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In [121]:



    


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



    


















    






Warning: Cannot change to a different GUI toolkit: qt. Using osx instead.

Loading and Preprocessing

Loading the hologic and synthetic datasets.





In [83]:



    


hologic = pd.DataFrame.from_csv("hologic_blobs.csv")
phantom = pd.DataFrame.from_csv("synthetic_blobs.csv")

Loading the meta data for the real and synthetic datasets.





In [84]:



    


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 [85]:



    


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 [86]:



    


hologic_blob_features = mia.analysis.features_from_blobs(hologic)
phantom_blob_features = mia.analysis.features_from_blobs(phantom)

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_blob_features['phantom_name'] = syn_feature_meta.phantom_name.tolist()
phantom_blob_features_subset = mia.analysis.create_random_subset(phantom_blob_features, 'phantom_name')

# hologic_blob_features['patient_id'] = hologic_meta['patient_id'].drop_duplicates()
# hologic_blob_features_subset = mia.analysis.create_random_subset(hologic_blob_features, 'patient_id')

Combine the features from both datasets.





In [88]:



    


features = pd.concat([hologic_blob_features, phantom_blob_features_subset])
assert features.shape[0] == 366
features.head()



    


















    
Out[88]:










  
    

      
      blob_count
      avg_radius
      std_radius
      min_radius
      max_radius
      small_radius_count
      med_radius_count
      large_radius_count
      density
      upper_dist_count
      25%
      50%
      75%
    

  
  
    

      p214-010-60001-cl.png
        56
       22.121831
       22.923389
       8
       128.000000
        52
       1
       3
       52.940812
       21
       8
       11.313708
       22.627417
    

    

      p214-010-60001-cr.png
        78
       19.054538
       17.506086
       8
        90.509668
        68
       4
       6
       40.749811
       22
       8
       11.313708
       22.627417
    

    

      p214-010-60001-ml.png
        98
       20.011191
       21.876304
       8
       128.000000
        90
       3
       5
       42.644057
       27
       8
       11.313708
       22.627417
    

    

      p214-010-60001-mr.png
       139
       15.309764
       15.307860
       8
       128.000000
       136
       1
       2
       38.287439
       40
       8
       11.313708
       16.000000
    

    

      p214-010-60005-cl.png
        97
       20.132590
       23.255605
       8
       181.019336
        94
       2
       1
       41.456308
       27
       8
       11.313708
       22.627417

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





In [89]:



    


selected_features = features.drop(['min_radius'], axis=1)

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_blob_features[col], 
                                phantom_blob_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/blob_features_ks.tex")
ks_test



    


















    
Out[90]:










  
    

      
      KS
      p-value
    

  
  
    

      blob_count
       0.341667
       2.774753e-07
    

    

      avg_radius
       0.847222
       1.360953e-42
    

    

      std_radius
       0.711111
       3.929143e-30
    

    

      max_radius
       0.363889
       3.327680e-08
    

    

      small_radius_count
       0.319444
       2.024353e-06
    

    

      med_radius_count
       0.338889
       3.583275e-07
    

    

      large_radius_count
       0.733333
       5.112303e-32
    

    

      density
       0.169444
       4.114705e-02
    

    

      upper_dist_count
       0.345833
       1.883393e-07
    

    

      25%
       0.358333
       5.726005e-08
    

    

      50%
       0.743056
       7.334764e-33
    

    

      75%
       0.777778
       5.796838e-36

Dimensionality Reduction

t-SNE

Running t-SNE to obtain a two dimensional representation.





In [91]:



    


kwargs = {
    'learning_rate': 300,
    'perplexity': 30,
    'verbose': 1
}



    











In [92]:



    


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



    


















    






[t-SNE] Computing pairwise distances...
[t-SNE] Computed conditional probabilities for sample 366 / 366
[t-SNE] Mean sigma: 0.989818
[t-SNE] Error after 83 iterations with early exaggeration: 12.840095
[t-SNE] Error after 284 iterations: 0.384253

















In [93]:



    


mia.plotting.plot_mapping_2d(SNE_mapping_2d, hologic_blob_features.index, phantom_blob_features_subset.index, labels)
plt.savefig('figures/mappings/blob_SNE_mapping_2d.png', dpi=300)

Running t-SNE to obtain a 3 dimensional mapping





In [94]:



    


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



    


















    






[t-SNE] Computing pairwise distances...
[t-SNE] Computed conditional probabilities for sample 366 / 366
[t-SNE] Mean sigma: 0.989818
[t-SNE] Error after 83 iterations with early exaggeration: 13.395568
[t-SNE] Error after 228 iterations: 0.412479

















In [126]:



    


mia.plotting.plot_mapping_3d(SNE_mapping_3d, hologic_blob_features.index, phantom_blob_features_subset.index, labels)



    


















    
Out[126]:








<matplotlib.axes._subplots.Axes3DSubplot at 0x11472cdd0>

Isomap

Running Isomap to obtain a 2 dimensional mapping





In [96]:



    


iso_kwargs = {
    'n_neighbors': 10,
}



    











In [97]:



    


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



    


















    






5.68455464542

















In [132]:



    


mia.plotting.plot_mapping_2d(iso_mapping_2d, hologic_blob_features.index, phantom_blob_features_subset.index, labels)
mia.io_tools.dump_mapping_to_json(iso_mapping_2d.loc[hologic_blob_features.index], [0,1], labels, 'data.json')
plt.savefig('figures/mappings/blob_iso_mapping_2d.png', dpi=300)



    











In [99]:



    


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



    


















    






4.26343423263

















In [123]:



    


mia.plotting.plot_mapping_3d(iso_mapping_3d, hologic_blob_features.index, phantom_blob_features_subset.index, labels)



    


















    
Out[123]:








<matplotlib.axes._subplots.Axes3DSubplot at 0x11230ecd0>

Locally Linear Embedding

Running locally linear embedding to obtain 2d mapping





In [101]:



    


lle_kwargs = {
    'n_neighbors': 10,
}



    











In [102]:



    


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



    


















    






1.17807316961e-07

















In [103]:



    


mia.plotting.plot_mapping_2d(lle_mapping_2d, hologic_blob_features.index, phantom_blob_features_subset.index, labels)
plt.savefig('figures/mappings/blob_lle_mapping_2d.png', dpi=300)



    


















    
























In [104]:



    


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



    











In [124]:



    


mia.plotting.plot_mapping_3d(lle_mapping_3d, hologic_blob_features.index, phantom_blob_features_subset.index, labels)



    


















    
Out[124]:








<matplotlib.axes._subplots.Axes3DSubplot at 0x1124fee10>

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 [106]:



    


max_k = 50



    











In [107]:



    


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 [108]:



    


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 [109]:



    


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/blob_trustworthiness_2d.png', dpi=300)



    


















    
























In [110]:



    


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 [111]:



    


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/blob_continuity_2d.png', dpi=300)



    


















    
























In [112]:



    


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 [113]:



    


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/blob_lcmc_2d.png', dpi=300)

3D Mappings





In [114]:



    


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 [115]:



    


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/blob_trustworthiness_3d.png', dpi=300)



    


















    
























In [116]:



    


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 [117]:



    


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/blob_continuity_3d.png', dpi=300)



    


















    
























In [118]:



    


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 [119]:



    


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/blob_lcmc_3d.png', dpi=300)

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