High dimensional mean change point detection via the largest eigenvalue

He propose to deal with the high-dimensional change point detection problem from a new perspective--via the largest eigenvalue.The data dimension p diverges with the sample size n and can be larger than n.An optimization approach is proposed to figure out both the unknown number of change points and multiple change point positions simultaneously. What's more, an adjustment term is introduced to handle sparse signals when the change only appears in few components out of the p dimensions.The computation time is controlled at O(n^2) by adopting a dynamic programming,regardless of the true number of change points k_0.Theoretical results are developed and various simulations are conducted to show the effectiveness of our method.