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import numpy as np | ||
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def vcorrcoef(X, y): # return a correlation between each row of X with y | ||
Xm = np.reshape(np.mean(X, axis=1), (X.shape[0], 1)) | ||
ym = np.mean(y) | ||
r_num = np.sum((X-Xm)*(y-ym), axis=1) | ||
r_den = np.sqrt(np.sum((X-Xm)**2, axis=1)*np.sum((y-ym)**2)) | ||
r = r_num/r_den | ||
return r | ||
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def elementwise_corrcoef(X, Y): | ||
# X and Y are each of shape num_observations X num_element | ||
# computes the correlation between each element of X and Y | ||
Xm = X.mean(axis=0) | ||
Ym = Y.mean(axis=0) | ||
r_num = np.sum((X-Xm)*(Y-Ym), axis=0) | ||
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r_den = np.sqrt(np.sum((X-Xm)**2, axis=0)*np.sum((Y-Ym)**2, axis=0)) | ||
r = r_num/r_den | ||
return r | ||
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def elementwise_spearman(X,Y): | ||
order = X.argsort(axis=0) | ||
X_ranks = order.argsort(axis=0) | ||
order = Y.argsort(axis=0) | ||
Y_ranks = order.argsort(axis=0) | ||
return elementwise_corrcoef(X_ranks, Y_ranks) | ||
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def dice_coefficient(mask1,mask2): | ||
dice = np.sum(mask1*mask2)*2.0 / (np.sum(mask1) + np.sum(mask2)) | ||
return dice | ||
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''' | ||
LINEAR REGRESSION --- CLOSED-FORM SOLUTION | ||
''' | ||
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def closed_form(X, Y, intercept=False): # functions that computes the Least Squares Estimates | ||
if intercept: | ||
X = np.concatenate((X, np.ones([X.shape[0], 1])), axis=1) | ||
return np.linalg.inv(X.transpose().dot(X)).dot(X.transpose()).dot(Y) | ||
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def mse(X, Y, w): # function that computes the Mean Square Error (MSE) | ||
return np.mean((Y-np.matmul(X, w))**2) | ||
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''' | ||
def closed_form_3d(X,Y): | ||
return np.matmul(np.matmul(np.linalg.inv(np.matmul(X.transpose(0,2,1),X)),X.transpose(0,2,1)),Y) | ||
def lme_stats_3d(X,Y): | ||
#add an intercept | ||
X=np.concatenate((X,np.ones((X.shape[0],X.shape[1],1))),axis=2) | ||
[num_comparisons,num_observations,num_predictors] = X.shape | ||
[num_comparisons,num_observations,num_features] = Y.shape | ||
w=closed_form_3d(X,Y) | ||
residuals = Y-np.matmul(X, w) | ||
MSE = (((residuals)**2).sum(axis=1)/(num_observations-num_predictors)) | ||
var_b = np.expand_dims(MSE, axis=1)*np.expand_dims(np.linalg.inv(np.matmul(X.transpose(0,2,1),X)).diagonal(axis1=1,axis2=2), axis=2) | ||
sd_b = np.sqrt(var_b) # standard error on the Betas | ||
ts_b = w/sd_b # calculate t-values for the Betas | ||
p_values =[2*(1-stats.t.cdf(np.abs(ts_b[:,i,:]),(num_observations-num_predictors))) for i in range(ts_b.shape[1])] # calculate a p-value map for each predictor | ||
return ts_b,p_values,w,residuals | ||
non_nan_idx = (np.isnan(voxelwise_array).sum(axis=(0,1))==0) | ||
# take out the voxels which have null values | ||
X=voxelwise_array[:,:6,non_nan_idx].transpose(2,0,1) | ||
Y=voxelwise_array[:,6:,non_nan_idx].transpose(2,0,1) | ||
ts_b,p_values,w,residuals = lme_stats_3d(X,Y) | ||
x_name=['Somatomotor','Dorsal Comp','DMN', 'Prior Modeling 1', 'Prior Modeling 2', 'Prior Modeling 3'] | ||
y_name=['group','temporal_std','VE_spatial','GS_corr','DVARS_corr','FD_corr'] | ||
fig,axes = plt.subplots(nrows=len(x_name), ncols=len(y_name),figsize=(12*len(y_name),3*len(x_name))) | ||
for i,x_label in zip(range(len(x_name)),x_name): | ||
for j,y_label in zip(range(len(y_name)),y_name): | ||
ax=axes[i,j] | ||
stat_map=np.zeros(voxelwise_array.shape[2]) | ||
stat_map[non_nan_idx]=ts_b[:,j,i] | ||
ax.set_title('T-value of {} on {}'.format(y_label,x_label), fontsize=15) | ||
plot_stat_map(analysis_functions.recover_3D(mask_file,stat_map),bg_img='DSURQE.nii.gz', axes=ax, cut_coords=(0,1,2,3,4,5), display_mode='y') | ||
''' |
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