用几何中位数降低降维结果波动，提升稳定性。
Median Consensus Embedding for Dimensionality Reduction
- 以多个嵌入的几何中位数作为最终结果，减少随机初始化影响。
- 理论证明其收敛速度呈指数级，实际应用中快速稳定。
- 适合对结果可靠性要求高的数据分析与缺失值处理场景。
本文提出中位共识嵌入（Median Consensus Embedding, MCE），用于缓解t-SNE等非线性降维方法因随机初始化导致的低维嵌入不一致问题。MCE定义为多个嵌入的几何中位数。基于大偏差理论，假设多个嵌入为独立同分布样本，证明了MCE在指数速率下具有一致性。进一步设计了基于数据点成对距离矩阵弗罗贝尼乌斯范数的距离函数，实现可操作的算法。实际数据实验表明，MCE收敛迅速，显著降低嵌入不稳定性。此外，将MCE与多重插补结合处理缺失值，并考虑多尺度超参数设置。结果验证了MCE能有效缓解由随机初始化及其他因素引发的嵌入方法不稳定问题。
原文摘要 · Abstract (English)
This study proposes median consensus embedding (MCE) to address variability in low-dimensional embeddings caused by random initialization in nonlinear dimensionality reduction techniques such as $t$-distributed stochastic neighbor embedding. MCE is defined as the geometric median of multiple embeddings. By assuming multiple embeddings as independent and identically distributed random samples and applying large deviation theory, we prove that MCE achieves consistency at an exponential rate. Furthermore, we develop a practical algorithm to implement MCE by constructing a distance function between embeddings based on the Frobenius norm of the pairwise distance matrix of data points. Application to actual data demonstrates that MCE converges rapidly and effectively reduces instability. We further combine MCE with multiple imputation to address missing values and consider multiscale hyperparameters. Results confirm that MCE effectively mitigates instability issues in embedding methods arising from random initialization and other sources.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。