Principal Component Analysis Based on Nonparametric Maximum Entropy

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In this paper, we propose an improved principal component analysis based on maximum entropy (MaxEnt) preservation, called MaxEnt-PCA, which is derived from a Parzen window estimation of
Renyi’s quadratic entropy. Instead of minimizing the reconstruction error either based on L2-norm or L1-norm, the MaxEnt-PCA attempts to preserve as much as possible the uncertainty information of the data measured by entropy. The optimal solution of MaxEnt-PCA consists of the eigenvectors of a
Laplacian probability matrix corresponding to the MaxEnt distribution. MaxEnt-PCA (1) is rotation invariant, (2) is free from any distribution assumption, and (3) is robust to outliers. Extensive experiments on real-world datasets demonstrate the effectiveness of the proposed linear method as compared to other related robust PCA methods.
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