訓練資料特徵對 VAE 隱變量和基於 CNN 之預測的影響

Abstract

本研究探討變分自編碼器（Variational Autoencoder, VAE）在不同資料型態上的應用，包含一維與二維高斯混合模型，以及從簡單圖像到複雜照片的影像資料訓練，藉此觀察 VAE 對不同資料結構的表現差異。為評估其於電阻抗斷層掃描（Electrical Impedance Tomography, EIT）領域的潛在應用，本研究進一步自行生成模擬的邊界電壓矩陣資料，並將不同矩陣形狀（例如 (120, 20) 與 (20, 900)）作為輸入進行訓練與重建，分析編碼與解碼過程中的誤差變化。實驗結果顯示，高維資料在數值重建誤差上雖顯著降低，但其與導電率變化的相關性也相對減弱，顯示模型可能僅學習到主要結構，而未能充分捕捉潛在的物理特徵。最後，本研究嘗試利用卷積神經網路（Convolutional Neural Network, CNN）學習邊界電壓矩陣與 VAE 潛在變量之間的對應關係，雖未能成功獲得穩定的映射結果，但此現象凸顯了該問題的挑戰性，也為後續模型設計與改進提供了方向。本研究結果顯示，資料結構特性對 VAE 的重建能力有明顯影響，並對 EIT 的資料驅動式影像重建方法提供了實驗性證據與啟示。

This study investigates the application of Variational Autoencoders (VAE) to different types of datasets, including one-dimensional and two-dimensional Gaussian mixture models, as well as image datasets ranging from simple to complex patterns, in order to examine the performance of VAE under various data structures. To explore its potential application in Electrical Impedance Tomography (EIT), we further generated simulated boundary voltage matrices and trained the VAE with different matrix shapes (e.g., (120, 20) and (20, 900)) to analyze reconstruction errors during the encoding and decoding processes. Experimental results show that although higher-dimensional data yield significantly lower numerical reconstruction errors, their correlation with conductivity variation is weaker, indicating that the model may capture only the dominant structure rather than the underlying physical features. Finally, we attempted to use a Convolutional Neural Network (CNN) to learn the mapping between the boundary voltage matrices and the VAE latent variables. While the CNN failed to produce stable and reliable mappings, this result highlights the complexity of the problem and provides valuable insights for future model design. Overall, the findings demonstrate that data structure plays a crucial role in VAE reconstruction performance and offer experimental evidence for advancing data-driven reconstruction methods in EIT.