亲和矩阵的平滑处理如何影响t-SNE中的邻域保持
How smoothing the affinity matrix affects neighborhood preservation in t-SNE
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中文总结 AI 辅助
本研究针对t-SNE的亲和矩阵，提出逐行幂变换方法，发现锐化可提升最近邻保持、平滑可提升中局部邻域保持，为优化t-SNE邻域保持提供了新视角。
中文摘要 AI 辅助
降维方法是高维数据可视化的重要工具，t-SNE因强调局部邻域保持而成为最广泛使用的方法之一。t-SNE的核心组成部分是亲和矩阵，它以对称概率的形式表示成对相似度，t-SNE的优化问题即基于该矩阵定义。本研究探讨该概率分布的锐度如何影响不同尺度下的邻域保持，引入由参数γ控制的逐行幂变换，该变换可在保持亲和矩阵稀疏性和秩顺序的同时平滑或锐化其每一行。研究表明，该变换等价于重新缩放高斯带宽，因此也等价于改变困惑度；但由于概率分布的锐度随每个数据点变化，固定γ会导致点依赖的有效困惑度，这与改变全局困惑度不同。实验发现，锐化处理可提升最近邻的保持效果，而平滑处理则能提升更宽泛局部邻域的保持效果，在中局部范围内的表现优于包括多尺度方法在内的其他亲和矩阵构造方式。
英文摘要
Dimensionality reduction methods are instrumental to visualize high-dimensional data, and t-SNE stands as one of the most widely used methods due to its emphasis on local neighborhood preservation. A central component of t-SNE is the affinity matrix, which expresses pairwise similarities in the form of symmetrized probabilities, over which the optimization problem of t-SNE is defined. We study how the sharpness of this probability distribution affects neighborhood preservation at different scales. We introduce a row-wise power transform controlled by a parameter gamma that can smooth or sharpen each row of the affinity matrix while preserving sparsity and rank order. We show that this transform is equivalent to rescaling the Gaussian bandwidth and thus to changing the perplexity. However, as the sharpness of the probability distribution varies per point, a fixed gamma leads to point-dependent effective perplexities, making it distinct from changing the global perplexity. Empirically, we find that sharpening improves preservation of the very nearest neighbors, while smoothing improves preservation of broader local neighborhoods, outperforming alternative affinity constructions including multiscale methods in the mid-local range.
发表机构
- Ghent University（根特大学）
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