Domain-decomposed image classification algorithms using linear discriminant analysis and convolutional neural networks

TL;DR

Two different domain decomposed CNN models are experimentally compared for different image classification problems and a novel decomposed LDA strategy is proposed which also relies on a localization approach and which is combined with a small neural network model.

Abstract

In many modern computer application problems, the classification of image data plays an important role. Among many different supervised machine learning models, convolutional neural networks (CNNs) and linear discriminant analysis (LDA) as well as sophisticated variants thereof are popular techniques. In this work, two different domain decomposed CNN models are experimentally compared for different image classification problems. Both models are loosely inspired by domain decomposition methods and in addition, combined with a transfer learning strategy. The resulting models show improved classification accuracies compared to the corresponding, composed global CNN model without transfer learning and besides, also help to speed up the training process. Moreover, a novel decomposed LDA strategy is proposed which also relies on a localization approach and which is combined with a small neural network model. In comparison with a global LDA applied to the entire input data, the presented decomposed LDA approach shows increased classification accuracies for the considered test problems.

Figures (4)

• Figure 1: Visualization of the CNN-DNN network architecture. Left: The original image is decomposed into $N=4$ nonoverlapping subimages. Middle: The $N=4$ subimages are used as input data for $N$ independent, local CNNs. Right: The probability values of the local CNNs are used as input data for a DNN. The DNN is trained to make a final classification for the decomposed image by weighting the local probability distributions. Figure taken from KLW:DNN-CNN:2023.
• Figure 2: Left: Exemplary images of the CIFAR-10 dataset Cifar10_TR. Right: Exemplary images of the TF-Flowers dataset tfflowers.
• Figure 3: Exemplary slices for one chest CT scan taken from the MosMedData dataset Chest_CT.
• Figure 4: Comparison of the training times for a global VGG9 model, and the two decomposed CNN models, that is, the CNN-DNN-transfer approach KLW:CNN-DNN_coh:2024 and the DD-CNN-transfer approach GuCai:2022:dd_transfer for the TF-Flowers dataset tfflowers. We show in gray the training time required for the global VGG9 model using the entire TF-Flowers images as input data. In blue, we show the training time for the local CNNs for CNN-DNN-transfer and DD-CNN-transfer, respectively, and in red the times for the subsequent training of the respective global net using the transfer learning strategy.