Dimensionality reduction techniques transform a dataset from a high-dimensional space into a lower-dimensional subspace. These techniques facilitate visualization of high-dimensional data in a 2D or 3D subspace. This work presents the application of two linear methods, PCA and FDA, which were used to generate two 2D visualizations. The PCA and FDA projections facilitated meaningful comparisons between the original MNIST images, their distorted versions (30,000 images), and the reconstructed versions (30,000 images), produced by a convolutional autoencoder (CAE). According to the Mahalanobis distance with respect to the 95% confidence ellipse, centered at the mean of the PCA projections of the MNIST training images, 94.40% of the distorted image projections fall inside. Similarly, 97.41% of the reconstructed image projections fall inside. On the other hand, according to the Mahalanobis distance with respect to the 95% confidence ellipses-each centered at the mean of the FDA projections of the MNIST training images of each digit class-an average of 99.25% of the distorted image projections fall outside the ellipses. In contrast, an average of 93.03% of the reconstructed image projections fall inside the ellipses. The PCA and FDA visualizations confirmed the capability of the CAE to reconstruct distorted MNIST images. PCA captured the patterns that maximize variance (spread) of the MNIST dataset, regardless of class. Similarly, FDA highlighted the separability between the reconstructed images by digit class.

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Visual Analysis of MNIST Convolutional Autoencoder Reconstructions via Linear Dimensionality Reduction

  • Rafael Castaneda-Diaz,
  • Daniela Lopez-Betancur,
  • Carlos Guerrero-Mendez,
  • Efren Gonzalez-Ramirez,
  • Flossi Puma-Ttito,
  • Rómulo Troncoso-Pacheco

摘要

Dimensionality reduction techniques transform a dataset from a high-dimensional space into a lower-dimensional subspace. These techniques facilitate visualization of high-dimensional data in a 2D or 3D subspace. This work presents the application of two linear methods, PCA and FDA, which were used to generate two 2D visualizations. The PCA and FDA projections facilitated meaningful comparisons between the original MNIST images, their distorted versions (30,000 images), and the reconstructed versions (30,000 images), produced by a convolutional autoencoder (CAE). According to the Mahalanobis distance with respect to the 95% confidence ellipse, centered at the mean of the PCA projections of the MNIST training images, 94.40% of the distorted image projections fall inside. Similarly, 97.41% of the reconstructed image projections fall inside. On the other hand, according to the Mahalanobis distance with respect to the 95% confidence ellipses-each centered at the mean of the FDA projections of the MNIST training images of each digit class-an average of 99.25% of the distorted image projections fall outside the ellipses. In contrast, an average of 93.03% of the reconstructed image projections fall inside the ellipses. The PCA and FDA visualizations confirmed the capability of the CAE to reconstruct distorted MNIST images. PCA captured the patterns that maximize variance (spread) of the MNIST dataset, regardless of class. Similarly, FDA highlighted the separability between the reconstructed images by digit class.