Source code for rsatoolbox.vis.model_plot

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Barplot for model comparison based on a results file
"""

import warnings
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import patches
from matplotlib.path import Path
from matplotlib import transforms
from matplotlib import cm
import networkx as nx
from networkx.algorithms.clique import find_cliques as maximal_cliques
from scipy.spatial.distance import squareform
from rsatoolbox.util.inference_util import all_tests, get_errorbars
from rsatoolbox.util.rdm_utils import batch_to_vectors


[docs]def plot_model_comparison(result, sort=False, colors=None, alpha=0.01, test_pair_comparisons=True, multiple_pair_testing='fdr', test_above_0=True, test_below_noise_ceil=True, error_bars='sem', test_type='t-test'): """ Plots the results of RSA inference on a set of models as a bar graph with one bar for each model indicating its predictive performance. The function also shows the noise ceiling whose upper edge is an upper bound on the performance the true model could achieve (given noise and inter- subject variability) and whose lower edge is an estimate of a lower bound on the performance of the true model. In addition, all pairwise inferential model comparisons are shown in the upper part of the figure. The only mandatory input is a "result" object containing model evaluations for bootstrap samples and crossvalidation folds. These are used here to construct confidence intervals and perform the significance tests. All string inputs are case insensitive. Args: result (rsatoolbox.inference.result.Result): model evaluation result sort (Boolean or string): False (default): plot bars in the order passed 'descend[ing]': plot bars in descending order of model performance 'ascend[ing]': plot bars in ascending order of model performance colors (list of lists, numpy array, matplotlib colormap): None (default): default blue for all bars single color: list or numpy array of 3 or 4 values (RGB, RGBA) specifying the color for all bars multiple colors: list of lists or numpy array (number of colors by 3 or 4 channels -- RGB, RGBA). If the number of colors matches the number of models, each color is used for the bar corresponding to one model (in the order of the models as passed). If the number of colors does not match the number of models, the list is linearly interpolated to assign a color to each model (in the order of the models as passed). For example, two colors will become a gradation, unless there are exactly two model. Instead of a list of lists or numpy array, a matplotlib colormap object may also be passed (e.g. colors = cm.coolwarm). alpha (float): significance threshold (p threshold or FDR q threshold) test_pair_comparisons (Boolean or string): False or None: do not plot pairwise model comparison results True (default): plot pairwise model comparison results using default settings 'arrows': plot results in arrows style, indicating pairs of sets between which all differences are significant 'nili': plot results as Nili bars (Nili et al. 2014), indicating each significant difference by a horizontal line (or each nonsignificant difference if the string contains a '2', e.g. 'nili2') 'golan': plot results as Golan wings (Golan et al. 2020), with one wing (graphical element) indicating all dominance relationships for one model. 'cliques': plot results as cliques of insignificant differences multiple_pair_testing (Boolean or string): False or 'none': do not adjust for multiple testing for the pairwise model comparisons 'FDR' or 'fdr' (default): control the false-discorvery rate at q = alpha 'FWER',' fwer', or 'Bonferroni': control the familywise error rate using the Bonferroni method test_above_0 (Boolean or string): False or None: do not plot results of statistical comparison of each model performance against 0 True (default): plot results of statistical comparison of each model performance against 0 using default settings ('dewdrops') 'dewdrops': place circular "dewdrops" at the baseline to indicate models whose performance is significantly greater than 0 'icicles': place triangular "icicles" at the baseline to indicate models whose performance is significantly greater than 0 Tests are one-sided, use the global alpha threshold and are automatically Bonferroni-corrected for the number of models tested. test_below_noise_ceil (Boolean or string): False or None: do not plot results of statistical comparison of each model performance against the lower-bound estimate of the noise ceiling True (default): plot results of statistical comparison of each model performance against the lower-bound estimate of the noise ceiling using default settings ('dewdrops') 'dewdrops': use circular "dewdrops" at the lower bound of the noise ceiling to indicate models whose performance is significantly below the lower-bound estimate of the noise ceiling 'icicles': use triangular "icicles" at the lower bound of the noise ceiling to indicate models whose performance is significantly below the lower-bound estimate of the noise ceiling Tests are one-sided, use the global alpha threshold and are automatically Bonferroni-corrected for the number of models tested. error_bars (Boolean or string): False or None: do not plot error bars True (default) or 'SEM': plot the standard error of the mean 'CI': plot 95%-confidence intervals (exluding 2.5% on each side) 'CI[x]': plot x%-confidence intervals (exluding (100-x)/2% on each side) i.e. 'CI' has the same effect as 'CI95' Confidence intervals are based on the bootstrap procedure, reflecting variability of the estimate across subjects and/or experimental conditions. 'dots': Draws dots for each data-point, i.e. first dimension of the evaluation tensor. This is primarily sensible for fixed evaluation where this dimension corresponds to the subjects in the experiment. test_type (string): which tests to perform: 't-test': performs a t-test based on the variance estimates in the result structs 'bootstrap': performs a bootstrap test, i.e. checks based on the number of samples defying H0 'ranksum': performs wilcoxon signed rank sum tests Returns: (matplotlib.pyplot.Figure, matplotlib.pyplot.Axis, matplotlib.pyplot.Axis): the figure and axes the plots were made into. This allows further modification, saving and printing. """ # Prepare and sort data evaluations = result.evaluations models = result.models noise_ceiling = result.noise_ceiling method = result.method model_var = result.model_var diff_var = result.diff_var noise_ceil_var = result.noise_ceil_var dof = result.dof if result.cv_method == 'fixed': n_bootstraps, n_models, _ = evaluations.shape perf = np.mean(evaluations, axis=0) perf = np.nanmean(perf, axis=-1) elif result.cv_method == 'crossvalidation': n_bootstraps, n_models, _ = evaluations.shape perf = np.mean(evaluations, axis=0) perf = np.nanmean(perf, axis=-1) if any([test_pair_comparisons, test_above_0, test_below_noise_ceil]): warnings.warn('tests deactivated as crossvalidation does not' + 'provide uncertainty estimate') test_pair_comparisons = False test_above_0 = False test_below_noise_ceil = False if error_bars and error_bars.lower() != 'dots': warnings.warn('errorbars deactivated as crossvalidation does not' + 'provide uncertainty estimate') error_bars = False else: while len(evaluations.shape) > 2: evaluations = np.nanmean(evaluations, axis=-1) evaluations = evaluations[~np.isnan(evaluations[:, 0])] n_bootstraps, n_models = evaluations.shape perf = np.mean(evaluations, axis=0) noise_ceiling = np.array(noise_ceiling) if sort is True: sort = 'descending' # descending by default if sort is True elif sort is False: sort = 'unsorted' if sort != 'unsorted': # 'descending' or 'ascending' idx = np.argsort(perf) if 'descend' in sort.lower(): idx = np.flip(idx) perf = perf[idx] evaluations = evaluations[:, idx] if model_var: model_var = model_var[idx] if noise_ceil_var: noise_ceil_var = noise_ceil_var[idx] if diff_var: diff_var = squareform(squareform(diff_var)[idx][:, idx]) models = [models[i] for i in idx] if not ('descend' in sort.lower() or 'ascend' in sort.lower()): raise Exception('plot_model_comparison: Argument ' + 'sort is incorrectly defined as ' + sort + '.') # run tests if any([test_pair_comparisons, test_above_0, test_below_noise_ceil]): p_pairwise, p_zero, p_noise = all_tests( evaluations, noise_ceiling, test_type, model_var=model_var, diff_var=diff_var, noise_ceil_var=noise_ceil_var, dof=dof) # Prepare axes for bars and pairwise comparisons fs, fs2 = 18, 14 # axis label font sizes l, b, w, h = 0.15, 0.15, 0.8, 0.8 fig = plt.figure(figsize=(12.5, 10)) if test_pair_comparisons is True: test_pair_comparisons = 'arrows' if test_pair_comparisons: if test_pair_comparisons.lower() in ['arrows', 'cliques']: h_pair_tests = 0.25 elif 'golan' in test_pair_comparisons.lower(): h_pair_tests = 0.3 elif 'nili' in test_pair_comparisons.lower(): h_pair_tests = 0.4 else: raise Exception('plot_model_comparison: Argument ' + 'test_pair_comparisons is incorrectly defined as ' + test_pair_comparisons + '.') ax = plt.axes((l, b, w, h*(1-h_pair_tests))) axbar = plt.axes((l, b + h * (1 - h_pair_tests), w, h * h_pair_tests * 0.7)) else: ax = plt.axes((l, b, w, h)) axbar = None # Define the model colors if colors is None: # no color passed... colors = [0, 0.4, 0.9, 1] # use default blue elif isinstance(colors, cm.colors.LinearSegmentedColormap): cmap = cm.get_cmap(colors) colors = cmap(np.linspace(0, 1, 100))[np.newaxis, :, :3].squeeze() colors = np.array([np.array(col) for col in colors]) if len(colors.shape) == 1: # one color passed... n_col, n_chan = 1, colors.shape[0] colors.shape = (n_col, n_chan) else: # multiple colors passed... n_col, n_chan = colors.shape if n_col == n_models: # one color passed for each model... cols2 = colors else: # number of colors passed does not match number of models... # interpolate colors to define a color for each model cols2 = np.empty((n_models, n_chan)) for c in range(n_chan): cols2[:, c] = np.interp(np.array(range(n_models)), np.array(range(n_col))/n_col*n_models, colors[:, c]) if sort != 'unsorted': colors = cols2[idx, :] else: colors = cols2 if colors.shape[1] == 3: colors = np.concatenate((colors, np.ones((colors.shape[0], 1))), axis=1) # Plot bars and error bars if method == 'neg_riem_dist': ax.bar(np.arange(evaluations.shape[1]), perf-np.min(perf), color=colors, bottom=np.min(perf)) else: ax.bar(np.arange(evaluations.shape[1]), perf, color=colors) if error_bars: limits = get_errorbars(model_var, evaluations, dof, error_bars, test_type) ax.errorbar(np.arange(evaluations.shape[1]), perf, yerr=limits, fmt='none', ecolor='k', capsize=0, linewidth=3) # Test whether model performance exceeds 0 (one sided) if test_above_0 is True: test_above_0 = 'dewdrops' if test_above_0: model_significant = p_zero < alpha / n_models half_sym_size = 9 if test_above_0.lower() == 'dewdrops': halfmoonup = Path.wedge(0, 180) ax.plot(model_significant.nonzero()[0], np.tile(0, model_significant.sum()), 'w', marker=halfmoonup, markersize=half_sym_size, linewidth=0) elif test_above_0.lower() == 'icicles': ax.plot(model_significant.nonzero()[0], np.tile(0, model_significant.sum()), 'w', marker=10, markersize=half_sym_size, linewidth=0) else: raise Exception( 'plot_model_comparison: Argument test_above_0' + ' is incorrectly defined as ' + test_above_0 + '.') # Plot noise ceiling noise_ceil_col = [0.5, 0.5, 0.5, 0.2] if noise_ceiling is not None: noise_lower = np.nanmean(noise_ceiling[0]) noise_upper = np.nanmean(noise_ceiling[1]) noiserect = patches.Rectangle((-0.5, noise_lower), len(perf), noise_upper-noise_lower, linewidth=0, facecolor=noise_ceil_col, zorder=1e6) ax.add_patch(noiserect) # Test whether model performance is below the noise ceiling's lower bound # (one sided) if test_below_noise_ceil is True: test_below_noise_ceil = 'dewdrops' if test_below_noise_ceil: model_below_lower_bound = p_noise < alpha / n_models if test_below_noise_ceil.lower() == 'dewdrops': halfmoondown = Path.wedge(180, 360) ax.plot(model_below_lower_bound.nonzero()[0], np.tile(noise_lower+0.0000, model_below_lower_bound.sum()), color='none', marker=halfmoondown, markersize=half_sym_size, markerfacecolor=noise_ceil_col, markeredgecolor='none', linewidth=0) elif test_below_noise_ceil.lower() == 'icicles': ax.plot(model_below_lower_bound.nonzero()[0], np.tile(noise_lower+0.0007, model_below_lower_bound.sum()), color='none', marker=11, markersize=half_sym_size, markerfacecolor=noise_ceil_col, markeredgecolor='none', linewidth=0) else: raise Exception( 'plot_model_comparison: Argument ' + 'test_below_noise_ceil is incorrectly defined as ' + test_below_noise_ceil + '.') # Pairwise model comparisons if test_pair_comparisons: if test_type == 'bootstrap': model_comp_descr = 'Model comparisons: two-tailed bootstrap, ' elif test_type == 't-test': model_comp_descr = 'Model comparisons: two-tailed t-test, ' elif test_type == 'ranksum': model_comp_descr = 'Model comparisons: two-tailed Wilcoxon-test, ' n_tests = int((n_models ** 2 - n_models) / 2) if multiple_pair_testing is None: multiple_pair_testing = 'uncorrected' if multiple_pair_testing.lower() == 'bonferroni' or \ multiple_pair_testing.lower() == 'fwer': significant = p_pairwise < (alpha / n_tests) elif multiple_pair_testing.lower() == 'fdr': ps = batch_to_vectors(np.array([p_pairwise]))[0][0] ps = np.sort(ps) criterion = alpha * (np.arange(ps.shape[0]) + 1) / ps.shape[0] k_ok = ps < criterion if np.any(k_ok): k_max = np.max(np.where(ps < criterion)[0]) crit = criterion[k_max] else: crit = 0 significant = p_pairwise < crit else: if 'uncorrected' not in multiple_pair_testing.lower(): raise Exception( 'plot_model_comparison: Argument ' + 'multiple_pair_testing is incorrectly defined as ' + multiple_pair_testing + '.') significant = p_pairwise < alpha model_comp_descr = _get_model_comp_descr( test_type, n_models, multiple_pair_testing, alpha, n_bootstraps, result.cv_method, error_bars, test_above_0, test_below_noise_ceil) fig.suptitle(model_comp_descr, fontsize=fs2/2) axbar.set_xlim(ax.get_xlim()) digits = [d for d in list(test_pair_comparisons) if d.isdigit()] if len(digits) > 0: v = int(digits[0]) else: v = None if 'nili' in test_pair_comparisons.lower(): if v: plot_nili_bars(axbar, significant, version=v) else: plot_nili_bars(axbar, significant) elif 'golan' in test_pair_comparisons.lower(): if v: plot_golan_wings(axbar, significant, perf, sort, colors, version=v) else: plot_golan_wings(axbar, significant, perf, sort, colors) elif 'arrows' in test_pair_comparisons.lower(): plot_arrows(axbar, significant) elif 'cliques' in test_pair_comparisons.lower(): plot_cliques(axbar, significant) # Floating axes if method == 'neg_riem_dist': ytoptick = noise_upper + 0.1 ymin = np.min(perf) else: ytoptick = np.floor(min(1, noise_upper) * 10) / 10 ymin = 0 ax.set_yticks(np.arange(ymin, ytoptick + 1e-6, step=0.1)) ax.spines['right'].set_visible(False) ax.spines['top'].set_visible(False) ax.set_xticks(np.arange(n_models)) ax.spines['left'].set_bounds(ymin, ytoptick) ax.spines['bottom'].set_bounds(0, n_models - 1) ax.yaxis.set_ticks_position('left') ax.xaxis.set_ticks_position('bottom') plt.rc('ytick', labelsize=fs2) # Axis labels y_label_string = _get_y_label(method) ylabel_fig_x, ysublabel_fig_x = 0.07, 0.095 trans = transforms.blended_transform_factory(fig.transFigure, ax.get_yaxis_transform()) ax.text(ylabel_fig_x, (ymin + ytoptick) / 2, 'RDM prediction accuracy', horizontalalignment='center', verticalalignment='center', rotation='vertical', fontsize=fs, fontweight='bold', transform=trans) ax.text(ysublabel_fig_x, (ymin+ytoptick)/2, y_label_string, horizontalalignment='center', verticalalignment='center', rotation='vertical', fontsize=fs2, fontweight='normal', transform=trans) if models is not None: ax.set_xticklabels([m.name for m in models], fontsize=fs2, rotation=45) return fig, ax, axbar
[docs]def plot_nili_bars(axbar, significant, version=1): """ plots the results of the pairwise inferential model comparisons in the form of a set of black horizontal bars connecting significantly different models as in the 2014 RSA Toolbox (Nili et al. 2014). Args: axbar: Matplotlib axes handle to plot in significant: Boolean matrix of model comparisons version: - 1 (Normal Nili bars, indicating significant differences) - 2 (Negative Nili bars in gray, indicating nonsignificant comparison results) Returns: --- """ k = 1 ns_col = [0.5, 0.5, 0.5] w = 0.2 for i in range(significant.shape[0]): drawn1 = False for j in range(i + 1, significant.shape[0]): if version == 1: if significant[i, j]: axbar.plot((i, j), (k, k), 'k-', linewidth=2) k += 1 drawn1 = True elif version == 2: if not significant[i, j]: axbar.plot((i, j), (k, k), '-', linewidth=2, color=ns_col) axbar.plot(((i+j)/2-w/2, (i+j)/2+w/2), (k, k), '-', linewidth=3, color='w') axbar.text((i+j)/2, k, 'n.s.', horizontalalignment='center', verticalalignment='center', fontsize=8, fontweight='normal', color=ns_col) k += 1 drawn1 = True if drawn1: k += 1 axbar.set_axis_off() axbar.set_ylim((0, k))
[docs]def plot_golan_wings(axbar, significant, perf, sort, colors=None, always_black=False, version=3): """ Plots the results of the pairwise inferential model comparisons in the form of black horizontal bars with a tick mark at the reference model and a circular bulge at each significantly different model similar to the visualization in Golan, Raju, Kriegeskorte (2020). Args: axbar: Matplotlib axes handle to plot in significant: Boolean matrix of model comparisons version: - 0 (single wing: solid circle anchor and open circles), - 1 (single wing: tick anchor and circles), - 2 (single wing: circle anchor and up and down feathers) - 3 (double wings: circle anchor, downward dominance-indicating feathers, from bottom to top in model order) - 4 (double wings: circle anchor, downward dominance-indicating feathers, from bottom to top in performance order) Returns: --- """ # Define wing order n_models = significant.shape[0] wing_order = np.array(range(n_models)) # to the right by default if 'ascend' in sort.lower(): wing_order = np.flip(wing_order) # to the left if bars are ascending if version == 4: wing_order = np.argsort(-perf) # Define vertical spacing bbox = axbar.get_window_extent().transformed( plt.gcf().dpi_scale_trans.inverted()) h_inch = bbox.height h = 1 for wo_i, i in enumerate(wing_order): if version in [3, 4]: js = np.concatenate((wing_order[0:wo_i], wing_order[wo_i+1:])).astype('int') js = js[np.logical_and(significant[i, js], perf[i] > perf[js])] else: js = wing_order[wo_i+1:][significant[i, wing_order[wo_i+1:]]] js = js[significant[i, js]] if len(js) > 0: h += 1 axbar.set_axis_off() axbar.set_ylim((0, h)) # Draw the wings if always_black or colors is None or colors.shape[0] == 1: colors = np.tile([0, 0, 0, 1], (n_models, 1)) tick_length_inch = 0.08 k = 1 for wo_i, i in enumerate(wing_order): if version in [3, 4]: js = np.concatenate((wing_order[0:wo_i], wing_order[wo_i+1:])).astype('int') js = js[np.logical_and(significant[i, js], perf[i] > perf[js])] else: js = wing_order[wo_i+1:][significant[i, wing_order[wo_i+1:]]] js = js[significant[i, js]] if len(js) > 0: if version != 1: # circle anchor axbar.plot(i, k, markersize=8, marker='o', markeredgecolor=colors[i, :], markerfacecolor=colors[i, :]) elif version == 1: # tick anchor axbar.plot((i, i), (k - tick_length_inch/h_inch*h, k), '-', linewidth=2, color=colors[i, :]) # tick for j in js: if version == 0: axbar.plot(j, k, markersize=8, marker='o', markeredgecolor=colors[i, :], markerfacecolor='w') elif version == 1: axbar.plot(j, k, markersize=8, marker='o', markeredgecolor=colors[i, :], markerfacecolor=colors[i, :]) elif version in [2, 3, 4]: if perf[i] > perf[j]: tick_ver_end = k - tick_length_inch/h_inch*h elif perf[i] < perf[j]: tick_ver_end = k + tick_length_inch/h_inch*h axbar.plot((j, j), (k, tick_ver_end), '-', linewidth=2, color=colors[i, :]) # wing line axbar.plot((min(i, js.min()), max(i, js.max())), (k, k), 'k-', linewidth=2, color=colors[i, :], zorder=-1) k += 1
[docs]def plot_arrows(axbar, significant): """ Summarizes the significances with arrows. The argument significant is a binary matrix of pairwise model comparisons. A nonzero value (or True) indicates that the model specified by the row index beats the model specified by the column index. Only the lower triangular part of compMat is used, so the upper triangular part need not be filled in symmetrically. The summary will be most concise if models are ordered by performance (using the sort argument of model_plot.py). """ # Preparations n = significant.shape[0] remaining = significant.copy() # make arrowheads verts_R = [(0, 0), (0, 1), (2, 0), (0, -1), (0, 0)] verts_L = [(-x, y) for (x, y) in verts_R] codes = [Path.MOVETO, Path.LINETO, Path.LINETO, Path.LINETO, Path.CLOSEPOLY] ah_R = Path(verts_R, codes) ah_L = Path(verts_L, codes) # Capture as many comparisons as possible with double arrows double_arrows = [] for ambiguity_span in range(0, n-1): # consider short double arrows first (these cover many comparisons) for i in range(n-1, ambiguity_span, -1): if significant[i:n, 0:i-ambiguity_span].all() and \ remaining[i:n, 0:i-ambiguity_span].any(): # add double arrow double_arrows.append((i-ambiguity_span-1, i)) remaining[i:n, 0:i-ambiguity_span] = 0 # Capture as many of the remaining comparisons as possible with arrows arrows = [] for dist2diag in range(1, n): for i in range(n-1, dist2diag-1, -1): if significant[i, 0:i-dist2diag+1].all() and \ remaining[i, 0:i-dist2diag+1].any(): arrows.append((i, i-dist2diag)) # add left arrow remaining[i, 0:i-dist2diag+1] = 0 if significant[i:n, i-dist2diag].all() and \ remaining[i:n, i-dist2diag].any(): arrows.append((i-dist2diag, i)) # add right arrow remaining[i:n, i-dist2diag] = 0 # Capture the remaining comparisons with lines lines = [] for i in range(1, n): for j in range(0, i-1): if remaining[i, j]: lines.append((i, j)) # add line # Plot expected_n_lines = 6 axbar.set_ylim((0, expected_n_lines)) axbar.set_axis_off() n_elements = len(double_arrows)+len(arrows)+len(lines) if n_elements == 0: return occupied = np.zeros((n_elements, 3*n)) for m in range(0, int(np.ceil(n/2))): double_arrows_left = [(i, j) for (i, j) in double_arrows if i == m] if len(double_arrows_left) > 0: i, j = double_arrows_left[0] double_arrows.remove((i, j)) if j < i: i, j = j, i k = 1 while occupied[k-1, i*3+2:j*3+1].any(): k += 1 if i == 0: draw_hor_arrow(axbar, i, j, k, '->', ah_L, ah_R) elif j == n-1: draw_hor_arrow(axbar, i, j, k, '<-', ah_L, ah_R) else: draw_hor_arrow(axbar, i, j, k, '<->', ah_L, ah_R) occupied[k-1, i*3+2:j*3+1] = 1 double_arrows_right = \ [(i, j) for (i, j) in double_arrows if j == n-1-m] if len(double_arrows_right) > 0: i, j = double_arrows_right[0] double_arrows.remove((i, j)) k = 1 while occupied[k-1, i*3+2:j*3+1].any(): k += 1 if i == 0: draw_hor_arrow(axbar, i, j, k, '->', ah_L, ah_R) elif j == n-1: draw_hor_arrow(axbar, i, j, k, '<-', ah_L, ah_R) else: draw_hor_arrow(axbar, i, j, k, '<->', ah_L, ah_R) occupied[k-1, i*3+2:j*3+1] = 1 for m in range(0, int(np.ceil(n/2))): arrows_left = [(i, j) for (i, j) in arrows if (i < j and i == m) or (j < i and j == m)] while len(arrows_left) > 0: i, j = arrows_left.pop() arrows.remove((i, j)) k = 1 while occupied[k-1, i*3+2:j*3+1].any() or \ occupied[k-1, j*3+2:i*3+1].any(): k += 1 draw_hor_arrow(axbar, i, j, k, '->', ah_L, ah_R) occupied[k-1, i*3+2:j*3+1] = 1 occupied[k-1, j*3+2:i*3+1] = 1 arrows_right = [(i, j) for (i, j) in arrows if (i < j and j == n-1-m) or (j < i and i == n-1-m)] while len(arrows_right) > 0: i, j = arrows_right.pop() arrows.remove((i, j)) k = 1 while occupied[k-1, i*3+2:j*3+1].any() or \ occupied[k-1, j*3+2:i*3+1].any(): k += 1 draw_hor_arrow(axbar, i, j, k, '->', ah_L, ah_R) occupied[k-1, i*3+2:j*3+1] = 1 occupied[k-1, j*3+2:i*3+1] = 1 for m in range(0, int(np.ceil(n/2))): lines_left = [(i, j) for (i, j) in lines if i == m] while len(lines_left) > 0: i, j = lines_left.pop() lines.remove((i, j)) if j < i: i, j = j, i k = 1 while occupied[k-1, i*3+2:j*3+1].any(): k += 1 axbar.plot((i, j), (k, k), 'k-', linewidth=2) occupied[k-1, i*3+2:j*3+1] = 1 lines_right = [(i, j) for (i, j) in lines if j == n-1-m] while len(lines_right) > 0: i, j = lines_right.pop() lines.remove((i, j)) if j < i: i, j = j, i k = 1 while occupied[k-1, i*3+2:j*3+1].any(): k += 1 axbar.plot((i, j), (k, k), 'k-', linewidth=2) occupied[k-1, i*3+2:j*3+1] = 1 h = occupied.sum(axis=1).nonzero()[0].max()+1 axbar.set_ylim((0, max(expected_n_lines, h)))
[docs]def draw_hor_arrow(ax, x1, x2, y, style, ah_L, ah_R): """ Draws a horizontal arrow from (x1, y) to (x2, y) if style is '->' and in the reverse direction if style is '<-'. If style is '<->', this function draws a double arrow. """ lw, s = 1.6, 0.45 ms, ms_a = 8, 18 if (x1 < x2 and style == '->') or (x2 < x1 and style == '<-'): mr = ah_R # arrow points right else: mr = ah_L # arrow points left if style == '<-': x1, x2 = x2, x1 # arrow from x1 to x2 now d = (x2-x1)/abs(x2-x1) if style == '<->': ax.plot(x1+d*s, y, 'k', markersize=ms_a, marker=ah_L) ax.plot((x1+d*s, x2-d*s), (y, y), 'k-', linewidth=lw) ax.plot(x2-d*s, y, 'k', markersize=ms_a, marker=ah_R) else: ax.plot(x1, y, 'k', markersize=ms, marker='o') ax.plot((x1, x2-d*s), (y, y), 'k-', linewidth=lw) ax.plot(x2-d*s, y, 'k', markersize=ms_a, marker=mr)
[docs]def plot_cliques(axbar, significant): """ plots the results of the pairwise inferential model comparisons in the form of a set of maximal cliques of models that are not significantly different in performance. One bar is drawn for each clique with open circles indicating the clique members. Within a clique of models, no pair comparison is significant. All pair comparisons not indicated as insignificant are significant. Args: axbar: Matplotlib axes handle to plot in significant: Boolean matrix of model comparisons Returns: --- """ G = nx.Graph(np.logical_not(significant)) cliques = list(maximal_cliques(G)) n = significant.shape[0] ns_col = [0.6, 0.6, 0.6] expected_n_lines = 6 axbar.set_ylim((0, expected_n_lines)) axbar.set_axis_off() occupied = np.zeros((len(cliques), 3*n)) for c in cliques: if len(c) > 1: i, j = min(c), max(c) k = 1 while occupied[k-1, i*3+1:j*3+2].any(): k += 1 occupied[k-1, i*3+1:j*3+2] = 1 axbar.plot((i, j), (k, k), '-', linewidth=2, color=ns_col) for i in c: axbar.plot(i, k, markersize=8, marker='o', markeredgecolor=ns_col, markerfacecolor='w') h = occupied.sum(axis=1).nonzero()[0].max()+1 axbar.set_ylim((0, max(expected_n_lines, h)))
def _get_model_comp_descr(test_type, n_models, multiple_pair_testing, alpha, n_bootstraps, cv_method, error_bars, test_above_0, test_below_noise_ceil): """constructs the statistics description from the parts Args: test_type : String n_models : integer multiple_pair_testing : String alpha : float n_bootstraps : integer cv_method : String error_bars : String test_above_0 : Bool test_below_noise_ceil : Bool Returns: model """ if test_type == 'bootstrap': model_comp_descr = 'Model comparisons: two-tailed bootstrap, ' elif test_type == 't-test': model_comp_descr = 'Model comparisons: two-tailed t-test, ' elif test_type == 'ranksum': model_comp_descr = 'Model comparisons: two-tailed Wilcoxon-test, ' n_tests = int((n_models ** 2 - n_models) / 2) if multiple_pair_testing is None: multiple_pair_testing = 'uncorrected' if multiple_pair_testing.lower() == 'bonferroni' or \ multiple_pair_testing.lower() == 'fwer': model_comp_descr = (model_comp_descr + 'p < {:<.5g}'.format(alpha) + ', Bonferroni-corrected for ' + str(n_tests) + ' model-pair comparisons') elif multiple_pair_testing.lower() == 'fdr': model_comp_descr = (model_comp_descr + 'FDR q < {:<.5g}'.format(alpha) + ' (' + str(n_tests) + ' model-pair comparisons)') else: if 'uncorrected' not in multiple_pair_testing.lower(): raise Exception( 'plot_model_comparison: Argument ' + 'multiple_pair_testing is incorrectly defined as ' + multiple_pair_testing + '.') model_comp_descr = (model_comp_descr + 'p < {:<.5g}'.format(alpha) + ', uncorrected (' + str(n_tests) + ' model-pair comparisons)') if cv_method in ['bootstrap_rdm', 'bootstrap_pattern', 'bootstrap_crossval']: model_comp_descr = model_comp_descr + \ '\nInference by bootstrap resampling ' + \ '({:<,.0f}'.format(n_bootstraps) + ' bootstrap samples) of ' if cv_method == 'bootstrap_rdm': model_comp_descr = model_comp_descr + 'subjects. ' elif cv_method == 'bootstrap_pattern': model_comp_descr = model_comp_descr + 'experimental conditions. ' elif cv_method in ['bootstrap', 'bootstrap_crossval']: model_comp_descr = model_comp_descr + \ 'subjects and experimental conditions. ' if error_bars[0:2].lower() == 'ci': model_comp_descr = model_comp_descr + 'Error bars indicate the' if len(error_bars) == 2: CI_percent = 95.0 else: CI_percent = float(error_bars[2:]) model_comp_descr = (model_comp_descr + ' ' + str(CI_percent) + '% confidence interval.') elif error_bars.lower() == 'sem': model_comp_descr = ( model_comp_descr + 'Error bars indicate the standard error of the mean.') elif error_bars.lower() == 'sem': model_comp_descr = (model_comp_descr + 'Dots represent the individual model evaluations.') if test_above_0 or test_below_noise_ceil: model_comp_descr = ( model_comp_descr + '\nOne-sided comparisons of each model performance ') if test_above_0: model_comp_descr = model_comp_descr + 'against 0 ' if test_above_0 and test_below_noise_ceil: model_comp_descr = model_comp_descr + 'and ' if test_below_noise_ceil: model_comp_descr = ( model_comp_descr + 'against the lower-bound estimate of the noise ceiling ') if test_above_0 or test_below_noise_ceil: model_comp_descr = (model_comp_descr + 'are Bonferroni-corrected for ' + str(n_models) + ' models.') return model_comp_descr def _get_y_label(method): """ generates y-label string Args: method : String Method for model evaluation used Returns: y_label : String """ if method.lower() == 'cosine': y_label = '[across-subject mean of cosine similarity]' if method.lower() in ['cosine_cov', 'whitened cosine']: y_label = '[across-subject mean of whitened-RDM cosine]' elif method.lower() == 'spearman': y_label = '[across-subject mean of Spearman r rank correlation]' elif method.lower() in ['corr', 'pearson']: y_label = '[across-subject mean of Pearson r correlation]' elif method.lower() in ['whitened pearson', 'corr_cov']: y_label = '[across-subject mean of whitened-RDM Pearson r correlation]' elif method.lower() in ['kendall', 'tau-b']: y_label = '[across-subject mean of Kendall tau-b rank correlation]' elif method.lower() == 'tau-a': y_label = '[across-subject mean of ' \ + 'Kendall tau-a rank correlation]' elif method.lower() == 'neg_riem_dist': y_label = '[across-subject mean of ' \ + 'negative riemannian distance]' return y_label