We present a versatile adaptation of existing dimensionality reduction (DR)
objectives, enabling the simultaneous reduction of both sample and feature
sizes. Correspondances between input and embedding samples are computed through
a semi-relaxed Gromov-Wasserstein optimal transport (OT) problem. When the
embedding sample size matches that of the input, our model recovers classical
popular DR models. When the embedding's dimensionality is unconstrained, we
show that the OT plan delivers a competitive hard clustering. We emphasize the
importance of intermediate stages that blend DR and clustering for summarizing
real data and apply our method to visualize datasets of images.

我们提出了一种适用于现有降维目标的通用适应方法，同时降低样本和特征大小。通过半松弛的 Gromov-Wasserstein 最优输运问题计算输入和嵌入样本之间的对应关系。当嵌入样本大小与输入大小匹配时，我们的模型恢复了经典的受欢迎的降维模型。当嵌入的维度不受限制时，我们展示了最优输运方案提供了一种有竞争力的硬聚类。我们强调了中间阶段将降维和聚类相结合以概括真实数据的重要性，并将我们的方法应用于可视化图像数据集。