关键词: 高维数据降维, 功能脑网络, 脑网络, 状态观测矩阵, 谱特征嵌入算法, 动态特性

Abstract: As the brain network state observation matrix based on functional Magnetic Resonance Imaging (fMRI) reconstruction is high-dimensional and characterless, a method of dimensionality reduction based on Spectral Embedding was presented. Firstly, the Laplacian matrix was constructed from the similarity measurement between the samples. Secondly, in order to achieve the purpose of mapping (reducing dimension) datasets from high dimension to low dimension, the first two main eigenvectors were selected to construct a two-dimensional eigenvector space through Laplacian matrix factorization. The method was applied to reduce the dimension of the matrix and visualize it in two-dimensional space, and the results were evaluated by category validity indicators. Compared with the dimensionality reduction algorithms such as Principal Component Analysis (PCA), Locally Linear Embedding (LLE), Isometric Mapping (Isomap), the mapping points in the low dimensional space got by the proposed method have obvious category significance. According to the category validity indicators, compared with Multi-Dimensional Scaling (MDS) and t-distributed Stochastic Neighbor Embedding (t-SNE) algorithms, the Di index (the average distance among within-class samples) of the proposed method was decreased by 87.1% and 65.2% respectively, and the Do index (the average distance among between-class samples) of it was increased by 351.3% and 25.5% respectively. Finally, the visualization results of dimensionality reduction show a certain regularity through a number of samples, and the effectiveness and universality of the proposed method are validated.

Key words: dimensionality reduction of high dimensional data, functional brain network, brain network, state observation matrix, Spectral Embedding algorithm, dynamic characteristics