Su‐Yun Huang

Toshinari Morimoto, Su-Yun Huang

In this paper, we propose a dimension reduction method specifically designed for tensor-structured feature data in deep neural networks. The method is implemented as a hidden layer, called the TensorProjection layer, which transforms input tensors into output tensors with reduced dimensions through mode-wise projections. The projection directions are treated as model parameters of the layer and are optimized during model training. Our method can serve as an alternative to pooling layers for summarizing image data, or to convolutional layers as a technique for reducing the number of channels. We conduct experiments on tasks such as medical image classification and segmentation, integrating the TensorProjection layer into commonly used baseline architectures to evaluate its effectiveness. Numerical experiments indicate that the proposed method can outperform traditional downsampling methods, such as pooling layers, in our tasks, suggesting it as a promising alternative for feature summarization.

Szu-Chi Chung, Shao-Hsuan Wang, Po-Yao Niu et al.

Principal component analysis (PCA) is arguably the most widely used dimension-reduction method for vector-type data. When applied to a sample of images, PCA requires vectorization of the image data, which in turn entails solving an eigenvalue problem for the sample covariance matrix. We propose herein a two-stage dimension reduction (2SDR) method for image reconstruction from high-dimensional noisy image data. The first stage treats the image as a matrix, which is a tensor of order 2, and uses multilinear principal component analysis (MPCA) for matrix rank reduction and image denoising. The second stage vectorizes the reduced-rank matrix and achieves further dimension and noise reduction. Simulation studies demonstrate excellent performance of 2SDR, for which we also develop an asymptotic theory that establishes consistency of its rank selection. Applications to cryo-EM (cryogenic electronic microscopy), which has revolutionized structural biology, organic and medical chemistry, cellular and molecular physiology in the past decade, are also provided and illustrated with benchmark cryo-EM datasets. Connections to other contemporaneous developments in image reconstruction and high-dimensional statistical inference are also discussed.