


HIT_REGRESSION Main function for PWA regression.
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DESCRIPTION
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[idmodes,F,xi,LDs,inliers]=hit_regression(Xid,yid)
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INPUT
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Xid: matrix containing the regressors. Each row is a datapoint.
yid: column vector containing the output datapoints.
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OUTPUT
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idmodes: structure containing all information on the identified models.
idmodes.par{i}: is the PVs of the i-th mode.
idmodes.regions(i): is the region of the i-th mode. Regions are
subsets of idpar.Regressor_set.
idmodes.cov{i}; is the covariance of the PV of the i-th mode.
idmodes.Regressor_set: automatically computed polytope defining the
regressor set. This field is present only if idpar.Regressor_set is
empty or nonexistent.
idmodes.s: meaningful number of modes estimated during regression (it
might differ from idpar.s).
idmodes.regions_sim(i): is the region for simulating the i-th mode.
These regions are subsets of idpar.Regressor_set_sim and are defined
only if idpar.Regressor_set_sim is defined.
idmodes.stat_reattr: fraction of points reattribted to modes, if
reattribution has been performed.
idmodes.clust_valid: structure containing information about the
clustering results.
idmodes.pattern_rec_valid: structure containing information about the
pattern recognition results.
idmodes.Weight_primal: weights used in creating LDs (usually it is a
vector of 1's)
idmodes.adjacences: each row is a pair (i,j), i<j indicating that the
regions i and j are adjacent The constraint i<j avoids storing both
pairs (i,j) and (j,i).
F: structure containing information about the mode datasets (the
classified datapoints that are also inliers, i.e. not discarded during
regression).
F.X{i}: matrix of regressors assigned to the i-th mode dataset.
F.y: cell array: F.y{i} vector of outputs assigned to the i-th mode
dataset.
F.pos{i}: indexes of the points assigned to the i-th mode dataset.
F.pos{i}(1)=5 means that Xid(5,:) and yid(5) are the first points
composing the i-th mode dataset.
xi: structure containing information about the xi-points (they are either
FVs or LPVs).
xi.points{i}: xi-point based on the i-th LDs.
xi.IR{i}: INVERSE of the covariance of the i-th xi-point.
xi.weights{i}: scalar confidence measure of the i-th feature vector.
LDs: structure containing information about local datasets (LDs)
and local models
LDs.X{i}: matrix of regressors belonging to the i-th local dataset
(each row is a point).
LDs.y{i}: vector of outputs belonging to the i-th local dataset.
LDs.pos{i}: vector of indexes of datapoints in the i-th local
dataset, e.g. Xid(LDs.pos{i}(1),:) is the first regressor in the i-th
LD.
LDs.weights{i} weight associated to the i-th datapoint used in
weighted LS for computing mode PVs.
LDs.meanX{i} average of regressors in the i-th local dataset.
LDs.models{i} parameters of the i-th local model.
LDs.models_var{i} INVERSE variance of the i-th local model.
LDs.X_ivar{i} INVERSE of the variance of the the regressors in the
i-th LD.
inliers: structure containing information on the inliers
inliers.pos(j): index of the j-th inlier in Xid and yid
(i.e.Xid(inliers.pos(j),:) and yid(inliers.pos(j)) are the j-th
inliers).
inliers.class(j): classification of the j-th inlier.