Linear discriminant analysis （LDA） is one of the most popular supervised dimensionality reduction （DR） tech- niques and obtains discriminant projections by maximizing the ratio of average-case between-class scatter to average- case within-class scatter. Two recent discriminant analysis algorithms （DAS）, minimal distance maximization （MDM） and worst-case LDA （WLDA）, get projections by optimiz- ing worst-case scatters. In this paper, we develop a new LDA framework called LDA with worst between-class separation and average within-class compactness （WSAC） by maximiz- ing the ratio of worst-case between-class scatter to average- case within-class scatter. This can be achieved by relaxing the trace ratio optimization to a distance metric learning prob- lem. Comparative experiments demonstrate its effectiveness. In addition, DA counterparts using the local geometry of data and the kernel trick can likewise be embedded into our frame- work and be solved in the same way.
本研究基于KISS(keep it simple and stupid)算法,利用似然比测试直接为矩阵模式定义度量,解决了现有大多数度量学习算法需要经过复杂优化过程的问题。通过在似然比测试中有目的地引入矩阵正态分布,该度量无需将矩阵模式通过向量化的方法变成向量模式,因而具有如下优点:(1)能够避免维数灾难;(2)比KISS更鲁棒;(3)无需计算大矩阵的逆和特征值分解,因此计算远快于KISS算法。最终的实验验证了该算法的优势。
We address the problem of metric learning for multi-view data. Many metric learning algorithms have been proposed, most of them focus just on single view circumstances, and only a few deal with multi-view data. In this paper, motivated by the co-training framework, we propose an algorithm-independent framework, named co-metric, to learn Mahalanobis metrics in multi-view settings. In its implementation, an off-the-shelf single-view metric learning algorithm is used to learn metrics in individual views of a few labeled examples. Then the most confidently-labeled examples chosen from the unlabeled set are used to guide the metric learning in the next loop. This procedure is repeated until some stop criteria are met. The framework can accommodate most existing metric learning algorithms whether types-of- side-information or example-labels are used. In addition it can naturally deal with semi-supervised circumstances under more than two views. Our comparative experiments demon- strate its competiveness and effectiveness.
