csm_toolbox.py

from utils import *
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np
from sklearn.decomposition import PCA
from scipy.linalg import subspace_angles


def chordal_distance(angles):
    '''
    Inputs : 
    @angles: The principal angles between the two flats to compare.

    This function returns the chordal distance of the two flats based on their principal angles.
        
    '''

    return (np.power(np.sin(angles),2)).mean()


def compute_chordal_distance(source,target):

   '''
    Inputs : 
    @source: DCTr features of the source
    @target : DCTr features of the target

    This function returns the chordal distance between the two flats that are respectively supporting source and target data.
    When it is 1, the two flats are orthogonal. When it is 0, the two flats are co-linear.
        
   '''

   pca = PCA(n_components=0.999)
   pca.fit(source)
   source_components=pca.components_

   pca.fit(target)
   target_components=pca.components_

   m=min(len(source_components),len(target_components))
   FlatSource=source_components[0:m]
   FlatTarget=target_components[0:m]

   return chordal_distance(subspace_angles(FlatSource.T, FlatTarget.T))

def harmonic_sum(n):
    i = 1
    s = 0.0
    for i in range(1, n+1):
        s = s + 1/i;
    return s;


class CSM:
      'This class provide methods useful to derive interesting information from a PE matrix'
      def __init__(self,csm_matrix,seed=0):
            '''
            Inputs : 
            @csm_matrix : The matrix M s.t. M[i,j] is the probability of error obtained training on i and evaluating on j.

            Attributes derived:
            @regret_matrix : Derived from csm_matrix. It's the matrix M s.t. M[i,j]=Regret_{i,j} (defined in the paper)
            
            '''
            self.csm_matrix=csm_matrix
            self.N=len(csm_matrix)
            self.regret_matrix=csm_matrix-np.tile(np.diag(csm_matrix).reshape(-1,1),(self.N)).T
            self.seed=seed
            
    
      def greedy_covering(self,epsilon=10):
          '''
          This is the clustering algorithm used for our experiments in the paper.

          Input:
          @epsilon : maximum regret accepted between a representative and the members of its cluster.

          Output :
          @greedy_covering : The covering obtained with the details in the shape of a dictionary where the keys are the clusters
          representatives and the values the sources they are covering.
          @representatives : The list of the representatives (linked to a number)
          @labels : The labels of each source enabling to assign to each source a cluster
        
          Aim:
          This method builds a clustering of the sources involved in the csm matrix.
          The core idea is to see the clustering problem as a set-covering problem and deduce a solution of this problem
          using a greedy algorithm. More details about this idea are given in the article.

          The pseudo-code is available in the article.

          '''  

          P={}
          greedy_covering={}
          not_already_included_in_the_greedy_covering=0
          size=[]

          for i in range(len(self.regret_matrix)):
            P[i]=np.where(self.regret_matrix[i]<epsilon)[0]
            P_size=len(P[i])
            size.append(P_size)
            not_already_included_in_the_greedy_covering+=P_size
       
          while not_already_included_in_the_greedy_covering>0:
              not_already_included_in_the_greedy_covering=0
              points_covered_by_unit_cost={} 

              for i in range(len(self.regret_matrix)):

                if len(P[i]):
                    points_covered_by_unit_cost[i]=len(P[i]) #/constant_cost

                else:
                    points_covered_by_unit_cost[i]=-100

              # we look for the representative covering the maximum number of sources (regret radius < epsilon) 
              k=np.argmax(list(points_covered_by_unit_cost.values()))
              greedy_covering[k]=np.array(list(set(P[k]).union({k}))) 
              #Note : Above, the representative is explicitly included in its own cluster to prevent that the algorithm
              #returns a covering where a representative is covered by an other representative.

              for i in range(len(self.regret_matrix)):
                  #all the sources already covered are deleted from the initial covering
                  P[i]=np.array(list(set(P[i])-set(greedy_covering[k]))) 
                  not_already_included_in_the_greedy_covering+=len(P[i])

          #Safe check : What is the maximum value of the maximum regrets between each representative and its members ? 
          #It should be lower than epsilon
          max_regrets=[]
          for cover in greedy_covering.keys():
              max_regrets.append(self.regret_matrix[cover,greedy_covering[cover]].max())

          print('Max max regrets : ', round(np.max(max_regrets),2))

          #The greedy algorithm used here has a theoretical guarantee giving us an idea about how far we are from an optimal covering
          print('Minimum number of sources for the optimal covering :', np.ceil(len(greedy_covering.keys())/harmonic_sum(max(size))))

          labels_assignement=np.zeros(len(self.regret_matrix))
          
          for j in greedy_covering.keys():
              for value in greedy_covering[j]:
                    labels_assignement[value]=j

    
          return greedy_covering,np.sort(np.unique(labels_assignement)),np.array(labels_assignement)
          
                
      def save_matrix(self,order=None,matrix_type='regret',title=None):
          '''
          This method enables to save an heatmap representing the PE or Regret matrix reordered according to an order
          proposed by the user. By default the order is the identity.

          Inputs : 
          @order : An ordering of the sources in self.csm_matrix 
          @matrix_type : The kind of matrix you want to plot (by default it's the regret matrix)
          @title : The title of the plot you are going to create
          
          '''

          if order is None:
            order=np.arange(0,len(self.csm_matrix))

          if title is None:
            title=f'{matrix_type}_matrix'

          order = np.arange(0,len(self.csm_matrix)) if order is None else order
          reordered_matrix=self.regret_matrix[order,:][:,order] if (matrix_type.lower()=='regret') else self.csm_matrix[order,:][:,order]

          num_ticks = len(reordered_matrix)

          # the index of the position of yticks
          yticks = np.linspace(0, num_ticks - 1, num_ticks,dtype=int)
          # the content of labels of these yticks
          yticklabels = [order[idx] for idx in yticks]

          plt.figure(figsize=(num_ticks,num_ticks))
          sns.heatmap(reordered_matrix, annot=True,cmap="flare",vmin=reordered_matrix.min(),vmax=reordered_matrix.max(),
          yticklabels=yticklabels,xticklabels=yticklabels)

          
          plt.savefig(f'{title}.pdf')
          plt.close()