Abstract We focus on an image classification task in which only several unlabeled images per class are available for learning and low computational complexity is required. We recall the state-of-the-art methods that are used to solve the task: autoencoder-based approaches and manifold-decomposition-based approaches. Next, we introduce our proposed method, which is based on a combination of the F-transform and (kernel) principal component analysis. F-transform significantly reduces the computation time of PCA and increases the robustness of PCA to translation, while PCA proposes more descriptive features. This combination performs 3D reduction: the F-transform reduces dimensionality over a single 2D image, while PCA reduces dimensionality through the whole set of processed images. Based on the benchmark results, our method may outperform deep-learning-based methods in limited settings. For completeness, we also address other image resampling algorithms that can be used instead of the F-transform, and we find that the F-transform is the most suitable.

中文翻译：

---

用于小数据集无监督学习的新型降维方法

摘要 我们专注于图像分类任务，其中每类只有几个未标记的图像可供学习，并且需要低计算复杂度。我们回顾了用于解决任务的最新方法：基于自动编码器的方法和基于流形分解的方法。接下来，我们介绍我们提出的方法，该方法基于 F 变换和（核）主成分分析的组合。F-transform 显着减少了 PCA 的计算时间，增加了 PCA 对翻译的鲁棒性，而 PCA 提出了更多的描述性特征。这种组合执行 3D 缩减：F 变换减少单个 2D 图像的维度，而 PCA 减少整个处理图像集的维度。根据基准测试结果，在有限的环境中，我们的方法可能优于基于深度学习的方法。为完整起见，我们还介绍了可以代替 F 变换使用的其他图像重采样算法，我们发现 F 变换是最合适的。