Multilinear Independent Components Analysis

Abstract

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.

Tensor-Based Shot Boundary Detection in Video Streams

“…Thus, for analysis and processing, more appropriate are methods that directly account for data dimensionality. In this respect, it was shown that tensor-based methods frequently offer many benefits, such as in the case of the tensorfaces, as well as view synthesis proposed by Vasilescu and Terzopoulos [48][49][50], or data dimensionality reduction by Wang and Ahuja [51,52], handwritten digits recognition proposed by Savas and Eldén [42] or road signs recognition by Cyganek [9], to name a few. In this section, we present a brief introduction to the tensor analysis necessary for understanding of further parts of this paper.…”

Fibre Centred Tensor Faces

“…Multilinear analysis was introduced to the computer vision community by Vasilescou and Terzopoulos [1][2][3][4]. Multilinear data represent the natural extension from scalars (0-D tensors), through vectors (1D tensor) and matrices (2D tensors) to general ndimensional data.…”

“…In [3] Vasilescou et al approximated the solution using a two step minimisation i.e. first they find the best linear parameters, rij...k that minimise:…”

Sparse non-negative tensor factorization using columnwise coordinate descent

“…It has been applied successfully in face recognition [24], psychometric [19], and image analysis [25]. Two popular models have been studied for tensor factorization including the parafac model [8,3] and the tucker model [23].…”

“…They have been commonly applied for the analysis of such data for data compression, visualization, and detection of hidden information (factors), e.g., in face recognition [24], psychometric [19] and image analysis [25]. Additionally, the basis can be constrained to be sparse which typically leads to an even more meaningful decomposition of the data.…”