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Dual-Symmetric Parallel Factor Analysis Using Procrustes Estimation And Khatri-Rao Factorization

M. Haardt, Peter Husar, Florian Roemer, Martin Weis
2012 Zenodo  
The new algorithm using alternating Procrustes estimation and Khatri-Rao factorization (ProKRaft) The algorithm presented here is based on a special unfolding for dual-symmetric tensors obeying a PARAFAC  ...  In Section 3 we present a new algorithm, based on alternating Procrustes estimation [13] and Khatri-Rao factorization (ProKRaft), which is able to exploit the special structure of the dual-symmetric  ... 
doi:10.5281/zenodo.52380 fatcat:og7vjxemhvdrhehwaysr3estvy

Tensor-Based Methods for Blind Spatial Signature Estimation in Multidimensional Sensor Arrays

Paulo R. B. Gomes, André L. F. de Almeida, João Paulo C. L. da Costa, João C. M. Mota, Daniel Valle de Lima, Giovanni Del Galdo
2017 International Journal of Antennas and Propagation  
In this paper, we propose two generalized iterative estimation algorithms to the case in which a multidimensional (R-D) sensor array is used at the receiver.  ...  The estimation of spatial signatures and spatial frequencies is crucial for several practical applications such as radar, sonar, and wireless communications.  ...  Recently in [12] , an iterative algorithm was proposed in a manner similar to Independent Component Analysis (ICA) based on the Orthogonal Procrustes Problem (OPP) and Khatri-Rao factorization [13]  ... 
doi:10.1155/2017/1615962 fatcat:pv7nnw7hanahflamusliaadi7i

Efficient Learning of Mixed Membership Models [article]

Zilong Tan, Sayan Mukherjee
2017 arXiv   pre-print
Our approach obtains competitive empirical results on both simulated and real data.  ...  This algorithm reduces the computational complexity of state-of-the-art tensor methods, which require decomposing an O(p^3) tensor, to factorizing O(p/k) sub-tensors each of size O(k^3).  ...  Moreover, × refers to the outer product and ⊙ denotes the Khatri-Rao product. · F and · 2 represent the Frobenius norm and spectral norm, respectively.  ... 
arXiv:1702.07933v3 fatcat:wcepzvuxfrcpfn5dqbergnkofq

Constructing fast approximate eigenspaces with application to the fast graph Fourier transforms [article]

Cristian Rusu, Lorenzo Rosasco
2021 arXiv   pre-print
We investigate numerically efficient approximations of eigenspaces associated to symmetric and general matrices.  ...  The eigenspaces are factored into a fixed number of fundamental components that can be efficiently manipulated (we consider extended orthogonal Givens or scaling and shear transformations).  ...  inc where * is the Khatri-Rao product, the Kronecker products between the corresponding columns ofT −T andT.  ... 
arXiv:2002.09723v3 fatcat:taejw5y5xneqxlydg3dawpbnrq

COPA: Constrained PARAFAC2 for Sparse & Large Datasets [article]

Ardavan Afshar, Ioakeim Perros, Evangelos E. Papalexakis, Elizabeth Searles, Joyce Ho, Jimeng Sun
2018 arXiv   pre-print
factors.  ...  Despite recent improvements on unconstrained PARAFAC2, its model factors are usually dense and sensitive to noise which limits their interpretability.  ...  N00174-17-1-0005 and by an Adobe Data Science Research Faculty Award.  ... 
arXiv:1803.04572v2 fatcat:d4yu5jqq2rcgxmp6xmuc27pufy

Author index to volumes 301–400

2005 Linear Algebra and its Applications  
Bentler, The asymptotic covariance matrix of maximum-likelihood estimates in factor analysis: the case of nearly singular matrix of estimates of unique variances 321 (2000) 153 He, J.-L., see Shao, J.  ...  -D. 390 (2004) 145 Liu, S., Local influence in multivariate elliptical linear regression models 354 (2002) 159 Liu, S., Several inequalities involving Khatri-Rao products of positive semidefinite matrices  ... 
doi:10.1016/s0024-3795(05)00125-4 fatcat:mrc33u36wnh57lis5jwcb7bmaa

Geometric Methods for Robust Data Analysis in High Dimension [article]

Joseph Anderson
2017 arXiv   pre-print
This is the first algorithmic use of the centroid body and it is of independent theoretical interest, since it effectively replaces the estimation of covariance from samples, and is more generally accessible  ...  Machine learning and data analysis now finds both scientific and industrial application in biology, chemistry, geology, medicine, and physics.  ...  The related Khatri-Rao power is defined by A = A · · · A ( times).  ... 
arXiv:1705.09269v1 fatcat:bfwqacnnhndojljuj7kglgrga4

Statistical signal processing of nonstationary tensor-valued data

Bruno Scalzo Dees, Danilo Mandic, Engineering And Physical Sciences Research Council
2020
Both matrices and vectors are lower-order tensors, and this gives us a unique opportunity to consider some matrix signal processing models under the more powerful framework of multilinear tensor algebra  ...  This helps to both enhance physical meaning in the analysis and reduce the dimensionality of tensor-valued problems.  ...  moments using the Khatri-Rao product structure intrinsic to the augmented complex multilinear algebra in Chapter 6.  ... 
doi:10.25560/81087 fatcat:yswajb44jrh6fpgi4y4wt3hrcm