中文摘要：

在有监督学习中,每类数据具有独特的特性且类与类之间是独立的.受此启发,提出了基于等同邻域的投影算法.新算法通过计算一组基函数为每类数据在低维空间中寻找高度对称的等同邻域空间.等同邻域可以通过构建正则单纯形得到,基函数可以通过凸优化得到.对于测试样本,可以通过基函数映射到低维的等同邻域空间,与各等同邻域空间中心的距离决定其类别归属,而不必计算与所有训练样本间的距离.实验证明了新方法的有效性.

英文摘要：

A new interesting algorithm, iso-neighborhood projection （ISONP）, is proposed for finding succinct representations in a supervised manner. Motivated by the fact that each class has its unique property and is independent from other classes, the recognition problem is cast as finding highly symmetric iso-neighborhood for all classes respectively, which is highly different from the traditional linear methods such as principal component analysis （PCA）, linear discriminant analysis （LDA）, and locality preserving projection （LPP）. The traditional linear methods, like PCA, LDA and LPP, find a certain optimal projection and then map the training data into a lower space in a batch. Given labeled input data, ISONP discovers basis functions which can map each data into its corresponding neighborhood while keeping the intrinsic structure of each class at the same time. The basis functions span the lower subspace, and can be computed by a convex optimization problem： an L2-eonstrained least square problem. When recognizing a test sample, the authors map the new data into the spanned lower suhspace and just compare the distance to the center of iso-neighborhoods instead of all training samples, which can enhance the recognizing speed. Experiments are conducted on several data sets and the results demonstrate the competence of the proposed algorithm.