Fuzzy Canonical Discriminant Analysis
Yu-Ting Cheng · Journal of Data Analysis · 2011
The main purpose of discriminant analysis is to apply a set of known observations to classify the observation of unknown groups into pre-defined groups. In traditional discriminant analysis, the classification of the data is limited to either belong or not belong to a specific set. As such some of the information contained in the data might have been ignored. In this paper, we propose fuzzy canonical discriminant analysis, a new classification method, to classify groups of known observations and determine the membership function of each set. This membership function is then taken to apply on the unknown observations. The fuzzy canonical discriminant analysis takes in data matrices with unknown observations which are weighted by membership degrees. To find out the correlation between parameters, this paper maximizes the ratio of the weighted sum of square between the ”between groups” and the ”within groups” by Lagrange Multiplier method. The initial value is given and then iterative algorithm is applied to calculate the estimation of the parameters.We compare fuzzy discriminant analysis with canonical discrimination, based on the example from three species of Iris. We found that it improves the accuracy of discriminant analysis when the sample size is small.