Non-negative tensor factorization with applications to statistics and computer vision

By Amnon Shashua, Tamir Hazan. International Conference on Machine Learning, 2005

574 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/3605d6dd16c087e7b194313e89d6bd5c921d0462

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In Computational Mathematics

In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

Nonnegative Matrix Factorization: A Comprehensive Review (2013, methodology): “This kind of generalization is indeed not trivial since NTF possesses many new properties varying from NMF [117], [118].”
Tensors for Data Mining and Data Fusion (2016, methodology): “In tensors, there exist algorithms that enforce nonnegativity constraints on the values of A , B , C and have been shown to be more effective in terms of interpretability [Shashua and Hazan 2005; Cichocki et al. 2009].”
Domain Adaptation by Mixture of Alignments of Second-or Higher-Order Scatter Tensors (2016, methodology): “For example, spatio-temporal third-order tensor on video data is proposed for action analysis in [18], non-negative tensor factorization is used for image denoising in [34], tensor textures are proposed for texture rendering in [43], and higher order tensors are used for face recognition in [42].”
Tensor Decompositions and Applications (2009, methodology): “Shashua and Hazan [193] derive an EM-based method to calculate a rank-one NNCP decomposition.”
A Block Coordinate Descent Method for Regularized Multiconvex Optimization with Applications to Nonnegative Tensor Factorization and Completion (2013, methodology): “For example, the multiplicative update in [53] is extended to solving (1.9) in [63].”
Tensor Representations via Kernel Linearization for Action Recognition from 3D Skeletons (2016, background): “For example, in [26], spatio-temporal third-order tensors on videos is proposed for action analysis, non-negative tensor factorization is used for image denoising in [27], tensor textures are proposed for texture rendering in [28], and higher order tensors are used for face recognition in [29].”
Probabilistic Models for Incomplete Multi-dimensional Arrays (2009, background): “Non-negative tensor decomposition has also been exploited in sparse image coding, e.g. Shashua and Hazan (2005) and Kim and Choi (2007).”
How hard is the tensor rank (2016, background): “We note that the rank decompositions have proved to be useful for studies in statistics [34], signal processing [26], complexity of computation [39], psychometrics [8], linguistics [38], chemometrics [10], and we refer the reader to the monograph [24] for a more complete survey of applications.”
Compression of Deep Convolutional Neural Networks for Fast and Low Power Mobile Applications (2015, methodology): “Two of the most popular tensor decomposition models are CANDECOMP/PARAFAC model (Carroll & Chang, 1970; Harshman & Lundy, 1994; Shashua & Hazan, 2005) and Tucker model (Tucker, 1966; De Lathauwer et al., 2000; Kim & Choi, 2007).”
Robust (Semi) Nonnegative Graph Embedding (2014, background): “NMF has been shown to be successful in a variety of applications, such as image processing [12]–[14] and text analysis [15].”
CANDECOMP/PARAFAC Decomposition of High-Order Tensors Through Tensor Reshaping (2012, background): “[12], separated representations for generic functions inv olved in quantum mechanics or kinetic theory descriptions of materials [13], classification, clusterin g [14], compression [15]–[17].”
Constrained Nonnegative Matrix Factorization for Image Representation (2012, unknown): “Nonnegative Tensor Factorization (NTF) [35].”
On Fast Computation of Gradients for CANDECOMP/PARAFAC Algorithms (2012, methodology): “ a common tensor factorization which has found applications such as in chemometrics, telecommunication, analysis of fMRI data, time-varying EEG spectrum, data mining [7,13], classiﬁcation, clustering [29], stochastic PD Es [15]. For example, CP was applied to analyze the auditory tones by Carroll an”
A Unified Algorithmic Framework for Block-Structured Optimization Involving Big Data: With applications in machine learning and signal processing (2015, methodology): “IEEE SIGNAL PROCESSING MAGAZINE [69] jANuARy 2016 Figure 6 and Table 5 show the performance of the resulting algorithm for dictionary learning in an image denoising problem.”
Low Rank Language Models for Small Training Sets (2011, background): “This approach allows one to reduce the space complexity to by explicitly encoding the parameters in the low-rank factored form of (2), which makes scaling to real-world datasets practical.”
TensorLy: Tensor Learning in Python (2016, methodology): “In particular, we CANDECOMP-PARAFAC (CP) decomposition e.g. [17]) Non-Negative CP decomposition [28]) Tucker decomposition (Higher-Order SVD) (e.g. [17]) Non-Negative Tucker decomposition [16]) Tensor Ridge regression (Tucker and Kruskal) [11, 32, 18] Table 2: Algorithms implemented propose an…”
Product Form Approximations for Communicating Markov Processes (2008, methodology): “The whole approach is motivated by the computation of tensor approximations for matrices where similar problems arise and similar approaches are used [21] and which have several applications in statistics and computer vision [23].”