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hit_regression

PURPOSE ^

HIT_REGRESSION Main function for PWA regression.

SYNOPSIS ^

function [idmodes,F,xi,LDs,inliers]=hit_regression(Xid,yid)

DESCRIPTION ^

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.

CROSS-REFERENCE INFORMATION ^

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