Canonical correspondence analysis

Faye, B., Lescourret, F., Dorr, N., Tillard, E., MacDermott, B. and McDermott, J., (1997a), Interrelationships between herd management practices and udder health status using canonical correspondence analysis . Preventive Veterinary Medicine, 32, 171-192. 

Figure 6. Canonical correspondence analysis for surface sediments of 41 lakes in British Columbia, Canada, that encompass a broad range of trophic states. Circles represent lakes and triangles represent the 25 most abundant diatom taxa. Arrows indicate environmental variables that correlate most strongly with the distribution of diatom taxa and lake-water chemistry, as detected by forward selection. Maximum depth (Zntax) and total phosphorus (TP) were transformed by using the In (x + 1) function. This analysis is discussed in detail in reference 46.

Figure 8. Normalized components of the first two eigenvectors of the Canonical Correspondence Analysis, showing the relative contributions from the 31 leaf characteristics. The order of the characteristics corresponds to that in Tables 4 and 5. Within each eigenvector, the components are normalized by the maximum value which are respectively, 1.08 and 0.88. [Used by permission of Geological Society of America, from Forest et al. (1999), Geol. Soc. Am. Bull., Vol. Ill, Fig. 11, p. 509.]...

Stull R (1989) An Introduction to Boundary Layer Meteorology. Kluwer Academic Publ. ter Braak CJF (1986) Canonical correspondence analysis A new eigenvector technique for multivariate direct gradient analysis. Ecology 67 1167-1179... 

Detrended Canonical Correspondence Analysis (ter Braak and Smilauer, 2002) was used successively to compare the macroinvertebrate communities at the three... 

Sometimes canonical correlation or canonical analysis is referred to as a central technique with factor and correspondence analysis considered in one branch (having no causal concepts) and multivariate regression and discriminant analysis in the other branch (based on causal concepts). 

Moreover, a lot of rather complicated problems in numerical analysis gives rise to the canonical problem, where a square (A -f-1) x (N-f l)-matrix of the corresponding system acquires a tridiagonal form... 

Because of the aforementioned EDA hypotheses, the ellipses of different categories present equal eccentricity and axis orientation they only differ for their location in the plane. By coimecting the intersection points of each couple of corresponding ellipses, a straight line is identified which corresponds to the delimiter between the two classes (see Eig. 2.15B). Eor this reason, this technique is called linear discriminant analysis. The directions which maximize the separation between classes are called EDA canonical variables. 

For k<3, it is possible, after canonic transformation, to determine to which type of geometric surface the given equation corresponds. It is known from mathematical analysis that there exist 17 second-order surfaces of standard form. By a canonic regression model, we can make this sorting by extreme types ... 

Relationships between the individual LOE can be examined via principal components analysis (PCA). Correlations among principal components for individual LOE indicate concordance or agreement. Relationships between different SQT LOE can also be assessed using other methods including Mantel s test (Legendre and Fortin, 1989) coupled with a measure of similarity or ordination canonical discriminant (or correspondence) analyses multidimensional scaling (MDS). 

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