Advances in Tensor Analysis and Visual Analytics

The field of tensor analysis and visual analytics is witnessing significant developments, with a focus on improving the accuracy and efficiency of tensor decomposition methods. Researchers are exploring new approaches to comparative analysis, enabling flexible comparison of tensors and aiding in visual analytics. The integration of discriminant analysis and contrastive learning schemes is also being investigated, allowing for more effective extraction of tensors' essential characteristics. Furthermore, there is a growing interest in understanding bias in perceiving dimensionality reduction projections and developing strategies to mitigate it. Another area of research is the compression of high-dimensional discrete distribution functions into non-negative tensor train formats, with applications in variational inference and density estimation. Noteworthy papers include:

  • Visual Analytics Using Tensor Unified Linear Comparative Analysis, which introduces a new tensor decomposition method enabling flexible comparative analysis.
  • Understanding Bias in Perceiving Dimensionality Reduction Projections, which conducts a user study to verify the existence of bias in selecting projections for analysis.
  • Variational inference and density estimation with non-negative tensor train, which proposes an efficient numerical approach for compressing high-dimensional discrete distribution functions.

Sources

Visual Analytics Using Tensor Unified Linear Comparative Analysis

Understanding Bias in Perceiving Dimensionality Reduction Projections

Variational inference and density estimation with non-negative tensor train

PC-JND: Subjective Study and Dataset on Just Noticeable Difference for Point Clouds in 6DoF Virtual Reality

Improved Analysis of Khatri-Rao Random Projections and Applications

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