Dimensionality reduction (DR) of data is a crucial issue for many machine learning tasks, such as pattern recognition and classification. In this paper, we present quantum algorithm circuit to efficiently perform linear discriminant analysis (LDA) dimensionality reduction. Firstly, the presented improves existing LDA avoid error caused by irreversibility between-class scatter matrix $S_B$ in or...

The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...