Determination of principal components in PCA model based on the PDF shape of the recovering error

In view of the limitation of Gaussian feature of the data in traditional FCA model, a novel approach based on controlling the shape of probability density function (PDF) of the recovering error and entropy minimization to determine the number of principal components is proposed in this paper. The unique variable of the PCA model is the number of principal components (PCs). The PDF of the recovering error is made to track the given narrow Gaussian-distribution PDF and the PC number is determined to make the tracking error be minimized. If the target PDF is unknown, the entropy of the recovering error is minimized to determine the number of principal components. For this approach, the limitation of the recovering error obeying Gaussian distribution required by mean squared error (MSE) criterion is eliminated. As the result, the application range of the PCA model is extended. Computer simulations illustrate the effectiveness of the proposed approach.