Regularization on Discrete Spaces
Regularization on Discrete Spaces
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DOI：
10.1007/11550518_45
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发表时间：
2005-08
期刊：
影响因子：
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通讯作者：
Dengyong Zhou;B. Scholkopf
中科院分区：
文献类型：
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作者：
Dengyong Zhou;B. Scholkopf
我们考虑的分类问题上的一个有限的对象集。其中一些是有标签的，任务是预测剩下的未标记的标签。这样的估计问题通常被称为转导推理。众所周知，许多有意义的归纳或监督方法可以从正则化框架中导出，该框架最小化损失函数加上正则化项。本着同样的精神，我们提出了一个一般的离散正则化框架定义在有限的对象集，它可以被认为是离散模拟经典正则化理论。一个家庭的转导推理计划，然后系统地来自框架，包括我们以前的算法转导推理，我们得到了令人鼓舞的结果，在许多实际的分类问题。离散正则化框架是建立在离散分析和我们自己开发的几何，其中构造了一些不同阶的离散微分算子，可以被认为是在连续的情况下，其对应物的离散模拟。
We consider the classification problem on a finite set of objects. Some of them are labeled, and the task is to predict the labels of the remaining unlabeled ones. Such an estimation problem is generally referred to as transductive inference. It is well-known that many meaningful inductive or supervised methods can be derived from a regularization framework, which minimizes a loss function plus a regularization term. In the same spirit, we propose a general discrete regularization framework defined on finite object sets, which can be thought of as discrete analogue of classical regularization theory. A family of transductive inference schemes is then systemically derived from the framework, including our earlier algorithm for transductive inference, with which we obtained encouraging results on many practical classification problems. The discrete regularization framework is built on discrete analysis and geometry developed by ourselves, in which a number of discrete differential operators of various orders are constructed, which can be thought of as discrete analogues of their counterparts in the continuous case.