Abstract: Recent research work shows that matrix normalization plays a key role in global covariance pooling,which helps to generate more discriminative representations,thus improving the performance of image recognition tasks.For different normalization methods,the matrix structure-wise normalization can make full use of the geometric structure of the covariance matrix,so it can obtain better performance.However,the structure-wise normalization generally depends on singular value decomposition(SVD) or eigenvalue decomposition(EIG) with high computational cost,which limits parallel computing ability of GPUs,beco-ming a computational bottleneck.Iterative matrix square root normalization(iSQRT) uses Newton-Schulz iteration to normalize the covariance matrix,which is faster than the methods based on SVD and EIG.However,with the increase of the number of itera-tions and dimensions,the time and memory of iSQRT will increase significantly,and this method cannot complete the normalization of general power,which limits its application scope.To solve the above problems,a covariance matrix normalization method based on the maximum singular value power is proposed by dividing the covariance matrix by the power of its maximum singular value which only depends on iterative power method to estimate the maximum singular value of the matrix.Detailed ablation experiments show that,compared with iSQRT,the proposed method is faster and occupies less memory,and is superior to iSQRT in terms of time complexity and space complexity,and its performance is comparable to or better than iSQRT.The proposed method has achieved state-of-the-art performance in large-scale image classification dataset and fine-grained visual recognition datasets,including Aircraft,Cars and Indoor67,where accuracy is 90.7%,93.3% and 83.9% respectively.The result fully demonstrates the robustness and generalization of the proposed method.

Key words: Image classification, Global covariance pooling, Matrix power normalization, Maximum singular value power normalization