Linear image coding for regression and classification using the tensor-rank principle

By Amnon Shashua, Anat Levin. 2001

231 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computational Mechanics, Computer Vision and Pattern Recognition

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Citations in the corpus

Tensor representation in high-frequency financial data for price change prediction (2017, methodology): “With advances in mathematical tools and algorithms dealing with tensor input, many multilinear discriminant techniques as well as tensor regression have been proposed for image and video classiﬁcation problems such as [18], [19], [20], [21], [22], [23], [24], [25], [26], [27].”
A survey of multilinear subspace learning for tensor data (2011, methodology): “Other MSL applications include handwritten digit recognition [27, 57], image compression [1, 27, 64], image/video retrieval [1, 87], and object categorization and recognition [46].”
Compression of facial images using the K-SVD algorithm (2008, background): “Indeed, this expected gain has been observed and exploited in several recent publications that offer tailored compression algorithms for facial images [2–17].”
Hyperspectral image noise reduction based on rank-1 tensor decomposition (2013, methodology): “Tensor (Lathauwer, 1997) and multilinear algebra have been receiving more and more attention and have recently been applied to both computer vision and pattern recognition (Lu et al., 2008; Shashua and Levin, 2001; Tao et al., 2007; Vasilescu and Terzopoulos, 2003).”
Discriminant analysis with tensor representation (2005, background): “Some recent works, however, have started to consider an object as a two dimensional matrix for unsupervised learning [8][17].”
Discriminant Locally Linear Embedding With High-Order Tensor Data (2008, methodology): “Other works [6], [12], [14], [27], [31]–[33], [35], [36], [48], [50], [52]–[54] employ an image-as-matrix representation, in which a 2-D gray-level image is directly represented as a secondorder data tensor (matrix), or is filtered by Gabor functions [8], [39] to obtain a set of images that comprise”
Non-negative tensor factorization with applications to statistics and computer vision (2005, methodology): “In computer vision, 3-way tensor decompositions, treating the training images as a 3D cube, have been also proposed ( Shashua & Levin, 2001; Vasilescu & Terzopoulos, 2002) with the idea of preserving certain features of the SVD.”
Beyond streams and graphs: dynamic tensor analysis (2006, methodology): “Ten sors have been recently used in machine vision research, for example by Shashua and Levin [26] for linear image coding, by Vasilescu and Terzopoulos [28] for face recognition.”
Multilinear Discriminant Analysis for Higher-Order Tensor Data Classification (2014, methodology): “In addition, we propose constrained multilinear discriminant analysis (CMDA) that learns the optimal tensor subspace by iteratively maximizing the scatter ratio criterion.”
Tensor Decompositions and Applications (2009, methodology): “Shashua and Levin [194] applied CP to image compression and classiﬁcation.”
Multilinear Discriminant Analysis for Face Recognition (2007, background): “Shasua’s work [18] is to consider the collection of sample matrices as a third-order tensor and search for an approximation of its tensor-rank.”
Multilinear Analysis of Image Ensembles: TensorFaces (2002, background): “As was pointed out by Shashua and Levin [12], the natural representation of a collection of images is a three-dimensional array, or 3rd-order tensor, rather than a simple matrix of vectorized images.”