This paper introduces a novel graph-based filter method for automatic feature
selection (abbreviated as GB-AFS) for multi-class classification tasks. The
method determines the minimum combination of features required to sustain
prediction performance while maintaining complementary discriminating abilities
between different classes. It does not require any user-defined parameters such
as the number of features to select. The methodology employs the
Jeffries-Matusita (JM) distance in conjunction with t-distributed Stochastic
Neighbor Embedding (t-SNE) to generate a low-dimensional space reflecting how
effectively each feature can differentiate between each pair of classes. The
minimum number of features is selected using our newly developed Mean
Simplified Silhouette (abbreviated as MSS) index, designed to evaluate the
clustering results for the feature selection task. Experimental results on
public data sets demonstrate the superior performance of the proposed GB-AFS
over other filter-based techniques and automatic feature selection approaches.
Moreover, the proposed algorithm maintained the accuracy achieved when
utilizing all features, while using only $7\%$ to $30\%$ of the features.
Consequently, this resulted in a reduction of the time needed for
classifications, from $15\%$ to $70\%$.

该论文介绍了一种用于多类别分类的自动特征选择的新型基于图的滤波方法（缩写为 GB-AFS），它确定了在维持预测性能的同时保持不同类别之间互补判别能力的最小特征组合。该方法不需要任何用户定义的参数，如要选择的特征数量。该方法使用 Jeffries-Matusita (JM) 距离结合 t 分布随机邻域嵌入（t-SNE）生成反映每个特征能够在每对类别之间区分性的低维空间。采用我们新开发的用于特征选择任务的平均简化 Silhouette (MSS) 指数选择最小特征数量，该指数旨在评估特征选择任务的聚类结果。在公开数据集上的实验结果表明，所提出的 GB-AFS 方法优于其他基于滤波的技术和自动特征选择方法的性能。此外，所提出的算法在仅使用特征的 7% 到 30% 的情况下保持了达到的准确性，从而将分类所需的时间减少了 15% 到 70%。

基于图的多类分类自动特征选择通过均值简化轮廓

Graph-Based Automatic Feature Selection for Multi-Class Classification  via Mean Simplified Silhouette

Widely used pipelines for the analysis of high-dimensional data utilize
two-dimensional visualizations. These are created, e.g., via t-distributed
stochastic neighbor embedding (t-SNE). When it comes to large data sets,
applying these visualization techniques creates suboptimal embeddings, as the
hyperparameters are not suitable for large data. Cranking up these parameters
usually does not work as the computations become too expensive for practical
workflows. In this paper, we argue that a sampling-based embedding approach can
circumvent these problems. We show that hyperparameters must be chosen
carefully, depending on the sampling rate and the intended final embedding.
Further, we show how this approach speeds up the computation and increases the
quality of the embeddings.

在这篇论文中，我们提出了一种基于采样的嵌入方法，用于解决在分析高维数据时使用二维可视化技术会导致次优嵌入的问题。我们展示了如何根据采样率和预期的最终嵌入选择合适的超参数，并说明了这种方法如何加快计算速度并提高嵌入的质量。

调整和计算基于采样的 t-SNE 嵌入的困惑度

Tuning the perplexity for and computing sampling-based t-SNE embeddings

This paper investigates the theoretical foundations of the t-distributed
stochastic neighbor embedding (t-SNE) algorithm, a popular nonlinear dimension
reduction and data visualization method. A novel theoretical framework for the
analysis of t-SNE based on the gradient descent approach is presented. For the
early exaggeration stage of t-SNE, we show its asymptotic equivalence to power
iterations based on the underlying graph Laplacian, characterize its limiting
behavior, and uncover its deep connection to Laplacian spectral clustering, and
fundamental principles including early stopping as implicit regularization. The
results explain the intrinsic mechanism and the empirical benefits of such a
computational strategy. For the embedding stage of t-SNE, we characterize the
kinematics of the low-dimensional map throughout the iterations, and identify
an amplification phase, featuring the intercluster repulsion and the expansive
behavior of the low-dimensional map, and a stabilization phase. The general
theory explains the fast convergence rate and the exceptional empirical
performance of t-SNE for visualizing clustered data, brings forth
interpretations of the t-SNE visualizations, and provides theoretical guidance
for applying t-SNE and selecting its tuning parameters in various applications.

本文对 t-SNE 算法的理论框架进行了研究，在梯度下降法的基础上提出了一种新的理论框架；对于 t-SNE 的 embedding 阶段，文中还对其低维映射的运动学进行了表征和说明。通过本文，我们发现了 t-SNE 的内在机制并说明其在可视化聚类数据方面具有非凡的实用性。