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Multi-type clustering using regularized tensor decomposition


Geospatial analytics increasingly rely on data fusion methods to extract patterns from data; however robust results are difficult to achieve because of the need for spatial and temporal regularization and latent structures within data. Tensor decomposition is a promising approach because it can accommodate multidimensional structure of data (e.g., trajectory information about users, locations, and time periods). To address these challenges, we introduce Multi-Type Clustering using Regularized tensor Decomposition (MCRD), an innovative method for data analysis that provides insight not just about groupings within data types (e.g., clusters of users), but also about the interactions between data types (e.g., clusters of users and locations) in the latent features of complex multi-type datasets. This is done by combining two innovations. First, a tensor representing spatiotemporal data is decomposed using a novel regularization method to account for structure within the data. Next, within- and cross-type groups are found through the application of novel hypergraph community detection methods to the decomposed results. Experimentation on both synthetic and real trajectory data demonstrates MCRD’s capacity to reveal the within- and cross-type grouping in data, and MCRD outperforms related methods including tensor decomposition without regularization, unfolding of tensors, Laplacian regularization, and tensor block models. The robust and versatile analysis provided by combining new regularization and clustering techniques outlined in this paper likely have utility in geospatial analytics beyond the movement applications explicitly studied.

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Availability of data and material

While the is not publicly available at this time, the method for creating the synthetic data used is described in Section 4.1 . As for the real-world data, we used a portion of the Porto dataset available at

Code Availability

The code is not publicly available at this time.


  1. Because it is an internal clustering index, the CH criterion is not as meaningful for comparing the results of clustering elements based on factor matrices with different number of factors.

  2. Several MATLAB packages for basic tensor operations are used [2, 3, 33].

  3. The data can be found at:

  4. The code used for this can be found at


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This work was supported by the US Army Engineer Research and Development Center, Geospatial Research Engineering basic research program. Any opinions expressed in this paper are those of the authors, and are not to be construed as official positions of the funding agency or the Department of the Army unless so designated by other authorized documents.


This work was supported by the U.S. Army Engineer Research and Development Center, Geospatial Research Engineering basic research program.

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Correspondence to Charlotte L. Ellison.

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Ellison, C.L., Fields, W.R. Multi-type clustering using regularized tensor decomposition. Geoinformatica (2022).

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  • Spatiotemporal reasoning
  • Trajectory analysis
  • Tensor
  • CP Decomposition
  • Co-Clustering