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plsfda

PLS factoriel discriminant analysis (PLS-FDA) with cross-validation: a PLS2 (Simpls) computes scores from the disjonctive matrix of the classes, then a factoriel discriminant analysis is applied to the scores, yielding new scores; each observation is attributed to a class using these new scores

Calling sequence

model = plsfda(x,y_class,split,lv,(metric),(scale),(threshold) )

Arguments

x:

a matrix (n x q) or a Div structure

y_class:

a conjunctive vector (n x 1) or a disjonctive matrix (n x nclass) or a Div structure

split:

for the cross-validation; the number of blocks or a vector of dimensions (n x 1) which identifies by a number the group of cross-validation of each observation

lv:

numbers of dimensions used for the PLS2 and the FDA

lv is a vector of dimensions 2; lv(1) is the dimension pf the PLS2, lv(2) is the dimension of the FDA; lv(2) should be lower or equal to nclass-1

(metric):

the metric used for the calculation of the distances between the observations and the samples

metric=0: Mahalanobis distance (by default)

metric=1: usual Euclidian distance

(scale):

the columns of x are always centered; scale defines the standardization

scale='c': no standardization

scale='cs': standardisation; the columns of x are divided by their standard deviation (by default)

(threshold):

the lowest value for attributing an observation to a class (by default= 1/nclass )

model.conf_cal_nobs:

the confusion matrices for calibration, expressed as numbers of observations

model.conf_cal is a list of lv objects, each of dimensions (nclass x nclass)

model.conf_cal:

the confusion matrices for calibration, expressed as percentages

model.conf_cal is a list of lv objects, each of dimensions (nclass x nclass)

model.conf_cv:

the confusion matrices for cross-validation, expressed as percentages

model.conf_cv is a list of lv objects, each of dimensions (nclass x nclass)

model.err:

the percentage of classification errors for calibrations (1st column) and cross-validations (2nd column)

model.err.d is a matrix (lv x 2)

model.errbycl_cal:

the percentage of calibration error, for each class

model.errbycl_cal.d is a matrix (lv x nclass)

model.errbycl_cv:

the percentage of cross-validation error, for each class

model.errbycl_cv.d is a matrix (lv x nclass)

model.notclassed:

the percentage of not-classed observations (all predictions lower than the threshold)

model.notclassed.d is a vector (lv x 1)

model.notclassed_bycl:

the percentage of not-classed observations (all predictions lower than the threshold), for each class

model.notclassed_bycl.d is a matrix (lv x nclass)

model.method:

the discriminant method; here: 'plsda'

model.xcal:

the original dataset (x); a div structure

model.xcal.d is of dimensions (n x q)

model.ycal:

the original classes (y_class)

model.ycal.d is of dimensions (n x nclass)

model.scores:

the observations scores from Simpls; a div structure

model.scores.d is of dimensions (n x lv)

model.rloadings:

the R matrix of simpls, verifying: T=XR

model.rloadings.d is a matrix of dimensions (q x lv)

model.classif_metric:

the metric used for the calculation of the distances between observations and groups

model.scale:

the applied standardization

model.threshold:

the applied threshold

Examples

[result1]=plsfda(x,y,30,[20,6])
[result1]=plsfda(x,y,30,[20,6],1,'cs',0.1)

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