Research On Weighted Laplacian Classifier Based On Information Theory

The tradition Laplacian classifier is a novel classifier in a kernel feature space related to theeigenspectrum of the Laplacian data matrix. The classifier criteria is based on theCauchy-Schwarz(CS) divergence of information theoretic,and in Mathematics can be attributed tomeasure the angle between class mean vectors in the kernel feature space. The classifier’s design doesnot need any optimization, which reduce the classification complexity. Experiments have shown that,the Laplacian classifier is better than Parzen window Bayes classifier, and in many cases isconsiderable with SVM. But the value of the classification cost function is inversely proportional tothe probability at test data, emphasizing the least probable regions, thus resulting the generalclassification result in higher probable regions. Against this problem, the paper did a series of work,and proposed two improved methods, namely, unilateral and bilateral weighted Laplacian classifier.The tradition Laplacian classifier emphasizes the least probable regions and has generalclassification result in higher probable regions.For this. By using weighted Parzen window probabilitydensity estimation on the small sample class, optimizing the corresponding weights using severaldifferent methods based on the CS divergence and according to the criteria of Laplacian classifier,Wedesign the unilateral weighted Laplacian classifier. The experiment shows that the unilateral weightedLaplacian classifier is better than Laplacian classifier, especially on the imbalance datasets, but whichhas the general classification effect on the balance datasets. For improving this, the bilateral weightedLaplacian classifier does it.For the bilateral weighted Laplacian classifier having the general classification effect on thebalance datasets, we design the bilateral weighted Laplacian classifier according to the criteria ofLaplacian classifier,and using weighted Parzen window probability density estimation on the twosample class,and optimazing the corresponding weights based on the CS divergence. The experimentshow that bilateral weighted Laplacian classifier comparable to the unilateral weighted Laplacianclassifier on unbalance datasets, and performs better on balance datasets significantly.