Data analysis often requires methods that are invariant with respect to specific transformations, such as rotations in case of images or shifts in case of images and time series. While principal component analysis (PCA) is a widely-used dimension reduction technique, it lacks robustness with respect to these transformations. Modern alternatives, such as autoencoders, can be invariant with respect to specific transformations but are generally not interpretable. We introduce General Transform-Invariant Principal Component Analysis (GT-PCA) as an effective and interpretable alternative to PCA and autoencoders. We propose a neural network that efficiently estimates the components and show that GT-PCA significantly outperforms alternative methods in experiments based on synthetic and real data.

翻译：数据分析通常需要能够对特定变换具有不变性的方法，如图像中的旋转或图像及时序数据中的平移。尽管主成分分析（PCA）是一种广泛使用的降维技术，但其对这些变换缺乏鲁棒性。现代替代方法（如自编码器）虽能对特定变换保持不变性，但通常缺乏可解释性。我们提出通用变换不变主成分分析（GT-PCA），作为PCA和自编码器的一种高效且可解释的替代方案。我们设计了一种神经网络高效估计成分，并实验证明GT-PCA在合成数据与真实数据实验中均显著优于现有方法。