VAX Method

The multiVariate dAta eXplanation (VAX) is a new Visual Analytics (VA) method to support identifying and visual interpreting patterns in multivariate datasets. VAX uses the concept of Jumping Emerging Patterns, inherent interpretable logic statements representing class-variable relationships (patterns) derived from random Decision Trees. VAX employs aggregated Jumping Emerging Patterns (JEPs) to capture intricate patterns in class-labeled datasets. A matrix-like visual metaphor is used for JEPs visualization, where patterns are rows, variables are columns, and data distribution conveyed using histograms are matrix cells. Based on matrix visualization, meaningful visual representations can be reached by filtering and ordering patterns (rows) and variables (columns). Furthermore, VAX supports similarity maps produced by Dimensionality Reduction (DR) techniques to convey a better overall image of a dataset (e.g., clusters and outliers) using the JEPs lens.

For presenting the method here, the Iris Dataset is employed.

Cite us: M. Popolin Neto and F. V. Paulovich, "Multivariate Data Explanation by Jumping Emerging Patterns Visualization," in IEEE Transactions on Visualization and Computer Graphics, 2022, doi: 10.1109/TVCG.2022.3223529.

BibTeX: @article{PopolinNeto:2022:VAX, author={Popolin{ }Neto, Mário and Paulovich, Fernando V.}, journal={IEEE Transactions on Visualization and Computer Graphics}, title={Multivariate Data Explanation by Jumping Emerging Patterns Visualization}, year={2022}, volume={}, number={}, pages={1-16}, doi={10.1109/TVCG.2022.3223529}}

Iris Dataset

import numpy as np
import sklearn.datasets as datasets


dataset = datasets.load_iris()

X = dataset.data
y = dataset.target

feature_names = dataset.feature_names
target_names = dataset.target_names

VAX

JEPs Extraction, Selection, and Aggregation

from vaxm import VAX


dtm = VAX( n_features = len( feature_names ), n_classes = len( target_names ), feature_names = np.array( feature_names ), class_names = np.array( target_names ), bins = 10, verbose = 0 )

dtm.fit( X, y, k_trees = 1024, save_stages = True, file_name = './IRIS-VAX-k1024', n_jobs = 4, random_seed = 1988 )
print('dtm.n_rules_', dtm.n_rules_)

dtm.n_rules_ 9

Similarity Map Creation

from sklearn.manifold import MDS


X_ext, y_pclass = dtm.extend_X( X, lam = 0.90 )

embedding = MDS( n_components = 2, dissimilarity = 'euclidean', normalized_stress = 'auto', n_jobs = 1, random_state = 1988  )
X_emb = embedding.fit_transform( X_ext )

94% Data Coverage

JEPs Visualization

exp = dtm.explanation( r_order = 'support', f_order = 'importance', data_coverage_max = 0.94 )

exp.create_svg( draw_row_labels = True, draw_col_labels = True, draw_rows_line = False, draw_cols_line = False, col_label_degrees = 10, draw_box_frame = False, inner_pad_row = 5, inner_pad_col = 5, cell_background = 'all', cell_background_color = '#f2f2f2',  draw_frame_top_legend = False, draw_box_row_left_legend = True, draw_frame_left_legend = False, rows_left_legend_show_value = True, draw_frame_right_legend = False, draw_box_row_right_legend = False, rows_right_legend_width = 75/3, binary_legend = [ '< 0.05', '>= 0.05' ], margin_left = 400, margin_top = 550, margin_right = 450, margin_bottom = 350, matrix_legend_ratio = 0.80 )

exp.save( 'JEPs-3P.png', pixel_scale = 5 )
exp.save( 'JEPs-3P.svg' )
exp.display_jn()

Similarity Map Visualization

import matplotlib.pyplot as plt


dtm.plot_map( X_emb, y, exp.rules_, plt, mode = 'horizontal', color_map1 = np.array( [ '#f2f2f2ff', '#1f77b3', '#ff7e0e', '#bcbc21' ] ), color_map2 = np.array( [ '#f2f2f2ff', '#e277c1', '#9367bc', '#bc0049', '#00aa79', '#ffdb00', '#d89c00', '#e41a1c', '#8c564b', '#ff9a75' ] ) )

plt.tight_layout()
plt.savefig( 'MAP-3P.png', dpi = 300, bbox_inches = 'tight' )
plt.savefig( 'MAP-3P.svg', bbox_inches = 'tight' )
plt.show()

Support Matrix Visualization

instance_names = np.array( [ 'i' + str( i ) for i in range( X.shape[ 0 ] ) ] )

exp.smatrix( y = y, instance_names = instance_names )

exp.create_svg_smatrix( height = 540, draw_row_labels = True, draw_col_labels = True, draw_box_frame = True, draw_cell_frame = True, inner_pad_row = 0, inner_pad_col = 0, cell_background_color = '#f2f2f2', col_label_degrees = 90, col_label_font_size = 12, info_text = 'Iris Dataset', margin_bottom = 75, margin_right = 250, matrix_legend_ratio = 0.80 )

exp.save_smatrix( 'SMATRIX-3P.png', pixel_scale = 5 )
exp.save_smatrix( 'SMATRIX-3P.svg' )
exp.display_smatrix_jn()

100% Data Coverage

JEPs Visualization

exp = dtm.explanation( r_order = 'support', f_order = 'importance' )

exp.create_svg( draw_row_labels = True, draw_col_labels = True, draw_rows_line = False, draw_cols_line = False, col_label_degrees = 10, draw_box_frame = False, inner_pad_row = 5, inner_pad_col = 5, cell_background = 'all', cell_background_color = '#f2f2f2',  draw_frame_top_legend = False, draw_box_row_left_legend = True, draw_frame_left_legend = False, rows_left_legend_show_value = True, draw_frame_right_legend = False, draw_box_row_right_legend = False, rows_right_legend_width = 75/3, binary_legend = [ '< 0.05', '>= 0.05' ], margin_left = 400, margin_top = 450, margin_right = 350, margin_bottom = 150, matrix_legend_ratio = 0.80 )

exp.save( 'JEPs.png', pixel_scale = 5 )
exp.save( 'JEPs.svg' )
exp.display_jn()

Similarity Map Visualization

dtm.plot_map( X_emb, y, exp.rules_, plt, mode = 'horizontal', color_map1 = np.array( [ '#f2f2f2ff', '#1f77b3', '#ff7e0e', '#bcbc21' ] ), color_map2 = np.array( [ '#f2f2f2ff', '#e277c1', '#9367bc', '#bc0049', '#00aa79', '#ffdb00', '#d89c00', '#e41a1c', '#8c564b', '#ff9a75' ] ), ncol_map2 = 7, bbox_to_anchor = ( 0.5, 1.19 ) )

plt.tight_layout()
plt.savefig( 'MAP.png', dpi = 300, bbox_inches = 'tight' )
plt.savefig( 'MAP.svg', bbox_inches = 'tight' )
plt.show()

Support Matrix Visualization

exp.smatrix( y = y, instance_names = instance_names )

exp.create_svg_smatrix( height = 540, draw_row_labels = True, draw_col_labels = True, draw_box_frame = True, draw_cell_frame = True, inner_pad_row = 0, inner_pad_col = 0, cell_background_color = '#f2f2f2', col_label_degrees = 90, col_label_font_size = 12, info_text = 'Iris Dataset', margin_bottom = 75, margin_right = 250, matrix_legend_ratio = 0.80 )

exp.save_smatrix( 'SMATRIX.png', pixel_scale = 5 )
exp.save_smatrix( 'SMATRIX.svg' )
exp.display_smatrix_jn()

References

VAX uses the Logic Rules Matrix package, which also supports the Explainable Matrix - ExMatrix method. Both ExMatrix and VAX employ a matrix-like visual metaphor for logic rules visualization, where rules are rows, features (variables) are columns, and rules predicates are cells.

The ExMatrix must be used for model (predictive) explanations (model interpretability/explainability), while VAX must be employed for data (descriptive) explanations (phenomenon understanding).

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[1] Popolin Neto, M. (2021). Random Forest interpretability - explaining classification models and multivariate data through logic rules visualizations. Doctoral Thesis, Instituto de Ciências Matemáticas e de Computação, University of São Paulo, São Carlos. doi:10.11606/T.55.2021.tde-03032022-105725.

BibTeX: @phdthesis{PopolinNeto:2021:Thesis, doi = {10.11606/t.55.2021.tde-03032022-105725}, publisher = {Universidade de Sao Paulo, Agencia {USP} de Gestao da Informacao Academica ({AGUIA})}, author = {M{'{a}}rio Popolin{ }Neto}, title = {Random Forest interpretability - explaining classification models and multivariate data through logic rules visualizations}}

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[2] M. Popolin Neto and F. V. Paulovich, "Explainable Matrix - Visualization for Global and Local Interpretability of Random Forest Classification Ensembles," in IEEE Transactions on Visualization and Computer Graphics, vol. 27, no. 2, pp. 1427-1437, Feb. 2021, doi: 10.1109/TVCG.2020.3030354.

BibTeX: @article{PopolinNeto:2020:ExMatrix, author={Popolin{ }Neto, Mário and Paulovich, Fernando V.}, journal={IEEE Transactions on Visualization and Computer Graphics}, title={Explainable Matrix - Visualization for Global and Local Interpretability of Random Forest Classification Ensembles}, year={2021}, volume={27}, number={2}, pages={1427-1437}, doi={10.1109/TVCG.2020.3030354}}

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[3] M. Popolin Neto and F. V. Paulovich, "Multivariate Data Explanation by Jumping Emerging Patterns Visualization," in IEEE Transactions on Visualization and Computer Graphics, 2022, doi: 10.1109/TVCG.2022.3223529.

BibTeX: @article{PopolinNeto:2022:VAX, author={Popolin{ }Neto, Mário and Paulovich, Fernando V.}, journal={IEEE Transactions on Visualization and Computer Graphics}, title={Multivariate Data Explanation by Jumping Emerging Patterns Visualization}, year={2022}, volume={}, number={}, pages={1-16}, doi={10.1109/TVCG.2022.3223529}}

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