基于边界判别投影的数据降维

为了提取具有较好判别性能的低维特征，提出了一种新的有监督的线性降维算法——边界判别投影，即，最小化同类样本间的最大距离，最大化异类样本间的最小距离，同时保持数据流形的几何形状.与经典的基于边界定义的算法相比，边界判别投影可以较好地保持数据流形的几何结构和判别结构等全局特性，可避免小样本问题，具有较低的计算复杂度，可应用于超高维的大数据降维.人脸数据集上的实验结果表明，边界判别分析是一种有效的降维算法，可应用于大数据上的特征提取.

Margin Discriminant Projection for Dimensionality Reduction

A novel supervised linear dimensionality reduction algorithm called margin discriminant projection (MDP) is proposed to extract low-dimensional features with good performance of discriminant. MDP aims to minimize maximum distance of samples belong to the same class and maximize minimum distance of samples belong to different classes, and at the sametime preserve the geometrical structure of data manifold. Compared with classical algorithms based on the definition of margin, MDP is good at preserving the global properties, such as geometrical and discriminant structure of data manifold, and can overcome small size sample problem. Due to its low cost of computation, MDP can be directly applied on ultra-high dimensional big data dimensionality reduction. Experimental results on five face data sets show its effectiveness for feature extraction on big data.