### Nonnegative Matrix Factorization Aided Principal Component Analysis for High-Resolution Partial Discharge Image Compression in Transformers

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#### Abstract

In this study, the development of nonnegative matrix factorization aided principal component analysis (NMF-PCA) algorithm is proposed to solve the problem that the covariance matrix cannot be computed due to the extremely high vector space caused by the “matrix-to-vector” transformation when principal component analysis (PCA) is applied to high-resolution image compression, which is further employed for PD gray image compression and recognition. In the proposed NMF-PCA algorithm, nonnegative matrix factorization (NMF) is firstly employed to decompose the high-resolution image into base matrices W and coefficient matrices H with lower dimension. Then, PCA is adopted to extract several principal components from the vectors of W and H as features. A fuzzy C-means (FCM) clustering method is responsible for PD classification and features evaluation. Using a traditional pulse current detector for PD experiment, 177 gray images associated with four PD defect types are obtained for NMF-PCA testing. The results of algorithm performance evaluation show that NMF and PCA both have fast responding time when r is less 3, which is suitable for PD on-line analysis and diagnosis. The recognition results of experimental PD samples demonstrate that only is the feature set FH extracted from the coefficient matrix H fit for PCA compression of PD gray images. Meanwhile, the maximum successful clustering rate 0.9661 is achieved by 3D features of FH with r = 2, which is much higher than 0.8023 of traditional PRPD operators. In addition, the FCM validity measures report that the features obtained by NMF-PCA have better aggregation characteristic than PRPD statistical operators. The obtained results demonstrate that the proposed NMF-PCA algorithm could provide an effective tool for PD diagnosis, and it is easy to extend to other image or matrix applications *Copyright © 2013 Praise Worthy Prize - All rights reserved.*

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