doi:10.1109/fgr.2006.58 · Cited by 14
“Third, given learned nonlinear mapping coefficients C1,C2, · · · ,CK , for training people 1, · · · ,K, the shape style parameters are decomposed by fitting an asymmetric bilinear [19] to the coefficient space:”
MethodCompact Root Bilinear CNNs for Content-Based Image Retrieval
Alzu’bi, A., Amira, A., & Ramzan, N. (2016) · International Conference on Image, Vision and Computing (ICIVC) · doi:10.1109/icivc.2016.7571271 · Cited by 15
“The proposed model is inspired by the bilinear models proposed by Tenenbaum and Freeman [11] to model the separation between the "content" and "style" factors of perceptual systems, and motivated by the promising results obtained using the bilinear CNNs applied on fme-grained categorization [12].”
MethodBecattini, F., Ferracani, A., Landucci, L., et al. (2016) · Lecture notes in computer science · doi:10.1007/978-3-319-48496-9_62 · Cited by 14
Semantic consistent adversarial cross-modal retrieval exploiting semantic similarity
Ou, W., Xuan, R., Gou, J., et al. (2019) · Multimedia Tools and Applications · doi:10.1007/s11042-019-7343-8 · Cited by 14
“Besides CCA, partial least squares (PLS) [34] and bilinear model (BLM) [38] are also utilized in cross-modal retrieval.”
MethodMemisevic, R. (2006) · International Conference on Machine Learning · doi:10.1145/1143844.1143924 · Cited by 14
“(Tenenbaum & Freeman, 2000)).”
Background
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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