Divines Perles: Bijoux et accessoires en perles by Dominique Nisen

By Dominique Nisen

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Then the main program is called hierclust. 5). dissim <- function(a, wt) { # Inputs. a: matrix, for which we want distances on rows, # wt: masses of each row. # Returns. matrix of dims. nrow(a) x nrow(a) with # wtd. sqd. Eucl. distances. 0 for (j in 1:m) { # We use the squared Euclidean distance, weighted. adiss[i1,i2] <- adiss[i1,i2] + (wt[i1]*wt[i2])/(wt[i1]+wt[i2]) * (a[i1,j]-a[i2,j])^2 } adiss[i2,i1] <- adiss[i1,i2] } } adiss } getnns <- function(diss, flag) { # Inputs. diss: full distance matrix.

Space Rm 1. n row points, each of m coordinates. 2. The j th coordinate is xij /xi . 3. The mass of point i is xi . 4. The χ2 distance between row points i and k is: x x 2 . d2 (i, k) = j x1j xiji − xkj k Hence this is a Euclidean distance, with respect to the weighting 1/xj (for all j), between profile values xij /xi , etc. 5. The criterion to be optimized: the weighted sum of squares of projections, where the weighting is given by xi (for all i). Space Rn 1. m column points, each of n coordinates.

Axes u and v, and factors φ and ψ, are associated with eigenvalue λ and best fitting higher-dimensional subspaces are associated with decreasing values of λ, determined in the diagonalization. The transition formulas allow supplementary rows or columns to be projected into either space. If ξj is the jth element of a supplementary row, with mass ξ, then a factor loading is simply obtained subsequent to the correspondence analysis: 1 ξj φj ψi = √ λ j ξ A similar formula holds for supplementary columns.

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