自适应加权t-SNE算法及其在脑网络状态观测矩阵降维中的应用研究

针对目前数据降维算法受高维空间样本分布影响效果不佳的问题，提出了一种自适应加权的t分布随机近邻嵌入（t-SNE）算法。该算法对两样本点在高维空间中的欧氏距离进行归一化后按距离的不同分布状况进行分组分析，分别按照近距离、较近距离和远距离三种情况在计算高维空间内样本点间的相似概率时进行自适应加权处理，以加权相对距离代替欧氏绝对距离，从而更真实地度量每一组不同样本在高维空间的相似程度。在高维脑网络状态观测矩阵中的降维实验结果表明，自适应加权t-SNE的降维聚类可视化效果优于其它降维算法，与传统t-SNE算法相比，聚类指标值DBI值平均降低了28.39%，DI值平均提高了161.84%，并且有效地消除了分散、交叉和散点等问题。

Adaptive weighted t-SNE algorithm and application in dimensionality reduction of human brain network state observation matrix

Focusing on the low performance in dimensionality reduction algorithm which caused by the sample distribution in high dimensional space, this paper proposed a adaptive weighted t-SNE lalgorithm. Firstly we calculated the Euclidean distance between every two samples and made a normalization, then we analyzed the values in groups and gave three kind of weight coefficient according short-distance, intermediate-distance and long-distance respectively. Secondly we computed the similarity probability of every two sample points in high dimensional space by using an adaptive weight, as a result the weighted relative distance is used as a substitute for absolute Euclidean distance which can represent the similarity of two samples in high dimensional space more accurately. We applied this algorithm to the dimensionality reduction of the high dimensional human brain network state observation matrix and the experimental results show that this adaptive weighted t-SNE method is more effective than some other dimensionality reduction algorithms in visualization. Compared with traditional t-SNE, the clustering index value Davies-Bouldin index value is reduced by 28.39% on average, and the value of Dunn index is increased by 161.84% on average, more over, the problems of scattering, cluster crossing and single point outside the clusters are improved noticeably.