中文摘要：

传统的Laplacian分类器通过Parzen窗估计概率密度函数，而后基于CauchySchwarz散度（Cauchy-SchwarzDivergence，CSD）定义分类准则进行分类，主要强调了小概率类别，致使对较高概率的类的分类效果较一般．针对此，提出了一个改进方法．关键是对小样本类用加权代替无权的Parzen窗概率密度估计，并用CSD作为代价函数优化相应的权值，而后依据Laplacian分类准则设计出加权Laplacian分类器（WeightedLaplacianClassifier，WLC）．在所用测试数据集，尤其是不平衡数据集上的实验表明，WLC的结果明显优于Lapalcian分类器．

英文摘要：

The traditional Laplacian Classifier proposed to classify the datasets is derived from Cauchy-Schwarz divergence（CSD） using Parzen window. The classification rule is expressed in terms of a weighted kernel expansion. The weighting associated with a data point is inversely proportional to the probability density at that point, emphasizing the least probable regions, which makes the classification result of the other regions not so well. Against this problem, we proposed a new classifier to improve it, named the weighted Laplacian classifier （WLC）. The classifier uses the weighted Parzen window which is used to estimate the probability density functions （pdf） on the small sample class, and the CSD is used as the cost function to optimal the weight. Besides, the quadratic programming is used as the optimal method to optimal the weight. Then the weighted classifier is designed according to the Laplacian classification rule. The classification cost function measures the angle between class mean vectors in the kernel feature space, the test data is classified to the smaller angle between the two datasets in the feature space. According to the experiment on toy dataset and the real dataset, the final experiment result shows that WLC is better than the Laplacian classifier＇s on the test datasets, especially on the imbalance datasets.