Publication details
Calculation of the tilts of curved lines
| Authors | |
|---|---|
| Year of publication | 2003 |
| Type | Article in Periodical |
| Magazine / Source | Chemomometrics and Inteligent Laboratory Systems |
| MU Faculty or unit | |
| Citation | |
| Field | Physical chemistry and theoretical chemistry |
| Keywords | singular value decomposition; loadings; Fourier transformation; Fourier coefficients; confidence ellipses |
| Description | Two methods for calculating a ratio of tilts of the curved lines are presented. The first one consists in singular value decomposition of the data matrix. If the variability in the data is caused by single effect, i.e., the first singular value is about 99 times larger than the second one, than the first loadings vector reflects the ratio of tilts. As the useful variants of this method the evolving and gliding calculation on the reduced data matrices were investigated. The other method comprises the Fourier transform of the data matrix. Only the first coefficient is used for each transformed vector of the data matrix. Its real and imaginary part can be calculated easy by multiplication and summation of suitable cosine and sine functions, respectively. In this cos-sine method each vector is represented by two co-ordinates (xf, yf) of a point and the whole data matrix can be visualised as a cluster of point which can be circumscribed by confidence ellipses. If the shorter half-axis in such an ellipse is negligible then the norms of the point vectors are in ratio of curve tilts. |
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