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<p>Convex tensor decomposition methods based on information geometry typically restrict the selection of the <i>e</i>-flat submanifold to those parameterized in the natural parameter space. However, in theory, <i>e</i>-flat submanifolds that are not parameterized in the natural parameter space can also be employed for tensor decomposition, leading to projections of the empirical distribution onto alternative submanifolds, a possibility that has not been explored. Here we extend information geometric approaches for decomposing non-negative tensors by introducing an alternative parameterization for <i>e</i>-flat submanifolds. The resulting method, called <i>General Nonnegative Convex Tensor Decomposition</i> (GNCTD), enables us to perform an <i>m</i>-projection of the input tensor onto any <i>e</i>-flat submanifold within a <i>log-linear model</i>. We demonstrate the effectiveness of this approach in both tensor completion and approximation tasks.</p>

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Generalized convex nonnegative tensor decomposition on statistical manifolds

  • 期刊论文

  • 发表日期：

    2026年2月14日

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  • Derun Zhou,
  • Mahito Sugiyama

摘要

Convex tensor decomposition methods based on information geometry typically restrict the selection of the e-flat submanifold to those parameterized in the natural parameter space. However, in theory, e-flat submanifolds that are not parameterized in the natural parameter space can also be employed for tensor decomposition, leading to projections of the empirical distribution onto alternative submanifolds, a possibility that has not been explored. Here we extend information geometric approaches for decomposing non-negative tensors by introducing an alternative parameterization for e-flat submanifolds. The resulting method, called General Nonnegative Convex Tensor Decomposition (GNCTD), enables us to perform an m-projection of the input tensor onto any e-flat submanifold within a log-linear model. We demonstrate the effectiveness of this approach in both tensor completion and approximation tasks.