Multilinear independent components analysis

By M. Alex O. Vasilescu, Demetri Terzopoulos. 2005

203 citations recorded by the source corpus.

Independent components analysis (ICA) maximizes the statistical independence of the representational components of a training image ensemble, but it cannot distinguish between the different factors, or modes, inherent to image formation, including scene structure, illumination, and imaging. We introduce a nonlinear, multifactor model that generalizes ICA. Our multilinear ICA (MICA) model of image ensembles learns the statistically independent components of multiple factors. Whereas ICA employs linear (matrix) algebra, MICA exploits multilinear (tensor) algebra. We furthermore introduce a multilinear projection algorithm which projects an unlabeled test image into the N constituent mode spaces to simultaneously infer its mode labels. In the context of facial image ensembles, where the mode labels are person, viewpoint, illumination, expression, etc., we demonstrate that the statistical regularities learned by MICA capture information that, in conjunction with our multilinear projection algorithm, improves automatic face recognition.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Signal Processing

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Citations in the corpus

Disentangling Factors of Variation via Generative Entangling (2012, methodology): “One of the earlier eﬀorts in this direction also used higher-order interactions of latent variables, speciﬁcally bilinear (Tenen-baum and Freeman, 2000; Grimes and Rao, 2005) and multilinear (Vasilescu and Terzopoulos, 2005) models.”
Render for CNN: Viewpoint Estimation in Images Using CNNs Trained with Rendered 3D Model Views (2015, methodology): “Synthesizing Images for Training Synthetic images rendered from 3D models have long been used in computer vision [25, 26, 37, 23].”
Multilinear Multitask Learning (2013, background): “In (Vasilescu & Terzopoulos, 2005), the authors propose multilinear independent component analysis, where the factors extracted for each mode are not only uncorrelated but also statistically independent.”
Early Visual Concept Learning with Unsupervised Deep Learning (2016, methodology): “…visual generative factors; 2) we devise a protocol to quantitatively compare the degree of disentanglement learnt by different models; and 3) we demonstrate how learning disentangled representations enables zero-shot inference and the emergence of basic visual concepts, such as “objectness”.”
Blind Haze Separation (2006, methodology): “2ICA has also been used in high-level vision [5, 13, 33].”
Denoising and Dimensionality Reduction Using Multilinear Tools for Hyperspectral Images (2008, methodology): “This representation intuitively implies processing techniques based on multilinear algebra [13], [15].”
RNNs Implicitly Implement Tensor Product Representations (2018, unknown): “For example, in face recognition, eigenfaces (Sirovich & Kirby, 1987; Turk & Pentland, 1991) and TensorFaces (Vasilescu & Terzopoulos, 2002; 2005) use such techniques to disentangle facial features, camera angle, and lighting.”
Nonlinearities and Contextual Influences in Auditory Cortical Responses Modeled with Multilinear Spectrotemporal Methods (2008, unknown): “Thus, the full model becomes the following: r̂ i c jkl wj twk f wl lMijkl itfl c2 Context i j 1, k c jkl wj twk f wl lMijkl itfl c2 mnp wm wn wp M i j 1, k mnp .”