基于概念格因子分解的零件三维CAD模型检索

针对影响概念格应用的重要问题—即使是一个小规模数据集也会产生大量的形式概念，文中提出了可以满足关系覆盖的用对象（属性）概念分解形式背景对应的布尔矩阵的新方法.用这种方法原对象属性间的二元关系可以用数量在对象（属性）概念个数以内的概念表达出来，成为概念格因子.文中给出了概念格因子生成的基本原理及其算法.通过分析三维CAD零件模型功能表面间的关系构建零件工程图结构模型，并将其映射为形式背景，从而完成概念格因子到零件关键结构的应用.最后，实例演示了概念格因子在基于零件工程图结构模型的零件CAD模型检索中的运用.

Concept Lattice Factorization Based 3D Model Retrieval of Mechanical Parts

A small set of data can result in a very large number of formal concepts. With regard to this important topic, we propose an objects (attributes) concept based approach to factor Boolean matrix for the formal context in this paper. We show that the original binary relations between objects and attributes can be represented by the objects (attributes) concept matrices whose total number of concepts (factors) does not exceed the number of objects (attributes) concepts. We propose an algorithm to generate the factors. This method relies on the fundamental finite factorization property of binary matrix factorization which we proposed and proved. After analyzing the function relation between the surfaces of the 3D CAD part models, building up the engineering drawing structure model, and mapping it to the formal context, we apply concept lattice factorization to the key parts structures. Experiments on parts CAD model retrieval have shown the competency and effectiveness of the concept lattice factorization.