We elaborate on the robustness assessment of a deep neural network (DNN) approach to dimensionality reduction for data visualization. The proposed DNN seeks to improve the class separability and compactness in a low-dimensional feature space, which is a natural strategy to obtain well-clustered visualizations. It consists of a DNN-based nonlinear generalization of Fisher's linear discriminant analysis and a DNN-based regularizer. Regarding data visualization, a well-regularized DNN guarantees to learn sufficiently similar data visualizations for different sets of samples that represent the data approximately equally well. Such a robustness against fluctuations in the data is essential for many real-world applications. Our results show that the combined DNN is considerably more robust than the generalized discriminant analysis alone. We further support this conclusion by examining feature representations from four comparative approaches. As a means of measuring the structural dissimilarity between different feature representations, we propose a hierarchical cluster analysis.

我们详细介绍了深度神经网络（DNN）降维数据可视化方法的鲁棒性评估。提出的DNN旨在提高低维特征空间中的类可分离性和紧凑性，这是获得聚类良好可视化效果的自然策略。它由基于DNN的Fisher线性判别分析的非线性概括和基于DNN的正则化器组成。关于数据可视化，规则良好的DNN可以保证对代表数据大致相同的不同样本集学习足够相似的数据可视化。对于许多实际应用而言，这种针对数据波动的鲁棒性至关重要。我们的结果表明，组合的DNN比单独的广义判别分析强大得多。我们通过检查四种比较方法的特征表示进一步支持这一结论。作为衡量不同特征表示之间结构差异的一种方法，我们提出了层次聚类分析。