Ns2 simulation in uttarakhand:
Ns2 simulation in uttarakhand Using the PCA method, basis functions are computed as arbitrary polynomials ns2 simulation in uttarakhandand determined adaptively from the covariance statistics of the original data. Therefore, estimating basis function in PCA requires multiple observations.
To illustrate the PCA method, consider a with observations, arranged as row The PCA method for computing ns2 simulation in uttarakhandbasis functions is based on the desire to find a new coordinate system that accounts for maximum variance in the data, or equivalently, the minimum mean squared error of approximation
Following the variance framework, a simpler and widely used approach to computing involves performing ns2 simulation in uttarakhandan eigenvalue decomposition on the autocorrelation matrix, , of where the matrix is a diagonal matrix with the th entry being the th eigenvalue .
Eigenvalues are positive and real, and they are typically arranged in order of descending value suchns2 simulation in uttarakhand that . For each eigenvalue, there is an associated eigenvector, which is contained in the columns of . These eigenvectors correspond to the PCA basis functions .
The th associated eigenvalue is proportional to the amount of variance accounted for by the th eigenvector ns2 simulation in uttarakhandTherefore, the first eigenvector explains the most variance in the data and is also associated with the eigenvalue that possesses the greatest value, .
An alternative method to EVD is to perform a singular value decomposition on , which finds the PCA basis ns2 simulation in uttarakhandfunctions in and avoids computation of the autocorrelation matrix . The SVD of is where columns of are the left singular
vectors corresponding to thens2 simulation in uttarakhand eigenvectors of and is a diagonal matrix of singular values with singular values arranged in order of descending value . The matrix is the same as in with columns representing the right singular vectors, or the eigenvectors of .