Slow feature analysis (SFA) is an unsupervised learning algorithm that extracts slowly varying features from a multi-dimensional time series. SFA has been extended to supervised learning (classification and regression) by an algorithm called graph-based SFA (GSFA). GSFA relies on a particular graph structure to extract features that preserve label similarities. Processing of high dimensional input data (e.g., images) is feasible via hierarchical GSFA (HGSFA), resulting in a multi-layer neural network. Although HGSFA has useful properties, in this work we identify a shortcoming, namely, that HGSFA networks prematurely discard quickly varying but useful features before they reach higher layers, resulting in suboptimal global slowness and an under-exploited feature space. To counteract this shortcoming, which we call unnecessary information loss, we propose an extension called hierarchical information-preserving GSFA (HiGSFA), where some features fulfill a slowness objective and other features fulfill an information preservation objective. The efficacy of the extension is verified in three experiments: (1) an unsupervised setup where the input data is the visual stimuli of a simulated rat, (2) the localization of faces in image patches, and (3) the estimation of human age from facial photographs of the MORPH-II database. Both HiGSFA and HGSFA can learn multiple labels and offer a rich feature space, feed-forward training, and linear complexity in the number of samples and dimensions. However, the proposed algorithm, HiGSFA, outperforms HGSFA in terms of feature slowness, estimation accuracy, and input reconstruction, giving rise to a promising hierarchical supervised-learning approach. Moreover, for age estimation, HiGSFA achieves a mean absolute error of 3.41 years, which is a competitive performance for this challenging problem.

中文翻译：

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改进的基于图的 SFA：信息保存补充了缓慢原则

慢特征分析 (SFA) 是一种无监督学习算法，可从多维时间序列中提取缓慢变化的特征。SFA 已通过一种称为基于图的 SFA (GSFA) 的算法扩展到监督学习（分类和回归）。GSFA 依靠特定的图结构来提取保留标签相似性的特征。通过分层 GSFA (HGSFA) 处理高维输入数据（例如图像）是可行的，从而产生多层神经网络。尽管 HGSFA 具有有用的特性，但在这项工作中，我们发现了一个缺点，即 HGSFA 网络在到达更高层之前过早地丢弃了快速变化但有用的特征，导致次优全局缓慢和未充分利用的特征空间。为了抵消这个缺点，我们称之为不必要的信息丢失，我们提出了一种称为分层信息保留 GSFA (HiGSFA) 的扩展，其中一些特征满足慢度目标，其他特征满足信息保留目标。扩展的有效性在三个实验中得到验证：（1）无监督设置，其中输入数据是模拟大鼠的视觉刺激，（2）图像块中面部的定位，以及（3）人类年龄的估计来自 MORPH-II 数据库的面部照片。HiGSFA 和 HGSFA 都可以学习多个标签，并提供丰富的特征空间、前馈训练以及样本数量和维度的线性复杂度。然而，所提出的算法 HiGSFA 在特征缓慢、估计精度和输入重建方面优于 HGSFA，从而产生了一种有前途的分层监督学习方法。