RESUMEN
The multilayer perceptron (MLP) neural network is interpreted from the geometrical viewpoint in this work, that is, an MLP partition an input feature space into multiple nonoverlapping subspaces using a set of hyperplanes, where the great majority of samples in a subspace belongs to one object class. Based on this high-level idea, we propose a three-layer feedforward MLP (FF-MLP) architecture for its implementation. In the first layer, the input feature space is split into multiple subspaces by a set of partitioning hyperplanes and rectified linear unit (ReLU) activation, which is implemented by the classical two-class linear discriminant analysis (LDA). In the second layer, each neuron activates one of the subspaces formed by the partitioning hyperplanes with specially designed weights. In the third layer, all subspaces of the same class are connected to an output node that represents the object class. The proposed design determines all MLP parameters in a feedforward one-pass fashion analytically without backpropagation. Experiments are conducted to compare the performance of the traditional backpropagation-based MLP (BP-MLP) and the new FF-MLP. It is observed that the FF-MLP outperforms the BP-MLP in terms of design time, training time, and classification performance in several benchmarking datasets. Our source code is available at https://colab.research.google.com/drive/1Gz0L8A-nT4ijrUchrhEXXsnaacrFdenn?usp = sharing.
RESUMEN
OBJECTIVE: Recent advances in light-sheet fluorescence microscopy (LSFM) enable 3-dimensional (3-D) imaging of cardiac architecture and mechanics in toto. However, segmentation of the cardiac trabecular network to quantify cardiac injury remains a challenge. METHODS: We hereby employed "subspace approximation with augmented kernels (Saak) transform" for accurate and efficient quantification of the light-sheet image stacks following chemotherapy-treatment. We established a machine learning framework with augmented kernels based on the Karhunen-Loeve Transform (KLT) to preserve linearity and reversibility of rectification. RESULTS: The Saak transform-based machine learning enhances computational efficiency and obviates iterative optimization of cost function needed for neural networks, minimizing the number of training datasets for segmentation in our scenario. The integration of forward and inverse Saak transforms can also serve as a light-weight module to filter adversarial perturbations and reconstruct estimated images, salvaging robustness of existing classification methods. The accuracy and robustness of the Saak transform are evident following the tests of dice similarity coefficients and various adversary perturbation algorithms, respectively. The addition of edge detection further allows for quantifying the surface area to volume ratio (SVR) of the myocardium in response to chemotherapy-induced cardiac remodeling. CONCLUSION: The combination of Saak transform, random forest, and edge detection augments segmentation efficiency by 20-fold as compared to manual processing. SIGNIFICANCE: This new methodology establishes a robust framework for post light-sheet imaging processing, and creating a data-driven machine learning for automated quantification of cardiac ultra-structure.
