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covsel_fda

variable selection using Covsel, then factorial discriminant analysis on the selected variables

Calling sequence

model = covsel_fda(x,y_class,split,lv,nbvar,(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:

the maximum number of latent variables or eigenvectors used for the building of the model

lv inf. to nclass

nbvar:

the number max of selected variables

nbvar sup. to lv

(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 (by default)

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

(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) in the general case, and of dimensions (nclass x nclass x nbvar) for covsel_fda

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) in the general case, and of dimensions (nclass x nclass x nbvar) for covsel_fda

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) in the general case, and of dimensions (nclass x nclass x nbvar) for covsel_fda

model.err:

the percentage of classification errors for calibrations and cross-validations

model.err.d is a matrix (lv x 2) in the general case, and (2 x lv x nbvar) for covsel_fda

model.errbycl_cal:

the percentage of calibration error, for each class

model.errbycl_cal.d is a matrix (lv x nclass) in the general case, and (nclass x lv x nbvar) for covsel_fda

model.errbycl_cv:

the percentage of cross-validation error, for each class

model.errbycl_cv.d is a matrix (lv x nclass) in the general case, and (nclass x lv x nbvar) for covsel_fda

model.notclassed:

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

model.notclassed.d is a vector (lv x 1) in the general case, (lv x nbvar) for covsel_fda

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) in the general case, and (lv x nclass x nbvar) for covsel_fda

model.method:

the discriminant method; here: 'covsel_fda'

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) if disjuctive, or (n x 1) if conjunctive

model.scores:

the observations scores T; they verify: T=XR, X being obtained by applying model.scale to x; T is a div structure

model.scores.d is of dimensions (n x lv) in the general case, and (n x lv x nbvar) for covsel_fda

model.rloadings:

the loadings R, a div structure

model.rloadings.d is a matrix of dimensions (q x lv) in the general case, and (q x lv x nbvar) for covsel_fda

model.classif_metric:

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

model.scale:

the standardization which was applied

model.threshold:

the threshold which was applied

Examples

[result1]=covsel_fda(x,y,30,20)
[result1]=covsel_fda(x,y,30,20,0,'cs',0.10)

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