Uncertainty of the Classification Result from a Linear Discriminant Analysis

Due to its simplicity and the ability for dimensional reduction, linear discriminant analysis (LDA) is considered as a classical classification algorithm and has been applied in many applications. Its properties and performance under various circumstances have been well studied in literature. However, for a new data input, although the algorithm is able to provide a decision about which class the new data most likely belongs, no information about the quality of the result is provided. This information is of great importance, especially for data in the boundary region where the result is more likely altered, or in the situation when multiple classification results disagree. In this paper, a statistical method of bootstrap sampling is applied for the purpose of providing an uncertainty for the result from the LDA algorithm. Using Bayesian inference, uncertainty associated with the posteriori probability of the classification result is derived. Numerical simulations are performed to demonstrate our analysis and to show the effectiveness of our proposed method.