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arXiv 2002.05747cs.LGmath.MGstat.APstat.ML
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结构化数据的多度量学习

Multiple Metric Learning for Structured Data

Royal Holloway University of London(伦敦大学皇家霍洛威学院)

Nicolo Colombo

摘要:

我们解决的问题,合并图和特征空间信息,同时学习从结构化数据的度量。现有的算法解决这个问题的不对称的方式,通过提取矢量化的图形结构的摘要或添加硬约束的特征空间算法。遵循不同的路径,我们定义了一个度量回归方案,我们训练度量约束的线性组合的相异性矩阵。其思想是输入矩阵可以是从任何类型的可用数据(例如节点属性或边结构)获得的预先计算的相异性度量。由于模型输入是距离度量,因此我们不需要假设任何潜在特征空间的存在。主要的挑战是,度量约束(特别是正定性和次可加性),不自动遵守,例如,如果线性组合的系数被允许为负。正约束和次加性约束都是线性不等式,但施加它们的计算复杂性为O(D3),其中D是输入矩阵的大小(即数据集的大小)。即使当D相对较小时,这也很快变得令人望而却步。我们提出了一种新的基于图形的技术,在这种约束下进行优化,并表明,在某些情况下,我们的方法可以减少原来的计算复杂性的优化过程中的一个数量级。与现有的方法不同,我们的方案适用于任何(可能是非凸的)度量约束的目标函数。

英文摘要:

We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph structure or adding hard constraints to feature-space algorithms. Following a different path, we define a metric regression scheme where we train metric-constrained linear combinations of dissimilarity matrices. The idea is that the input matrices can be pre-computed dissimilarity measures obtained from any kind of available data (e.g. node attributes or edge structure). As the model inputs are distance measures, we do not need to assume the existence of any underlying feature space. Main challenge is that metric constraints (especially positive-definiteness and sub-additivity), are not automatically respected if, for example, the coefficients of the linear combination are allowed to be negative. Both positive and sub-additive constraints are linear inequalities, but the computational complexity of imposing them scales as O(D3), where D is the size of the input matrices (i.e. the size of the data set). This becomes quickly prohibitive, even when D is relatively small. We propose a new graph-based technique for optimizing under such constraints and show that, in some cases, our approach may reduce the original computational complexity of the optimization process by one order of magnitude. Contrarily to existing methods, our scheme applies to any (possibly non-convex) metric-constrained objective function.

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。

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