From 16fd4612a88e603a34f0e8a0079932ecf080bc1f Mon Sep 17 00:00:00 2001
From: Francois Fleuret <francois@fleuret.org>
Date: Wed, 27 Mar 2013 12:48:50 +0100
Subject: [PATCH] Added comments in the main method.

---
 clusterer.cc | 30 ++++++++++++++++++++++++++++++
 1 file changed, 30 insertions(+)

diff --git a/clusterer.cc b/clusterer.cc
index 47d9ac3..9c5e7cb 100644
--- a/clusterer.cc
+++ b/clusterer.cc
@@ -167,12 +167,21 @@ scalar_t Clusterer::uninformative_lp_cluster_association(int nb_points, scalar_t
   glp_set_prob_name(lp, "uninformative_lp_cluster_association");
   glp_set_obj_dir(lp, GLP_MIN);
 
+  // We have one constraint per points and one per cluster/class
+
   glp_add_rows(lp, nb_points + _nb_clusters * nb_classes);
 
+  // (A) For each point, the constraint is that the sum of its
+  // association coefficients will be equal to 1.0
+
   for(int n = 1; n <= nb_points; n++) {
     glp_set_row_bnds(lp, n, GLP_FX, 1.0, 1.0);
   }
 
+  // (B) For each cluster and each class, the sum of the association
+  // coefficient to this cluster for this class is equal to the number
+  // of sample of that class, divided by the number of clusters
+
   for(int k = 1; k <= _nb_clusters; k++) {
     for(int c = 1; c <= nb_classes; c++) {
       int row = nb_points + (k - 1) * nb_classes + c;
@@ -181,6 +190,9 @@ scalar_t Clusterer::uninformative_lp_cluster_association(int nb_points, scalar_t
     }
   }
 
+  // Each one of the constraints above involve a linear combination of
+  // all the association coefficients
+
   glp_add_cols(lp, nb_points * _nb_clusters);
 
   for(int k = 1; k <= _nb_clusters; k++) {
@@ -194,13 +206,24 @@ scalar_t Clusterer::uninformative_lp_cluster_association(int nb_points, scalar_t
         dist += 0.5 * log(_cluster_var[k-1][d]);
       }
 
+      // The LP weight on this association coefficient is the distance
+      // (normalized) of that sample to the centroid of that cluster
+
       glp_set_obj_coef(lp, r, dist);
+
+      // And this association coefficient is in [0,1]
+
       glp_set_col_bnds(lp, r, GLP_DB, 0.0, 1.0);
     }
   }
 
   int l = 1;
 
+  // We build the matrix of the LP coefficients
+
+  // The sums of the association coefficients per points for the
+  // constraints (A) above.
+
   for(int n = 1; n <= nb_points; n++) {
     for(int k = 1; k <= _nb_clusters; k++) {
       int row = n;
@@ -211,6 +234,9 @@ scalar_t Clusterer::uninformative_lp_cluster_association(int nb_points, scalar_t
     }
   }
 
+  // And the sums of coefficients for each pair class/cluster for
+  // constraint (B) above.
+
   for(int k = 1; k <= _nb_clusters; k++) {
     for(int c = 1; c <= nb_classes; c++) {
       int row = nb_points + (k - 1) * nb_classes + c;
@@ -229,8 +255,12 @@ scalar_t Clusterer::uninformative_lp_cluster_association(int nb_points, scalar_t
 
   glp_load_matrix(lp, nb_coeffs, ia, ja, ar);
 
+  // Now a miracle occurs
+
   glp_simplex(lp, NULL);
 
+  // We retrieve the result
+
   scalar_t total_dist = glp_get_obj_val(lp);
 
   for(int k = 1; k <= _nb_clusters; k++) {
-- 
2.20.1