Study And Application Of Scoring Functions In Flexible Discriminant Analysis

Flexible discriminant analysis is a classification method of machine learning,classification problems are widespread in the real life, scoring function of flexible discriminant analysis can affect classification result. Hence, it is necessary that scoring function of flexible discriminant analysis is studied sufficiently. However, the existing research results mostly regard scoring function as linear function, less research and application have been done for other forms of scoring function about flexible discriminant analysis.Firstly, started with the origin of scoring function about flexible discriminant analysis in this article, it is proved that the existence of scoring function in flexible discriminant analysis can improve the classification accuracy, in addition, flexible discriminant analysis with scoring function not only can used for binary classification problems, can also solve multi-classification problems. Secondly, analyze function character and tectonic conditions of the scoring function, some important conclusions are obtained:1. Monotonicity of scoring function decides if there is indication of the function;2. Concavity and convexity of scoring function decides indicative obvious degree of the function;3. Progressivity of scoring function can cause that function definition is not complete or used scope is limited.According to the conclusion above, scoring function in flexible discriminate analysis is generalized. Define the specific form of nonlinear scoring function, such as exponential scoring function, logarithmic scoring function, quadratic scoring function and so on. Specific form of scoring function which is defined newly is analyzed, the analysis of theoretical rationality and suitable conditions to use in practical application have been done. Therewith,the conclusions as follow:1. Because of monotone increasing and concavity of scoring function, exponential scoring function and quadratic scoring function score usually apply to all situations;2. Because of monotone increasing and convexity of scoring function, logarithmic scoring function generally applicable to the situation that sample size is larger;3. With progressivity, especially in domain of scoring definition, the monotonedecreasing function with progressivity is unfit for scoring function, also does not apply to any situations.Application of scoring function eventually implements to the application of flexible discriminant analysis, flexible discriminant analysis was applied to banknote authentication and protein localization problem in this paper. According to the characteristics of data,supervised learning method is used to the problems above in this paper. Because of sample size, data set is divided into training data set and test data set. Evaluation index of classification effect, this paper uses the classification accuracy. In most cases, the classification effect of flexible discriminant analysis is better than the linear discriminant analysis. Moreover, for the same kind of method, classification accuracy of training data set is higher than the test data set.