矩阵分解与测地距离的解释
Matrix factorisation and the interpretation of geodesic distance
摘要：
给定一个图或相似矩阵，我们考虑恢复节点之间的真实距离的概念的问题，因此它们的真实位置。我们表明，这可以完成两个步骤：矩阵分解，其次是非线性降维。这种组合是有效的，因为在第一步中获得的点云接近于其中潜在距离被编码为测地线距离的流形。因此，近似测地线距离的非线性降维工具可以通过简单的变换来恢复潜在位置。我们给出了一个详细的说明的情况下，使用光谱嵌入，其次是Isomap，并提供了令人鼓舞的实验证据，其他技术的组合。
英文摘要：
Given a graph or similarity matrix, we consider the problem of recovering a notion of true distance between the nodes, and so their true positions. We show that this can be accomplished in two steps: matrix factorisation, followed by nonlinear dimension reduction. This combination is effective because the point cloud obtained in the first step lives close to a manifold in which latent distance is encoded as geodesic distance. Hence, a nonlinear dimension reduction tool, approximating geodesic distance, can recover the latent positions, up to a simple transformation. We give a detailed account of the case where spectral embedding is used, followed by Isomap, and provide encouraging experimental evidence for other combinations of techniques.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
