The TEC data are acquired from the NASA Global Differential GPS (GDGPS) system.2. Method2.1. PCA U0126 msds and 2DPCA2DPCA performing is essentially PCA on the rows of the data if each row is viewed as a computational unit. For 2DPCA, let data be represented by a matrix B with the dimension of m �� n. Linear projection of the matrix B is considered as follows [3�C5]:y=Bx.(1)Here x is an n dimensional project axis, and y is the projected feature of this data on x called principal component vector. E is mean:Wx=E(y?Ey)(y?Ey)T.(2)Here Wxis the covariance matrix of the project feature vector.The trace of Wxis where??S=E[(B?EB)T(B?EB)].(4)The?defined,J(x)=tr?(Wx)(3)tr?(Wx)=tr?xTSx, matrix Wx is called covariance matrix. The alternation criterion is expressed by J(x) = tr (xTWx), where the data inner-scatter matrix Wx is computed in a straightforward manner where??B?=1m��1mBk.

(5)The vector x????????byWx=1m��k=1m(Bk?B?)T(Bk?B?), maximizing (4) corresponds to the largest (principal) eigenvalue of Wx which represented the main characteristics of data. 2DPCA is another version of PCA. Therefore large principal eigenvalue of 2DPCA also indicates earthquake-related TEC anomaly. If the PCA is used to transform a matrix with low dimension into the PCA domain, then the dimension of this matrix in the PCA domain will be too small after reducing and become small sample size (SSS) data. Therefore the SSS problem will be caused by using PCA. The SSS problem causes larger data reconstruction error when data in the PCA domain are transformed back to their original domain, and corresponding principal eigenvalue is not very precise to represent main characteristics of data.

The SSS problem will be removed when performing 2DPCA due to a different algorithm from the PCA. More detailed contents about the algorithm of 2DPCA can be read from the studies of Fukunnaga [3], Kong et al. [4], and Sanguansat [5].2.2. TEC Data Processing Using PCA and 2DPCAThe previouly examined TEC data are processed by using PCA and 2DPCA, and no earthquake-related anomaly is found. Only during the time period from 04:20 to 04:45 on August 28, 2012 (UT) related to the Philippines earthquake and the time period from 04:35 to 04:45 on August 27, 2012 (UT) related to the Puerto earthquake, earthquake-related TEC anomalies are detectable by using 2DPCA. Therefore the procedure of TEC data processing during the previous Cilengitide time periods is represented in this study. Figure 1(a) shows the Global ionospheric TEC maps (GIMs) during the time period from 04:20 to 04:45 UT on August 28, 2012. The TEC data of each GIM in Figure 1(a) are divided into 600 smaller grids 12�� in longitude and 9�� in latitude, respectively. The resolution of the TEC data for this GPS system is 5 and 2.