Multiview learning promises richer representations by combining complementary perspectives. However, generating views that are both diverse and informative remains challenging. To explore this, we study digit classification using a multiview stacking model that integrates four spatial quadrants of each MNIST image plus a topological view derived from persistent homology (TDA). We use a random forest as both the base and meta learner in a stacking ensemble. By systematically combining subsets of spatial and topological views, we generate 32 distinct multiview variants. Evaluating these on 44,800 training and 11, 200 test images—sampled from \(80\%\) of the 70,000-image MNIST dataset across 30 random splits—we find that adding the topological view increases mean accuracy from \(0.9668 \pm 0.001\) to \(0.9848 \pm 0.001\) , a 1.66 percentage point gain with very large effect size. Notably, in an extreme low-data setting with just 70 training and 30 test samples, the topological view continued to improve accuracy by \(0.14-0.24\) percentage points across 140 runs, while additional spatial views contribute little. These findings suggest that persistent homology captures complementary global structure missing from pixel-level partitions, and that incorporating TDA into a late-fusion framework offers a simple, architecture-independent path to robust classification under data scarcity.

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MNIST Dataset Classification via Multiview Topological Data Analysis

  • Kaled Corona-Romero,
  • Enrique Garcia-Ceja,
  • Omar Mendoza-Montoya

摘要

Multiview learning promises richer representations by combining complementary perspectives. However, generating views that are both diverse and informative remains challenging. To explore this, we study digit classification using a multiview stacking model that integrates four spatial quadrants of each MNIST image plus a topological view derived from persistent homology (TDA). We use a random forest as both the base and meta learner in a stacking ensemble. By systematically combining subsets of spatial and topological views, we generate 32 distinct multiview variants. Evaluating these on 44,800 training and 11, 200 test images—sampled from \(80\%\) of the 70,000-image MNIST dataset across 30 random splits—we find that adding the topological view increases mean accuracy from \(0.9668 \pm 0.001\) to \(0.9848 \pm 0.001\) , a 1.66 percentage point gain with very large effect size. Notably, in an extreme low-data setting with just 70 training and 30 test samples, the topological view continued to improve accuracy by \(0.14-0.24\) percentage points across 140 runs, while additional spatial views contribute little. These findings suggest that persistent homology captures complementary global structure missing from pixel-level partitions, and that incorporating TDA into a late-fusion framework offers a simple, architecture-independent path to robust classification under data scarcity.