X-Git-Url: https://www.fleuret.org/cgi-bin/gitweb/gitweb.cgi?a=blobdiff_plain;f=clusterer.cc;h=d4a70a6c5413ac6dd1a754501fe2b34499de6e4a;hb=379b91965f8d18b05cc40c4a14044eda29a6e82c;hp=04a9af4eb35f243effc4192897ce5e9a5373eedb;hpb=04d2b44ba34a811e1fab0b90d38ebd06cd918c52;p=clueless-kmeans.git

diff --git a/clusterer.cc b/clusterer.cc
index 04a9af4..d4a70a6 100644
--- a/clusterer.cc
+++ b/clusterer.cc
@@ -35,8 +35,6 @@ Clusterer::~Clusterer() {
 }
 
 scalar_t Clusterer::distance_to_centroid(scalar_t *x, int k) {
-  // We take the variance into account + the normalization term. This
-  // is between k-mean and EM with a diagonal covariance
   scalar_t dist = 0;
   for(int d = 0; d < _dim; d++) {
     dist += sq(_cluster_means[k][d] - x[d]) / (2 * _cluster_var[k][d]);
@@ -97,9 +95,9 @@ scalar_t Clusterer::baseline_lp_cluster_association(int nb_points, scalar_t **po
                                                     scalar_t **gamma)  {
   glp_prob *lp;
 
-  int *ia = new int[nb_points * _nb_clusters + 1];
-  int *ja = new int[nb_points * _nb_clusters + 1];
-  scalar_t *ar = new scalar_t[nb_points * _nb_clusters + 1];
+  int *coeff_row = new int[nb_points * _nb_clusters + 1];
+  int *coeff_col = new int[nb_points * _nb_clusters + 1];
+  scalar_t *coeff_wgt = new scalar_t[nb_points * _nb_clusters + 1];
 
   lp = glp_create_prob();
 
@@ -121,18 +119,18 @@ scalar_t Clusterer::baseline_lp_cluster_association(int nb_points, scalar_t **po
     }
   }
 
-  int l = 1;
+  int n_coeff = 1;
 
   for(int n = 1; n <= nb_points; n++) {
     for(int k = 1; k <= _nb_clusters; k++) {
-      ia[l] = n;
-      ja[l] = n + nb_points * (k - 1);
-      ar[l] = 1.0;
-      l++;
+      coeff_row[n_coeff] = n;
+      coeff_col[n_coeff] = n + nb_points * (k - 1);
+      coeff_wgt[n_coeff] = 1.0;
+      n_coeff++;
     }
   }
 
-  glp_load_matrix(lp, nb_points * _nb_clusters, ia, ja, ar);
+  glp_load_matrix(lp, nb_points * _nb_clusters, coeff_row, coeff_col, coeff_wgt);
 
   glp_simplex(lp, NULL);
 
@@ -145,9 +143,9 @@ scalar_t Clusterer::baseline_lp_cluster_association(int nb_points, scalar_t **po
     }
   }
 
-  delete[] ia;
-  delete[] ja;
-  delete[] ar;
+  delete[] coeff_row;
+  delete[] coeff_col;
+  delete[] coeff_wgt;
 
   glp_delete_prob(lp);
 
@@ -157,13 +155,38 @@ scalar_t Clusterer::baseline_lp_cluster_association(int nb_points, scalar_t **po
 scalar_t Clusterer::uninformative_lp_cluster_association(int nb_points, scalar_t **points,
                                                          int nb_classes, int *labels,
                                                          scalar_t **gamma)  {
+  // N points
+  // K clusters
+  // dist(n,k) distance of samples n to cluster k
+  //
+  // We want to optimize the
+  //
+  // \gamma(n,k) is the association of point n to cluster k
+  //
+  // to minimize
+  //
+  // \sum_{n,k} \gamma(n,k) dist(n,k)
+  //
+  // under
+  //
+  // (A) \forall n, k, \gamma(n, k) >= 0
+  // (B) \forall n, \sum_k \gamma(n,k) = 1
+  // (C) \forall k, \sum_n \gamma(n,k) = N/K
+
   glp_prob *lp;
 
+  // The coefficients for the constraints are passed to the glpk
+  // functions with a sparse representation.
+
+  // ** GLPK USES INDEXES STARTING AT 1, NOT 0. **
+
   int nb_coeffs = nb_points * _nb_clusters + nb_points * _nb_clusters;
 
-  int *ia = new int[nb_coeffs + 1];
-  int *ja = new int[nb_coeffs + 1];
-  scalar_t *ar = new scalar_t[nb_coeffs + 1];
+  int *coeff_row = new int[nb_coeffs + 1];
+  int *coeff_col = new int[nb_coeffs + 1];
+  scalar_t *coeff_wgt = new scalar_t[nb_coeffs + 1];
+
+  int n_coeff = 1;
 
   scalar_t *nb_samples_per_class = new scalar_t[nb_classes];
   for(int c = 0; c < nb_classes; c++) {
@@ -179,88 +202,76 @@ 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 point and one per cluster/class
+  // We have one column per coefficient gamma
 
-  glp_add_rows(lp, nb_points + _nb_clusters * nb_classes);
-
-  // (A) For each point, the constraint is that the sum of its
-  // association coefficients is equal to 1.0
+  glp_add_cols(lp, nb_points * _nb_clusters);
 
-  for(int n = 1; n <= nb_points; n++) {
-    int row = n;
-    glp_set_row_bnds(lp, row, GLP_FX, 1.0, 1.0);
-  }
+  // The column for gamma[n][k] point 1<=n<=nb_points and cluster
+  // 1<=k<=_nb_clusters is nb_points * (k - 1) + n;
 
-  // (B) For each pair cluster/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
+  // The constraints (A) will be expressed by putting directly bounds
+  // on the variables (i.e. one per column). So we need one row per
+  // (B) constraint, and one per (C) constraint.
 
-  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;
-      scalar_t tau = nb_samples_per_class[c-1] / scalar_t(_nb_clusters);
-      glp_set_row_bnds(lp, row, GLP_FX, tau, tau);
-    }
-  }
-
-  // Each one of the constraints above involve a linear combination of
-  // all the association coefficients
+  glp_add_rows(lp, nb_points + _nb_clusters * nb_classes);
 
-  glp_add_cols(lp, nb_points * _nb_clusters);
+  // First, we set the weights for the objective function, and the (A)
+  // constraints on the individual gammas
 
   for(int k = 1; k <= _nb_clusters; k++) {
     for(int n = 1; n <= nb_points; n++) {
       int col = n + nb_points * (k - 1);
 
-      // The LP weight on this association coefficient for the global
-      // loss is the normalized distance of that sample to the
-      // centroid of that cluster
+      // The LP weight on the gammas for the global loss is the
+      // normalized distance of that sample to the centroid of that
+      // cluster
 
       glp_set_obj_coef(lp, col, distance_to_centroid(points[n-1], k-1));
 
-      // And all the association coefficient is in [0,1]
+      // The (A) constraints: Each column correspond to one of the
+      // gamma, and it has to be in [0,1]
 
       glp_set_col_bnds(lp, col, 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.
+  // The (B) constraints: for each point, the sum of its gamma is
+  // equal to 1.0
 
   for(int n = 1; n <= nb_points; n++) {
+    int row = n;
+    glp_set_row_bnds(lp, row, GLP_FX, 1.0, 1.0);
     for(int k = 1; k <= _nb_clusters; k++) {
-      int row = n;
-      ia[l] = row;
-      ja[l] = nb_points * (k - 1) + n;
-      ar[l] = 1.0;
-      l++;
+      coeff_row[n_coeff] = row;
+      coeff_col[n_coeff] = nb_points * (k - 1) + n;
+      coeff_wgt[n_coeff] = 1.0;
+      n_coeff++;
     }
   }
 
-  // And the sums of coefficients for each pair class/cluster for
-  // constraint (B) above.
+  // The (C) constraints: For each pair cluster/class, the sum of the
+  // gammas for this cluster and 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;
+      scalar_t tau = nb_samples_per_class[c-1] / scalar_t(_nb_clusters);
+      glp_set_row_bnds(lp, row, GLP_FX, tau, tau);
       for(int n = 1; n <= nb_points; n++) {
         if(labels[n-1] == c - 1) {
-          ia[l] = row;
-          ja[l] = (k-1)  * nb_points + n;
-          ar[l] = 1.0;
-          l++;
+          coeff_row[n_coeff] = row;
+          coeff_col[n_coeff] = (k-1)  * nb_points + n;
+          coeff_wgt[n_coeff] = 1.0;
+          n_coeff++;
         }
       }
     }
   }
 
-  ASSERT(l == nb_coeffs + 1);
+  ASSERT(n_coeff == nb_coeffs + 1);
 
-  glp_load_matrix(lp, nb_coeffs, ia, ja, ar);
+  glp_load_matrix(lp, nb_coeffs, coeff_row, coeff_col, coeff_wgt);
 
   // Now a miracle occurs
 
@@ -278,9 +289,9 @@ scalar_t Clusterer::uninformative_lp_cluster_association(int nb_points, scalar_t
   }
 
   delete[] nb_samples_per_class;
-  delete[] ia;
-  delete[] ja;
-  delete[] ar;
+  delete[] coeff_row;
+  delete[] coeff_col;
+  delete[] coeff_wgt;
   glp_delete_prob(lp);
 
   return total_dist;