Learning Low-Dimensional Latent Graph Structures: A Density Estimation Approach
Learning Low-Dimensional Latent Graph Structures: A Density Estimation Approach
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DOI：
10.1109/tnnls.2019.2917696
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发表时间：
2020-04-01
影响因子：
10.4
通讯作者：
Li, Ren-cang
中科院分区：
文献类型：
--
作者：
Wang, Li;Li, Ren-cang
我们的目标是基于统一的密度估计框架从高维无监督数据中自动学习低维空间中的潜在图结构，用于特征提取和特征选择，其中潜在结构被认为是高维数据的紧凑和信息表示。基于这个框架，提出了两种新的方法与现有的方法非常不同，但直观的学习标准。所提出的特征提取方法可以通过自然地将输入数据的判别信息与结构学习相结合来学习低维空间中的一组嵌入点，从而可以发现数据的多个不连通的嵌入结构。所提出的特征选择方法只保留最优特征集上的成对距离，并同时选择这些特征。它不仅获得了最佳的特征集，而且还学习了可视化的结构和嵌入。大量的实验表明，我们提出的方法可以实现有竞争力的定量（往往更好）的判别评价性能方面的结果，并能够获得光滑的骨架结构的嵌入，并选择最佳的功能，揭示正确的图结构的高维数据集。
We aim to automatically learn a latent graph structure in a low-dimensional space from high-dimensional, unsupervised data based on a unified density estimation framework for both feature extraction and feature selection, where the latent structure is considered as a compact and informative representation of the high-dimensional data. Based on this framework, two novel methods are proposed with very different but intuitive learning criteria from existing methods. The proposed feature extraction method can learn a set of embedded points in a low-dimensional space by naturally integrating the discriminative information of the input data with structure learning so that multiple disconnected embedding structures of data can be uncovered. The proposed feature selection method preserves the pairwise distances only on the optimal set of features and selects these features simultaneously. It not only obtains the optimal set of features but also learns both the structure and embeddings for visualization. Extensive experiments demonstrate that our proposed methods can achieve competitive quantitative (often better) results in terms of discriminant evaluation performance and are able to obtain the embeddings of smooth skeleton structures and select optimal features to unveil the correct graph structures of high-dimensional data sets.