线性不动点近邻嵌入分析方法

Linear Fix-Point Neighbor Embedding Analysis Method

针对t分布随机近邻嵌入分析方法(t-SNE)存在的样本外问题和实际应用中利用快速下降法进行梯度最优化过程时多参数设定及调整的不可行性,提出线性不动点近邻嵌入分析方法.该方法在t-SNE的基础上引入线性投影变换矩阵,揭示数据的本质低维结构,然后在最小化原空间和子空间两个概率分布的KL散度准则下建立目标函数.通过简单不动点迭代法求解目标函数的最小值,有效提高t-SNE迭代最优过程的效率和鲁棒性.在人工合成数据和COIL-20图像库上的实验表明,文中方法具有较好的可视化能力.

To solve the out-of-sample problem of t-distributed stochastic neighbor embedding （t-SNE） analysis method and overcome the unfeasibility of manually adjusting the involved parameters in practice, a linear fix-point neighbor embedding （LFNE） analysis method is proposed based on a fix-point optimization algorithm. Based on t-SNE, the linear projection matrix is introduced to reveal the underlying structure of data manifold in LFNE. Then, the penalty function is built by minimizing the Kullback-Leibler divergence of original space and subspace. Furthermore, the efficiency and the robustness of LFNE optimization are improved by the fix-point optimization algorithm. The proposed method is evaluated on artificial synthetic data and COIL-20 database. Experimental results demonstrate the better effectiveness of visualization by LFNF.