pgaussclassification

Performs gauss clustering on a set of objects.

Synopsis

pgaussclassification attr_base attr_in attr_out [col_base|-] [col_in|-] [col_out|-]

Description

pgaussclassification is a partitioning method for a group of n objects into k clusters. The basic idea supposes that the class distribution has a gaussian distribution, and for each object x to be classified the principle is to find the class that has the maximum probability to contain x.

Practically, pgaussclassification finds the class i that minimizes:

                                                            
   f(x,i) = ln(det A(i)) + ^t(x - m(i)).A(i)^-1.(x - m(i)) - ln(P(i)²)

where x is the feature vector for the object x;
A(i) is the covariance matrix for the class i ;
m(i) is mean vector the for class i ;
P(i) is the a priori probability to find class i.

These values can be calculated from the operator parraycovarmat.

Parameters

attr_base is the base name for the gaussian features. If there exists n clusters and p features:
- attr_base.mean is an array of n*p values which contains at the index [i*n+j] the mean of the j+1th feature of the i-1 cluster.
- attr_base.det is an array of n reals which contains at the index [i-1] the determinant det(A(i)).
- attr_base.inv is an array of p*p values which contains at the index [k*p*p + i*p +j] the value of k-1th matrix cell of the A^-1[i,j]. (These 3 attributes can be calculted thanks to the operator parraycovarmat.) attr_base.pap is an array of n reals which contains a priori probabilities of each cluster. (This array can be omitted; in this case probabilities are supposed equiprobable).
attr_in is the base name of the feature vector of the objects to be classified. The vectors are named attr_in.1, attr_in.2, ..., attr_in.n in the input collection. The item j of the array attr_in.i contains the (i)th feature of the (j+1)th object. They are Double arrays.
attr_out is the name of the output array. Each item i of the array contains the cluster index from which the (i)th object is assigned. attr_out is an array of unsigned longs where attr_out[i] specifies the cluster index for the object i.

Inputs

col_base: a collection which contains the learned parameters.
col_in: a collection which contains the objects to be classified.

Outputs

col_out: a collection which contains classified objects.

Result

Returns SUCCESS or FAILURE.

Examples

Classifies beans into the jellybean.pan image from sample of each bean stored in the directory 'base' (Unix version).

# Learning
classes=1
for i in base/*.pan
do
    pim2array ind $i /tmp/tmp1 
    parray2array ind.1 Float /tmp/tmp1| parray2array ind.2 Float | parray2array ind.3 Float - a.pan
    parraycovarmat ind ind a.pan i-01.pan
    if [ -f base.pan ]
    then pcolcatenateitem i-01.pan base.pan base.pan
    else cp i-01.pan base.pan
    fi
    classe=`expr $classe + 1`
done
rm /tmp/tmp1

# Classification
pim2array ind jellybeans.pan a.pan
parray2array ind.1 Float a.pan| parray2array ind.2 Float | parray2array ind.3 Float - b.pan
pgaussclassification ind ind ind base.pan b.pan | parray2im $ncol $nrow 0 ind | pim2rg - out.pan

C++ prototype

Errc PGaussClassification(const std::string &a_base, const Collection &c_base, const std::string &a_in, const Collection &c_in, const std::string &a_out, Collection &c_out);

Version française

Classification utilisant un modèle gaussien.

Author: Alexandre Duret-Lutz