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In [131]:



    


%matplotlib inline
import pandas as pd
import numpy as np
import scipy.stats as stats
import matplotlib.pyplot as plt
import mia

Loading and Preprocessing

Loading the hologic and synthetic datasets.





In [82]:



    


hologic = pd.DataFrame.from_csv("real_intensity.csv")
hologic.drop(hologic.columns[:2], axis=1, inplace=True)
hologic.drop('breast_area', axis=1, inplace=True)

phantom = pd.DataFrame.from_csv("synthetic_intensity.csv")
phantom.drop(phantom.columns[:2], axis=1, inplace=True)
phantom.drop('breast_area', axis=1, inplace=True)

Loading the meta data for the real and synthetic datasets.





In [83]:



    


hologic_meta = mia.analysis.create_hologic_meta_data(hologic, "meta_data/real_meta.csv")
phantom_meta = mia.analysis.create_synthetic_meta_data(phantom, 
                                                        "meta_data/synthetic_meta.csv")
phantom_meta.index.name = 'img_name'

Prepare the BI-RADS/VBD labels for both datasets.





In [84]:



    


hologic_labels = hologic_meta.drop_duplicates().BIRADS
phantom_labels = phantom_meta['VBD.1']

class_labels = pd.concat([hologic_labels, phantom_labels])
class_labels.index.name = "img_name"
labels = mia.analysis.remove_duplicate_index(class_labels)[0]

Creating Features

Create blob features from distribution of blobs





In [85]:



    


hologic_intensity_features = mia.analysis.group_by_scale_space(hologic)
phantom_intensity_features = mia.analysis.group_by_scale_space(phantom)

Take a random subset of the real mammograms. This is important so that each patient is not over represented.





In [86]:



    


hologic_intensity_features['patient_id'] = hologic_meta.drop_duplicates()['patient_id']
hologic_intensity_features_subset = mia.analysis.create_random_subset(hologic_intensity_features, 
                                                                      'patient_id')

Take a random subset of the phantom mammograms. This is important so that each case is not over represented.





In [87]:



    


syn_feature_meta = mia.analysis.remove_duplicate_index(phantom_meta)
phantom_intensity_features['phantom_name'] = syn_feature_meta.phantom_name.tolist()
phantom_intensity_features_subset \
    = mia.analysis.create_random_subset(phantom_intensity_features, 'phantom_name')

Combine the features from both datasets.





In [88]:



    


features = pd.concat([hologic_intensity_features_subset, phantom_intensity_features_subset])
assert features.shape[0] == 96
features.head()



    


















    
Out[88]:










  
    

      
      count
      mean
      std
      min
      25%
      50%
      75%
      max
      skew
      kurtosis
      ...
      count_9
      mean_9
      std_9
      min_9
      25%_9
      50%_9
      75%_9
      max_9
      skew_9
      kurtosis_9
    

  
  
    

      p214-010-60001-cr.png
       256
       0.558904
       0.087279
       0.328763
       0.510450
       0.570363
       0.622144
       0.724731
      -0.406150
      -0.127657
      ...
       131044
       0.541212
       0.118465
       0.141845
       0.462988
       0.546140
       0.624509
       0.921247
      -0.150691
       0.148522
    

    

      p214-010-60005-ml.png
       256
       0.579815
       0.090863
       0.314655
       0.530318
       0.591799
       0.644746
       0.759436
      -0.575184
       0.634554
      ...
       131044
       0.541212
       0.118465
       0.141845
       0.462988
       0.546140
       0.624509
       0.921247
      -0.150691
       0.148522
    

    

      p214-010-60008-cr.png
       256
       0.493326
       0.074813
       0.296470
       0.447373
       0.496014
       0.544188
       0.679322
      -0.100948
       0.021890
      ...
       131044
       0.523970
       0.099598
       0.148544
       0.455340
       0.521359
       0.589320
       0.936893
      -0.017659
       0.898368
    

    

      p214-010-60012-ml.png
       256
       0.469238
       0.081322
       0.254982
       0.415496
       0.473583
       0.527386
       0.660004
      -0.204323
      -0.192516
      ...
       131044
       0.541212
       0.118465
       0.141845
       0.462988
       0.546140
       0.624509
       0.921247
      -0.150691
       0.148522
    

    

      p214-010-60013-mr.png
       256
       0.524458
       0.087562
       0.285158
       0.467286
       0.534160
       0.588593
       0.704526
      -0.407108
       0.041762
      ...
       131044
       0.554975
       0.131461
       0.138075
       0.463040
       0.552301
       0.645746
       0.949791
       0.038416
      -0.374100
    

  



5 rows × 100 columns

Filter some features, such as the min, to remove noise.





In [89]:



    


selected_features = features.copy()

Compare Real and Synthetic Features

Compare the distributions of features detected from the real mammograms and the phantoms using the Kolmogorov-Smirnov two sample test.





In [90]:



    


ks_stats = [list(stats.ks_2samp(hologic_intensity_features[col], 
                                phantom_intensity_features[col]))
                                for col in selected_features.columns]

ks_test = pd.DataFrame(ks_stats, columns=['KS', 'p-value'], index=selected_features.columns)
ks_test.to_latex("tables/intensity_features_ks.tex", longtable=True)
ks_test



    


















    
Out[90]:










  
    

      
      KS
      p-value
    

  
  
    

      count
       0.000000
       1.000000e+00
    

    

      mean
       1.000000
       3.587622e-59
    

    

      std
       0.876389
       1.515491e-45
    

    

      min
       1.000000
       3.587622e-59
    

    

      25%
       1.000000
       3.587622e-59
    

    

      50%
       1.000000
       3.587622e-59
    

    

      75%
       1.000000
       3.587622e-59
    

    

      max
       1.000000
       3.587622e-59
    

    

      skew
       0.891667
       3.923764e-47
    

    

      kurtosis
       0.568056
       2.209941e-19
    

    

      count_1
       0.000000
       1.000000e+00
    

    

      mean_1
       1.000000
       3.587622e-59
    

    

      std_1
       0.981944
       4.539903e-57
    

    

      min_1
       1.000000
       3.587622e-59
    

    

      25%_1
       1.000000
       3.587622e-59
    

    

      50%_1
       1.000000
       3.587622e-59
    

    

      75%_1
       1.000000
       3.587622e-59
    

    

      max_1
       0.997222
       7.598385e-59
    

    

      skew_1
       0.784722
       1.335838e-36
    

    

      kurtosis_1
       0.466667
       3.216681e-13
    

    

      count_2
       0.000000
       1.000000e+00
    

    

      mean_2
       1.000000
       3.587622e-59
    

    

      std_2
       1.000000
       3.587622e-59
    

    

      min_2
       1.000000
       3.587622e-59
    

    

      25%_2
       1.000000
       3.587622e-59
    

    

      50%_2
       1.000000
       3.587622e-59
    

    

      75%_2
       1.000000
       3.587622e-59
    

    

      max_2
       0.994444
       1.605940e-58
    

    

      skew_2
       0.501389
       3.410114e-15
    

    

      kurtosis_2
       0.436111
       1.342503e-11
    

    

      ...
      ...
      ...
    

    

      count_7
       0.000000
       1.000000e+00
    

    

      mean_7
       1.000000
       3.587622e-59
    

    

      std_7
       0.955556
       4.577742e-54
    

    

      min_7
       1.000000
       3.587622e-59
    

    

      25%_7
       1.000000
       3.587622e-59
    

    

      50%_7
       1.000000
       3.587622e-59
    

    

      75%_7
       1.000000
       3.587622e-59
    

    

      max_7
       0.740278
       1.280685e-32
    

    

      skew_7
       0.319444
       2.024353e-06
    

    

      kurtosis_7
       0.304167
       7.344875e-06
    

    

      count_8
       0.000000
       1.000000e+00
    

    

      mean_8
       1.000000
       3.587622e-59
    

    

      std_8
       0.929167
       3.823290e-51
    

    

      min_8
       1.000000
       3.587622e-59
    

    

      25%_8
       1.000000
       3.587622e-59
    

    

      50%_8
       1.000000
       3.587622e-59
    

    

      75%_8
       1.000000
       3.587622e-59
    

    

      max_8
       0.736111
       2.943248e-32
    

    

      skew_8
       0.547222
       5.120902e-18
    

    

      kurtosis_8
       0.395833
       1.248634e-09
    

    

      count_9
       0.000000
       1.000000e+00
    

    

      mean_9
       1.000000
       3.587622e-59
    

    

      std_9
       0.956944
       3.195999e-54
    

    

      min_9
       1.000000
       3.587622e-59
    

    

      25%_9
       1.000000
       3.587622e-59
    

    

      50%_9
       1.000000
       3.587622e-59
    

    

      75%_9
       0.997222
       7.598385e-59
    

    

      max_9
       0.794444
       1.674259e-37
    

    

      skew_9
       0.702778
       1.934059e-29
    

    

      kurtosis_9
       0.891667
       3.923764e-47
    

  



100 rows × 2 columns

Dimensionality Reduction

t-SNE

Running t-SNE to obtain a two dimensional representation.





In [91]:



    


real_index = hologic_intensity_features_subset.index
phantom_index = phantom_intensity_features_subset.index



    











In [92]:



    


kwargs = {
    'learning_rate': 200,
    'perplexity': 20,
    'verbose': 1
}



    











In [93]:



    


SNE_mapping_2d = mia.analysis.tSNE(selected_features, n_components=2, **kwargs)



    


















    






[t-SNE] Computing pairwise distances...
[t-SNE] Computed conditional probabilities for sample 96 / 96
[t-SNE] Mean sigma: 2.693481
[t-SNE] Error after 65 iterations with early exaggeration: 12.552178
[t-SNE] Error after 136 iterations: 1.190411

















In [94]:



    


mia.plotting.plot_mapping_2d(SNE_mapping_2d, real_index, phantom_index, labels)
plt.savefig('figures/mappings/intensity_SNE_mapping_2d.png', dpi=300)

Running t-SNE to obtain a 3 dimensional mapping





In [95]:



    


SNE_mapping_3d = mia.analysis.tSNE(selected_features, n_components=3, **kwargs)



    


















    






[t-SNE] Computing pairwise distances...
[t-SNE] Computed conditional probabilities for sample 96 / 96
[t-SNE] Mean sigma: 2.693481
[t-SNE] Error after 100 iterations with early exaggeration: 16.755029
[t-SNE] Error after 314 iterations: 2.633436

















In [127]:



    


mia.plotting.plot_mapping_3d(SNE_mapping_3d, real_index, phantom_index, labels)



    


















    
Out[127]:








<matplotlib.axes._subplots.Axes3DSubplot at 0x108bf72d0>

Isomap

Running Isomap to obtain a 2 dimensional mapping





In [97]:



    


iso_kwargs = {
    'n_neighbors': 4,
}



    











In [98]:



    


iso_mapping_2d = mia.analysis.isomap(selected_features, n_components=2, **iso_kwargs)



    











In [99]:



    


mia.plotting.plot_mapping_2d(iso_mapping_2d, real_index, phantom_index, labels)
plt.savefig('figures/mappings/intensity_iso_mapping_2d.png', dpi=300)



    


















    
























In [100]:



    


iso_mapping_3d = mia.analysis.isomap(selected_features, n_components=3, **iso_kwargs)



    











In [129]:



    


mia.plotting.plot_mapping_3d(iso_mapping_3d, real_index, phantom_index, labels)



    


















    
Out[129]:








<matplotlib.axes._subplots.Axes3DSubplot at 0x108ea9090>

Locally Linear Embedding

Running locally linear embedding to obtain 2d mapping





In [102]:



    


lle_kwargs = {
    'n_neighbors': 4,
}



    











In [103]:



    


lle_mapping_2d = mia.analysis.lle(selected_features, n_components=2, **lle_kwargs)



    











In [104]:



    


mia.plotting.plot_mapping_2d(lle_mapping_2d, real_index, phantom_index, labels)
plt.savefig('figures/mappings/intensity_lle_mapping_2d.png', dpi=300)



    


















    
























In [105]:



    


lle_mapping_3d = mia.analysis.lle(selected_features, n_components=3, **lle_kwargs)



    











In [130]:



    


mia.plotting.plot_mapping_3d(lle_mapping_3d, real_index, phantom_index, labels)



    


















    
Out[130]:








<matplotlib.axes._subplots.Axes3DSubplot at 0x10a9fe950>

Quality Assessment of Dimensionality Reduction

Assess the quality of the DR against measurements from the co-ranking matrices. First create co-ranking matrices for each of the dimensionality reduction mappings





In [107]:



    


max_k = 50



    











In [108]:



    


SNE_mapping_2d_cm = mia.coranking.coranking_matrix(selected_features, 
                                                   SNE_mapping_2d)
iso_mapping_2d_cm = mia.coranking.coranking_matrix(selected_features, 
                                                   iso_mapping_2d)
lle_mapping_2d_cm = mia.coranking.coranking_matrix(selected_features, 
                                                   lle_mapping_2d)

SNE_mapping_3d_cm = mia.coranking.coranking_matrix(selected_features, 
                                                   SNE_mapping_3d)
iso_mapping_3d_cm = mia.coranking.coranking_matrix(selected_features, 
                                                   iso_mapping_3d)
lle_mapping_3d_cm = mia.coranking.coranking_matrix(selected_features, 
                                                   lle_mapping_3d)

2D Mappings





In [109]:



    


SNE_trustworthiness_2d = [mia.coranking.trustworthiness(SNE_mapping_2d_cm, k) 
                          for k in range(1, max_k)]
iso_trustworthiness_2d = [mia.coranking.trustworthiness(iso_mapping_2d_cm, k) 
                          for k in range(1, max_k)]
lle_trustworthiness_2d = [mia.coranking.trustworthiness(lle_mapping_2d_cm, k) 
                          for k in range(1, max_k)]



    











In [110]:



    


trustworthiness_df = pd.DataFrame([SNE_trustworthiness_2d,
                                   iso_trustworthiness_2d,
                                   lle_trustworthiness_2d], 
                                   index=['SNE', 'Isomap', 'LLE']).T
trustworthiness_df.plot()
plt.savefig('figures/quality_measures/intensity_trustworthiness_2d.png', dpi=300)



    


















    
























In [111]:



    


SNE_continuity_2d = [mia.coranking.continuity(SNE_mapping_2d_cm, k) 
                     for k in range(1, max_k)]
iso_continuity_2d = [mia.coranking.continuity(iso_mapping_2d_cm, k) 
                     for k in range(1, max_k)]
lle_continuity_2d = [mia.coranking.continuity(lle_mapping_2d_cm, k) 
                     for k in range(1, max_k)]



    











In [112]:



    


continuity_df = pd.DataFrame([SNE_continuity_2d,
                              iso_continuity_2d,
                              lle_continuity_2d], 
                              index=['SNE', 'Isomap', 'LLE']).T
continuity_df.plot()
plt.savefig('figures/quality_measures/intensity_continuity_2d.png', dpi=300)



    


















    
























In [113]:



    


SNE_lcmc_2d = [mia.coranking.LCMC(SNE_mapping_2d_cm, k) 
               for k in range(2, max_k)]
iso_lcmc_2d = [mia.coranking.LCMC(iso_mapping_2d_cm, k) 
               for k in range(2, max_k)]
lle_lcmc_2d = [mia.coranking.LCMC(lle_mapping_2d_cm, k) 
               for k in range(2, max_k)]



    











In [114]:



    


lcmc_df = pd.DataFrame([SNE_lcmc_2d,
                        iso_lcmc_2d,
                        lle_lcmc_2d], 
                        index=['SNE', 'Isomap', 'LLE']).T
lcmc_df.plot()
plt.savefig('figures/quality_measures/intensity_lcmc_2d.png', dpi=300)

3D Mappings





In [115]:



    


SNE_trustworthiness_3d = [mia.coranking.trustworthiness(SNE_mapping_3d_cm, k) 
                          for k in range(1, max_k)]
iso_trustworthiness_3d = [mia.coranking.trustworthiness(iso_mapping_3d_cm, k) 
                          for k in range(1, max_k)]
lle_trustworthiness_3d = [mia.coranking.trustworthiness(lle_mapping_3d_cm, k) 
                          for k in range(1, max_k)]



    











In [116]:



    


trustworthiness3d_df = pd.DataFrame([SNE_trustworthiness_3d,
                                   iso_trustworthiness_3d,
                                   lle_trustworthiness_3d], 
                                   index=['SNE', 'Isomap', 'LLE']).T
trustworthiness3d_df.plot()
plt.savefig('figures/quality_measures/intensity_trustworthiness_3d.png', dpi=300)



    


















    
























In [117]:



    


SNE_continuity_3d = [mia.coranking.continuity(SNE_mapping_3d_cm, k) 
                     for k in range(1, max_k)]
iso_continuity_3d = [mia.coranking.continuity(iso_mapping_3d_cm, k) 
                     for k in range(1, max_k)]
lle_continuity_3d = [mia.coranking.continuity(lle_mapping_3d_cm, k) 
                     for k in range(1, max_k)]



    











In [118]:



    


continuity3d_df = pd.DataFrame([SNE_continuity_3d,
                              iso_continuity_3d,
                              lle_continuity_3d], 
                              index=['SNE', 'Isomap', 'LLE']).T
continuity3d_df.plot()
plt.savefig('figures/quality_measures/intensity_continuity_3d.png', dpi=300)



    


















    
























In [119]:



    


SNE_lcmc_3d = [mia.coranking.LCMC(SNE_mapping_3d_cm, k) 
               for k in range(2, max_k)]
iso_lcmc_3d = [mia.coranking.LCMC(iso_mapping_3d_cm, k) 
               for k in range(2, max_k)]
lle_lcmc_3d = [mia.coranking.LCMC(lle_mapping_3d_cm, k)
               for k in range(2, max_k)]



    











In [120]:



    


lcmc3d_df = pd.DataFrame([SNE_lcmc_3d,
                        iso_lcmc_3d,
                        lle_lcmc_3d], 
                        index=['SNE', 'Isomap', 'LLE']).T
lcmc3d_df.plot()
plt.savefig('figures/quality_measures/intensity_lcmc_3d.png', dpi=300)

Content source: samueljackson92/major-project

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