Linear Manifold Modeling and Graph Estimation based on Multivariate Functional Data with Different Coarseness Scales
针对函数数量超过样本量的高维场景，提出一种稀疏估计方法，用于识别线性流形并估计函数节点间的无向图，支持多粗糙度尺度下的联合图估计，通过fMRI和模拟数据验证效果。
We develop a high-dimensional graphical modeling approach for functional data where the number of functions exceeds the available sample size. This is accomplished by proposing a sparse estimator for a concentration matrix when identifying linear manifolds. As such, the procedure extends the ideas of the manifold representation for functional data to high-dimensional settings where the number of functions is larger than the sample size. By working in a penalized setting it enriches the functional data framework by estimating sparse undirected graphs that show how functional nodes connect to other functional nodes. The procedure allows multiple coarseness scales to be present in the data and proposes a simultaneous estimation of several related graphs. Its performance is illustrated using a real-life fMRI dataset and with simulated data.