A Weighted Fisher Criterion Based Uncorrelated Discriminant Analysis Method For Image Recognition

Feature extraction has been one of the most important tasks in image recognition. Theinter-class scatter matrix of traditional Fisher criterion is not optimal, because it only considers ofseparating the center of each class from the overall sample center. However, it does not take therelationship between each two-class sample centers into consideration. Therefore, it may make thecenters of samples with different class close to each other, causing a large number of samples in thelow-dimensional space more inseparable. Therefore, we proposed an improved weighted Fishercriterion to extract more discriminative features, which replaces Mahalanobis distance with simplerEuclidean distance and gives greater weight to the sample centers close to each other in Euclideandistance.For improved weighted Fisher criterion, the acquired discriminative vectors still have someredundant information. In order to obtain better projection space, under the framework of theimproved Fisher criterion, we add the statistical uncorrelated constraints to the target function andpropose a weighted criterion based uncorrelated discriminant analysis method. The method removesthe redundancy of feature vectors for that the obtained feature vectors are uncorrelated betweeneach other. Thus, it guarantees that samples projected by the projection direction have the bestclassification results.Next, we consider that the conventional statistical methods use the mean of all samples toestimate expectation of the samples. However, the sample set generally does not satisfy Gaussiandistribution, so that the estimation will bring about large deviations when the number of sample issmall. We use the mean of local samples replacing the overall sample mean to achieve moreaccurate clustering and further propose a weighted Fisher criterion based local uncorrelateddiscriminant Analysis (WLUDA).Finally, taking the reality of non-linear image samples into account, we propose weightedFisher criterion based local uncorrelated kernel discriminant analysis (WKLUDA).We compare our proposed methods with some related works on AR, USPS and Coil databases.Our proposed methods have improved to some extent with the compared methods in terms ofrecognition performance and on demonstrate the efficacy of the proposed methods.