相似性的二值表示

Binary Representation of Similarity

在模式识别与机器学习领域,相似性具有重要作用.但是相似性具有不同的解释.讨论了相似性在原型理论、样例理论下的不同解释,指出几乎所有的非负度量都有对应的相似性解释,说明了一定程度上相似性反映了对象的全局性质.作为一般相似性的例子,给出了图像、模糊集合的相似性解释,指出模糊集合是研究论域内对象与概念相似性的有效工具之一,并根据韦特海默对比不变性原则(Wertheimer's contrast invariant principle),导出了相似对比不变性准则.据此建立了有界非负矩阵的二值表示.这些结果可以得到相似矩阵的最优二值分解.由于相似性的广泛性,该模型可望有很多应用.

In pattern recognition and machine learning, similarity plays an important role. It is well known that similarity has different definitions. Discussed in this paper are different explanations of similarity under exemplar theory and prototype theory. As for exemplar theory, similarity is defined as pair similarity between two objects; and for prototype theory, similarity is defined between an object and a prototype. According to the above analysis, it is pointed out that almost nonnegative physical measures have their interpretations of similarity and similarity measure reflects some global properties in some sense. For instance, similarity can offer a new interpretation for image and fuzzy set. More importantly, also introduced is a new interpretation of Wertheimer＇s contrast invariant principle from similarity point of view. When using similarity, a binary decision： yes or no, is often made. Therefore, it is very interesting to get a binary representation of similarity. A mathematical model between similarity and a binary variable is established by using Taylor expansion. Based on such a result, the binary representation of nonnegative bounded matrix is presented, which leads to the optimal binary decomposition of the similarity matrix. As many applications use similarity matrix, such model is potentially useful.