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Artificial Immune Linear Discriminant Analysis
Authors: Amin Allahyar and Hadi Sadoghi Yazdi
Number of views: 527
In Linear Discriminant Analysis (LDA), it is assumed that each class has a Gaussian distribution. This assumption rarely holds in the real world problems. However, by removing this assumption, the problem become intractable and cannot be solved in analytic form. Quite recently, a group of evolutionary algorithms is introduced to solve this problem. These algorithms used a combination of fisher criterion and fuzzy membership function as their fitness function. It is widely acknowledged that computing the fitness function in an evolutionary algorithm needs to be very fast. Unfortunately, calculating fisher criterion for each chromosome in iterations of an evolutionary algorithm has a high computational cost. Furthermore it is known that the fuzzy membership function has an assumption of Gaussian distribution, thus using it as a fitness function will have same assumption issue that LDA had previously. In this paper, we suggest a new fisher criterion to incorporate in fitness function and show that it is theoretically faster than previous introduced criterion. In addition we theoretically prove the equality of proposed criterion. Next, in order to eliminate the Gaussian assumption, we offer a substitution for fuzzy membership fitness function which does not have Gaussian assumption. Moreover, the superior speed introduced fitness function theoretically investigated. At last, in order to confirm the effectiveness of proposed fitness functions, comprehensive experiments using twelve UCI repository dataset and two real world problems in face and object recognition is performed and the results is compared in both speed and accuracy.