Nonnegative Canonical Tensor Decomposition with Linear Constraints: nnCANDELINC

Alexandrov, Boian S.; DeSantis, Derek; Manzini, Gianmarco; Skau, Erik

doi:10.48550/arxiv.1909.07570

Cited by 1 publication

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“…Hence, in RESCAL we need to know the multi-rank rather the rank of the analyzed tensor. In the case of nonnegative decomposition and even in presence of deficiency of the factors we can apply NMF to the corresponding unfoldings of the tensor, to find the minimal multi rank [17].…”

Section: Introductionmentioning

confidence: 99%

Determination of Latent Dimensionality in International Trade Flow

Truong,

Skau,

Valtchinov

et al. 2020

Preprint

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Currently, high-dimensional data is ubiquitous in data science, which necessitates the development of techniques to decompose and interpret such multidimensional (aka tensor) datasets. Finding a low dimensional representation of the data, that is, its inherent structure, is one of the approaches that can serve to understand the dynamics of low dimensional latent features hidden in the data. Nonnegative RESCAL is one such technique, particularly well suited to analyze self-relational data, such as dynamic networks found in international trade flows. Nonnegative RESCAL computes a low dimensional tensor representation by finding the latent space containing multiple modalities. Estimating the dimensionality of this latent space is crucial for extracting meaningful latent features. Here, to determine the dimensionality of the latent space with nonnegative RESCAL, we propose a latent dimension determination method which is based on clustering of the solutions of multiple realizations of nonnegative RESCAL decompositions. We demonstrate the performance of our model selection method on synthetic data and then we apply our method to decompose a network of international trade flows data from International Monetary Fund and validate the resulting features against empirical facts from economic literature.

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Section: Introductionmentioning

confidence: 99%