The triangularization process can be realized by any of the orthogonal transformation components; Givens rotations, Householder transformation and Modified Gram-Schmidt orthogonalization [6,8].
Since the vector norm is invariant of the orthogonal transformation Q(k), we apply QR decomposition to transform the information matrix to generate an upper right triangular matrixR(k).
We define the orthogonal transformation
matrix Q(n) as in (2.
To complete the orthogonal reduction, we apply an orthogonal transformation that involves the bottom p +1 rows of the system and produces a system of the form
This is followed by an orthogonal transformation involving the bottom p + 1 rows of the system as before.
Principal component analysis is an optimal image compression orthogonal transformation, the aim is to find a set of data space vectors to interpret the data as much as possible the variance of the data from the R-dimensional space down to the original M-dimensional (R [much greater than] M), after the dimensionality of the data stored in the main information to make the data easier to handle.
Unlike the Fourier transform of this transformation, discrete cosine transform, orthogonal transformation, which transforms the transform kernel is fixed, while the KL transform is a collection of images with different statistical properties of the nuclear matrix have different transformations that transform the nuclear matrix is a collection of images to determine the statistical properties, so the discrete KL transform is a transformation based on the demographic characteristics of the image.
7) can be constructed efficiently as the product of 2 x 2 orthogonal transformations.
The remaining orthogonal transformations in Z are either Givens rotations or Householder transformations applied to only two rows.
OLDA obtains easily the optimal transformation matrix by only orthogonal transformations
without computing any eigen-decomposition and matrix inverse.
He assumes readers to be familiar with basic techniques of numerical linear algebra such as norm estimates, orthogonal transformations
, and factorizations.
3 guarantees that corresponding condensed forms under orthogonal transformations
also exist, see also .