缓解多维缩放方法中的随机一致性OA

In the field of machine learning,the phenomena of sample randomness and random consistency are widely encountered in tasks such as classification and clustering.When the samples are limited,due to the existence of sample randomness,the eigenvalue decomposition of the sample covariance matrix may have random consistency,and there will be an error when using the sample ei-genvalues and eigenvectors to estimate the overall eigenvalues and eigenvectors.Similarly,the multiple dimensional scaling(MDS)method involves the eigenvalue decomposition of the inner product matrix B.The results may also have random consistency,and the final low-dimensional sample coordinates obtained may have errors,resulting in a degradation of the model performance.In order to improve the estimation accuracy of the model and the stability of the algorithm,this paper focuses on investigating the random con-sistency problem in the eigenvalue decomposition of the inner product matrix B of the MDS method,and introducing the averaging idea,using the average eigenvectors to represent the overall eigenvectors.In order to better fit the true distribution of the data,first,the data are sampled multiple times;second,the significance and necessity of mitigating the random consistency during the covari-ance decomposition are analyzed;and finally,the Expectation-based Multiple Dimensional Scaling(EMDS)is proposed to mitigate the random consistency.The classification experiments are validated on six public UCI datasets,and the experimental results show that the EMDS dimensionality reduction has a higher accuracy rate compared to the original MDS method.