Abstract
T-product based tensor principal component analysis (ℓ2-tPCA) was used for dimensionality reduction, data preprocessing, compression, and visualization of multivariate data. However, ℓ2-tPCA may amplify the influence of outliers and large-magnitude noise. To explore robustness against heavily corrupted third-order data, we consider the ℓ1-norm tPCA model (ℓ1-tPCA). We develop an effective proximal alternating maximization method and prove that within finitely many steps, the algorithm stops at a point satisfying certain optimality conditions. Numerical experiments on color face reconstruction and recognition demonstrate the efficiency of the proposed algorithms, confirming that ℓ1-tPCA is more resilient to outliers compared to ℓ2-tPCA.
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