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Parametric UMAP Embeddings for Representation and Semisupervised Learning
Neural Computation ( IF 2.7 ) Pub Date : 2021-10-12 , DOI: 10.1162/neco_a_01434
Tim Sainburg 1 , Leland McInnes 2 , Timothy Q Gentner 1
Affiliation  

UMAP is a nonparametric graph-based dimensionality reduction algorithm using applied Riemannian geometry and algebraic topology to find low-dimensional embeddings of structured data. The UMAP algorithm consists of two steps: (1) computing a graphical representation of a data set (fuzzy simplicial complex) and (2) through stochastic gradient descent, optimizing a low-dimensional embedding of the graph. Here, we extend the second step of UMAP to a parametric optimization over neural network weights, learning a parametric relationship between data and embedding. We first demonstrate that parametric UMAP performs comparably to its nonparametric counterpart while conferring the benefit of a learned parametric mapping (e.g., fast online embeddings for new data). We then explore UMAP as a regularization, constraining the latent distribution of autoencoders, parametrically varying global structure preservation, and improving classifier accuracy for semisupervised learning by capturing structure in unlabeled data.1



中文翻译:

用于表示和半监督学习的参数化 UMAP 嵌入

UMAP 是一种基于非参数图的降维算法,它使用应用的黎曼几何和代数拓扑来查找结构化数据的低维嵌入。UMAP 算法包括两个步骤:(1) 计算数据集的图形表示(模糊单纯复形)和(2)通过随机梯度下降,优化图的低维嵌入。在这里,我们将 UMAP 的第二步扩展到对神经网络权重的参数优化,学习数据和嵌入之间的参数关系。我们首先证明参数 UMAP 的性能与其非参数对应物相当,同时赋予学习参数映射的好处(例如,新数据的快速在线嵌入)。然后我们探索 UMAP 作为正则化,1

更新日期:2021-10-14
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