A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
CubeSVD: a novel approach to personalized Web search
WWW '05 Proceedings of the 14th international conference on World Wide Web
Algorithm 862: MATLAB tensor classes for fast algorithm prototyping
ACM Transactions on Mathematical Software (TOMS)
Cross-language information retrieval using PARAFAC2
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
GraphScope: parameter-free mining of large time-evolving graphs
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
Efficient MATLAB Computations with Sparse and Factored Tensors
SIAM Journal on Scientific Computing
Incremental tensor analysis: Theory and applications
ACM Transactions on Knowledge Discovery from Data (TKDD)
Unsupervised Multiway Data Analysis: A Literature Survey
IEEE Transactions on Knowledge and Data Engineering
Scalable Tensor Decompositions for Multi-aspect Data Mining
ICDM '08 Proceedings of the 2008 Eighth IEEE International Conference on Data Mining
A comparison of algorithms for fitting the PARAFAC model
Computational Statistics & Data Analysis
Tensor Decompositions and Applications
SIAM Review
Multiresolution approach in computing NTF
SCIA'07 Proceedings of the 15th Scandinavian conference on Image analysis
FacetCube: a framework of incorporating prior knowledge into non-negative tensor factorization
CIKM '10 Proceedings of the 19th ACM international conference on Information and knowledge management
RanKloud: scalable multimedia and social media retrieval and analysis in the cloud
Proceedings of the 9th workshop on Large-scale and distributed informational retrieval
Utilizing common substructures to speedup tensor factorization for mining dynamic graphs
Proceedings of the 21st ACM international conference on Information and knowledge management
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Tensors (multi-dimensional arrays) are widely used for representing high-order dimensional data, in applications ranging from social networks, sensor data, and Internet traffic. Multi-way data analysis techniques, in particular tensor decompositions, allow extraction of hidden correlations among multi-way data and thus are key components of many data analysis frameworks. Intuitively, these algorithms can be thought of as multi-way clustering schemes, which consider multiple facets of the data in identifying clusters, their weights, and contributions of each data element. Unfortunately, algorithms for fitting multi-way models are, in general, iterative and very time consuming. In this paper, we observe that, in many applications, there is a priori background knowledge (or metadata) about one or more domain dimensions. This metadata is often in the form of a hierarchy that clusters the elements of a given data facet (or mode). In this paper, we investigate whether such single-mode data hierarchies can be used to boost the efficiency of tensor decomposition process, without significant impact on the final decomposition quality. We consider each domain hierarchy as a guide to help provide higher- or lower-resolution views of the data in the tensor on demand and we rely on these metadata-induced multi-resolution tensor representations to develop a multiresolution approach to tensor decomposition. In this paper, we focus on an alternating least squares (ALS) based implementation of the PARAllel FACtors (PARAFAC) decomposition (which decomposes a tensor into a diagonal tensor and a set of factor matrices). Experiment results show that, when the available metadata is used as a rough guide, the proposed multiresolution method helps fit PARAFAC models with consistent (for both dense and sparse tensor representations, under different parameters settings) savings in execution time and memory consumption, while preserving the quality of the decomposition.