On the positive semi-definite property of similarity matrices

Abstract The notion of similarity is a fundamental concept in different scientific fields. Similarity measures aim at quantifying the extent to which objects resemble each other. This paper is concerned with the analysis of the properties of similarity matrices. More specifically, we focus on their positive semi-definite property, which is important to derive useful distances between data sets. Based on some general results, we show that most of classical similarity matrices have this property.