Generalized PCA Method and Its Application in Uncertainty Reasoning

Principal Component Analysis (PCA) is an important mathematical dimension reduction method. In the process of uncertain reasoning, as the elements in the recognition framework increase, the evidence dimension increases exponentially, The computation required also increases exponentially, which greatly affects the application of uncertainty theory in practical engineering. To solve this problem, the PCA algorithm is used to reduce the dimension of evidence in uncertain reasoning. However, in evidence theory, the focal elements in evidence are not completely independent, which is the essential difference between evidence theory and probability theory. This is also the advantage of evidence theory in dealing with uncertain data. Due to the PCA algorithm cannot be used to reduce the dimension of evidence directly. This paper proposes a generalized PCA method and gives strict mathematical proof. The traditional PCA algorithm is a special case of the generalized PCA algorithm proposed in this paper. Finally, the application of a generalized PCA algorithm in uncertainty reasoning is given in this paper, with example results showing that the generalized PCA proposed can greatly reduce the computation required and obtain good evidence combination effect.