Embedding high-dimensional data onto a low-dimensional manifold is of both theoretical and practical value. In this paper, we propose to combine deep neural networks (DNN) with mathematics-guided embedding rules for high-dimensional data embedding. We introduce a generic deep embedding network (DEN) framework, which is able to learn a parametric mapping from high-dimensional space to low-dimensional space, guided by well-established objectives such as Kullback-Leibler (KL) divergence minimization. We further propose a recursive strategy, called deep recursive embedding (DRE), to make use of the latent data representations for boosted embedding performance. We exemplify the flexibility of DRE by different architectures and loss functions, and benchmarked our method against the two most popular embedding methods, namely, t-distributed stochastic neighbor embedding (t-SNE) and uniform manifold approximation and projection (UMAP). The proposed DRE method can map out-of-sample data and scale to extremely large datasets. Experiments on a range of public datasets demonstrated improved embedding performance in terms of local and global structure preservation, compared with other state-of-the-art embedding methods.
翻译:深神经网络(DNN)与高数据嵌入的数学引导嵌入规则相结合。我们引入了一个通用的深嵌入网络(DEN)框架,这个框架能够学习从高空间到低维空间的参数绘图,以Kullback-Leiper(KL)差异最小化(KL)等既定目标为指导,从高空间到低维空间,从高维空间到低维空间,在Kullback-Leiber(KLLL)差异最小化(KLL)差异最小化(KLLLL)等既定目标的指导下,从高维数据和实际价值中嵌入数据。我们进一步提议了一项循环战略,称为深循环嵌入嵌入(DRE),以利用潜在数据表示提升嵌入性性绩效。我们通过不同的架构和损失功能展示DRE的灵活性,并对照两种最受欢迎的嵌入方法,即,即,将相异型相交的相异型相近的邻居嵌入(t-SNENS)以及统一的多重近和投影。拟议DRE方法可以绘制出数据和规模至极大数据集。在一系列公共数据保存的比较结构中,用其他州嵌入性结构的实验。