In light of the degradation of the feature extraction from the second or higher-order statistic in the context of Alpha stable noise, a new feature extraction method of PF(product functions) components is introduced.The distribution properties of PF are validated by the tails and the estimation of α of the probability density function (PDF). Then, the bearing feature matrix is constructed based on the optimal fractional low-order statistics (FLOS) and covariant low-dimensional popular mapping matrix in order to reduce the error of the second-order and high-order statistics in describing the characteristics of signal components. Thus, various bearing faults are described accurately and intuitively.The comparisons with traditional methods show that lower-order features better describe the PF components with higher accuracy and clearer distinction. The feasibility indicates the advantages of the proposed method in practical applications.