A Novel Method of Efficient Max-min Metric for Classification

Abstract Distance metric learning is an important method to study distance metrics that reflect the interaction between features and labels. Because of the high computational complexity and the fact that existing studies on algorithms that measure the similarities with Euclidean distances cannot reflect the real correlations between pairs of samples, learning a suitable distance metric is quite demanding for many data mining tasks. This paper innovatively proposes an extended efficient max-min metric (EMM) that maximizes the total distance between different pairs and minimizes the total distance between similar pairs as much as possible. Simultaneously, the adoption of the local preserving projection framework changes the solution process of the algorithm and improves the speed of the algorithm without losing accuracy. Because traditional EMM only considers pairwise constraints and ignores sample distribution, this study extends EMM based on sample distribution and successfully solves the multi-manifold problem. In the process of data realization, compared with the vector representation method, the use of high-order tensors will make the image representation more accurate and natural. To maintain the structure of higher-order tensors, a tensor-efficient max-min metric (TEMM) is proposed. In order to prove the accuracy and superiority of the research method in this paper, a large number of experiments have been carried out on image processing. The experimental results show that the method proposed in this paper has a good effect.