Optimal Sparse Singular Value Decomposition for High-Dimensional High-Order Data

Zhang, Anru; Han, Rungang

doi:10.1080/01621459.2018.1527227

Cited by 55 publications

(37 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition, various dimension-reduced structures are imposed on the singular vectors or subspace of the low-rank tensor decomposition model to better capture other intrinsic properties of the data, such as sparsity (Sun et al, 2017;Zhang and Han, 2019), blocking (Han et al, 2020), non-negativity (Xu and Yin, 2013) and many others. The most relevant paper to our work is the spatial/temporal structure, which is incorporated to characterize time/location-varying patterns for one or more of the tensor modes.…”

Section: Related Workmentioning

confidence: 99%

“…The resulting number of estimated eigenfunctions is often in the same order as the number of variables, making the eigenfunctions hard to interpret when the variable mode is high-dimensional. Another important class of works utilize the high-order structure of the tensor data via different types of low-rank tensor decomposition models, such as (sparse) CP low-rankness (Anandkumar et al, 2014b;Sun et al, 2017), (sparse) Tucker lowrankness (Zhang and Xia, 2018;Zhang and Han, 2019), tensor-train (Oseledets, 2011;Zhou et al, 2020b), or decomposable tensor covariance (Dawid, 1981;Tsiligkaridis and Hero, 2013;Zhou, 2014).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Guaranteed Functional Tensor Singular Value Decomposition

Han¹,

Shi²,

Zhang³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

This paper introduces the functional tensor singular value decomposition (FTSVD), a novel dimension reduction framework for tensors with one functional mode and several tabular modes. The problem is motivated by high-order longitudinal data analysis. Our model assumes the observed data to be a random realization of an approximate CP low-rank functional tensor measured on a discrete time grid. Incorporating tensor algebra and the theory of Reproducing Kernel Hilbert Space (RKHS), we propose a novel RKHS-based constrained power iteration with spectral initialization. Our method can successfully estimate both singular vectors and functions of the low-rank structure in the observed data. With mild assumptions, we establish the non-asymptotic contractive error bounds for the proposed algorithm. The superiority of the proposed framework is demonstrated via extensive experiments on both simulated and real data.

show abstract

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Guaranteed Functional Tensor Singular Value Decomposition

Han¹,

Shi²,

Zhang³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…where SV D r represents the first r left singular vectors of the matrix. To address the high computation complexity issue, we use the latest development of the HOSVD method, the Sparse Tensor Alternating Thresholding SVD (STAT-SVD), to truncate after each projection before SVD and QR [36].…”

Section: Spatiotemporal Profile Tensor Inferencementioning

confidence: 99%

Entity Resolution in Sparse Encounter Network Using Markov Logic Network

Huang

Xiang

2021

IEEE Access

View full text Add to dashboard Cite

Entity Resolution, which identifies different descriptions referring to the same real-world entity, is a fundamental stage in data integration process essential for quality data analysis. Identities recognition is important in encounter network as it defines the entities of encounters. It is usually not a problem if unique identifier information, e.g., mobile phone number, is available. However, in the circumstances where unique identifier is not available or in question, further investigated is required to perform the entity resolution on the encounter dataset. Often the encounter network is a sparse network with very limited information collected from close-range person-to-person contact reporting, as in epidemiology contact tracing or traffic collision reports. In this paper, we provide an automatic method to resolve the ambiguity of entities in sparse encounter network. We develop a Bayesian spatiotemporal inference system to infer the probability of entity's visits on places of interest. Then, we propose a hierarchical Markov logic network to tackle the inference of the entities in the network which analyses the connection strength of network with multiple types of entities. Experimental results on encounter networks of synthetic and commercial traffic encounter datasets demonstrate that the proposed method achieves better accuracy than existing collective classifications.

show abstract

“…Schmidt [5] further proposed an approximation theorem, proving that SVD can be used to obtain the optimal low-rank approximation of an operator. Beyond these classic work, SVD theories continue to expand in recent decades [6,7,8,9,10], and theoretical works with application purpose are also actively studied especially in recent years [11,12,13,14].…”

Section: Introductionmentioning

confidence: 99%

Enhancing the SVD Compression

Wang¹,

Zhang²,

Zhao³

2021

Preprint

View full text Add to dashboard Cite

Orthonormality is the foundation of matrix decomposition. For example, Singular Value Decomposition (SVD) implements the compression by factoring a matrix with orthonormal parts and is pervasively utilized in various fields. Orthonormality, however, inherently includes constraints that would induce redundant degrees of freedom, preventing SVD from deeper compression and even making it frustrated as the data fidelity is strictly required. In this paper, we theoretically prove that these redundancies resulted by orthonormality can be completely eliminated in a lossless manner. An enhanced version of SVD, namely E-SVD, is accordingly established to losslessly and quickly release constraints and recover the orthonormal parts in SVD by avoiding multiple matrix multiplications. According to the theory, advantages of E-SVD over SVD become increasingly evident with the rising requirement of data fidelity. In particular, E-SVD will reduce 25% storage units as SVD reaches its limitation and fails to compress data. Empirical evidences from typical scenarios of remote sensing and Internet of things further justify our theory and consistently demonstrate the superiority of E-SVD in compression. The presented theory sheds insightful lights on the constraint solution in orthonormal matrices and E-SVD, guaranteed by which will profoundly enhance the SVD-based compression in the context of explosive growth in both data acquisition and fidelity levels.

show abstract

Optimal Sparse Singular Value Decomposition for High-Dimensional High-Order Data

Cited by 55 publications

References 34 publications

Guaranteed Functional Tensor Singular Value Decomposition

Guaranteed Functional Tensor Singular Value Decomposition

Entity Resolution in Sparse Encounter Network Using Markov Logic Network

Enhancing the SVD Compression

Contact Info

Product

Resources

About