LASS：一个简单的Laplacian平滑分配模型
LASS: a simple assignment model with Laplacian smoothing
摘要：
我们考虑的问题，学习软分配的$N$项目到$K$类别给定两个来源的信息：一个项目类别相似性矩阵，鼓励项目被分配到类别，他们是相似的（和不被分配到类别，他们是不相似的），和一个项目项目相似性矩阵，鼓励类似的项目有类似的分配。我们提出了一个简单的二次规划模型，捕捉这种直觉。我们给出了它的解决方案是唯一的必要条件，定义了一个样本外映射，并推导出一个简单，有效的训练算法的基础上交替方向法的乘数。该模型甚至可以从几个相似度值中预测合理的分配，并且可以被视为半监督学习的推广。当项目自然地属于多个类别时，例如当用关键字或带有标签的图片注释文档时，或者当类别具有未知的复杂相互关系（例如分层）时，它特别有用。
英文摘要：
We consider the problem of learning soft assignments of $N$ items to $K$ categories given two sources of information: an item-category similarity matrix, which encourages items to be assigned to categories they are similar to (and to not be assigned to categories they are dissimilar to), and an item-item similarity matrix, which encourages similar items to have similar assignments. We propose a simple quadratic programming model that captures this intuition. We give necessary conditions for its solution to be unique, define an out-of-sample mapping, and derive a simple, effective training algorithm based on the alternating direction method of multipliers. The model predicts reasonable assignments from even a few similarity values, and can be seen as a generalization of semisupervised learning. It is particularly useful when items naturally belong to multiple categories, as for example when annotating documents with keywords or pictures with tags, with partially tagged items, or when the categories have complex interrelations (e.g. hierarchical) that are unknown.
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。
