def plot_training_ex(X, Y_act, Y_pred, plot_title, axh=None):
"""Plot input/output data for flip-flop model."""
# Create figure if an axis handle is not provided
if axh is None:
fh, axh = pt.create_subplot(n_row=1, n_col=1)
axh = axh[0]
else:
fh = None
# Set axis labels
axh.set_xlabel('Timestep')
axh.set_ylabel('Input/Output')
axh.set_title(plot_title)
# Loop over input/output pairs and plot
n_ex = X.shape[0]
for i in range(n_ex):
x = X[i, :]
y_act = Y_act[i, :]
y_pred = Y_pred[i, :]
# Scale y-axis values to be between i - .4 and i + .4
x = (x * 0.4) + i + 1
y_act = (y_act * 0.4) + i + 1
y_pred = (y_pred * 0.4) + i + 1
axh.plot(x, color='black')
axh.plot(y_act, color='red')
axh.plot(y_pred, color='orange')
axh.set_yticks(np.arange(n_ex) + 1)
return fh
def calc_movement_onset(df):
import numpy as np
import plottools as pt
import matplotlib as mpl
mpl.use('PDF')
import matplotlib.pyplot as plt
import copy
# Define speed threshold used for movement onset
s_thresh = 0.2
# Create figure
ax_hndl = pt.create_subplot(1, 1)
# Iterate over trials and calculate speed
n_trials = df.shape[0]
s_all = []
onset_idx = []
for i in range(n_trials):
# Get velocity, time, calculate speed
v = df['vel'][i][0:2, :]
t = df['time'][i]
s = np.sqrt(np.sum(v**2, 0))
# First get timing events -- trajectory onset/offset
traj_onset = df['trajectoryOnset'][i]
traj_offset = df['trajectoryOffset'][i]
# Get time of max speed. Find this between trajectory onset and offset
s_temp = copy.copy(s) # Create a copy of s
s_temp[
t <
traj_onset] = 0 # zero out all speeds pre-trajectory onset (movement onset can't occur here)
s_temp[
t >
traj_offset] = 0 # also zero-out all speeds post-trajectory offset
max_ind = np.argmax(s_temp) # Index corresponding to the max speed
s_max = s[max_ind]
t_max = t[max_ind]
# Define masks used to find movement onset
s_mask = s < (s_max * s_thresh) # All speeds less than the threshold
t_onset_mask = t > traj_onset
t_max_mask = t < t_max
mask = s_mask & t_onset_mask & t_max_mask # All time points after trajectory onset but before max speed
valid_idx = np.nonzero(
mask) # Get list of valid indices (speeds less than the threshold)
onset_idx.append(
valid_idx[0][-1] + 1
) # Movement onset will be the first time point after the last non-zero value
# Add speed to list
s_all.append(s)
# Add movement onset and speed to dataframe
df['speed'] = s_all
df['onset_idx'] = onset_idx
return None
def plot_history(history, axh=None):
"""Plot model training history."""
# Create figure if an axis handle is not provided
if axh is None:
fh, axh = pt.create_subplot(n_row=1, n_col=1)
axh = axh[0]
else:
fh = None
# Plot training error and validation error
loss_h, = axh.plot(history.history['loss'])
val_loss_h, = axh.plot(history.history['val_loss'])
# Add axis labels and legend
axh.set_xlabel('Epoch')
axh.set_ylabel('MSE')
axh.legend((loss_h, val_loss_h), ('Training error', 'Validation error'))
axh.set_title('Training history')
return fh
def plot_speed_profile(df):
import numpy as np
import plottools as pt
import matplotlib as mpl
mpl.use('PDF')
import matplotlib.pyplot as plt
import copy
# Create figure
ax_hndl = pt.create_subplot(1, 1)
# Iterate over trials and calculate speed
n_trials = df.shape[0]
s_all = []
for i in range(n_trials):
# Get time, speed
t = df['time'][i]
s = df['speed'][i]
# Align time so t=0 occurs at movement onset
onset_idx = df['onset_idx'][i]
t = t - t[onset_idx]
# Plot trajectory
plt.plot(t, s, 'k')
plt.plot(t[onset_idx], s[onset_idx], 'ko')
# Format figure
plt.xlim([-500, 1000])
plt.xlabel('Time (ms)')
plt.ylabel('Speed')
plt.suptitle('Reach speed')
# Save figure
fig_name = 'SpeedProfile'
plt.savefig('results/{}.pdf'.format(fig_name))
return None
mpl.use('PDF')
mpl.rcParams['font.sans-serif'] = ['Helvetica']
mpl.rcParams['pdf.fonttype'] = 42
mpl.rcParams['ps.fonttype'] = 42
# Create some data to plot
x = np.linspace(-1.0, 1.0, 100)
y = x**2
# Sample data
x_samp = np.random.uniform(-1.0, 1.0, 1000)
e_samp = np.random.normal(0, 0.05, 1000)
y_samp = x_samp**2 + e_samp
# Create subplots
ax_hndl = pt.create_subplot(1, 2)
# Set first axis to be active
plot_no = 0
plt.sca(ax_hndl[plot_no])
# Plot -- scatter-style plot without a line
plt.plot(x_samp,
y_samp,
color=[0.75, 0.75, 0.75],
marker='o',
linestyle='None')
# Plot -- basic line with markers
plt.plot(x, y, color='k', linewidth=2)
# Format plot
def pca_analysis(model, X):
"""Run PCA analysis on model to visualize hidden layer activity.
To get the values of the intermediate layer, a new model needs to be
created. This model takes the normal input from the RNN, and returns the
output of the rnn layer. The values of the hidden layer can then be found
using the 'predict()' method.
"""
# --- Get hidden layer activations and run PCA ---
# Create new model and predict input
inputs = model.input
outputs = [model.layers[0].output, model.layers[1].output]
act_model = tf.keras.Model(inputs=inputs, outputs=outputs)
activations = act_model.predict(X)
# Format activations into dimensions x observations
# Input dimensions: (obs x time x units)
n_inputs = X.shape[2]
n_rnn = activations[0].shape[2]
A = np.transpose(activations[0], (2, 0, 1)) # Now (units x obs x time)
Y = np.transpose(activations[1], (2, 0, 1))
A = A.reshape((n_rnn, -1), order='C') # Now (units x (obs*time))
Y = Y.reshape((n_inputs, -1), order='C')
# Run PCA (note that this is actually PPCA)
from sklearn.decomposition import PCA
pca = PCA(n_components=20)
pca.fit(A.T)
Z = pca.transform(A.T)
# --- Plot results ---
# Create colormap for points. Use an RGB map of the output
color = np.copy(Y.T)
color[color < -1] = -1
color[color > 1] = 1
color = (color + 1) / 2 # Colors must be between 0 and 1
# Figure 1: Variance explained and 2D projections
# Setup figure
fh, ax_h = pt.create_subplot(n_row=1, n_col=4)
# Subplot 1: Plot fraction of variance explained
idx = 0
dims = np.arange(pca.n_components_) + 1
ax_h[idx].plot(dims, pca.explained_variance_ratio_, color='k', marker='.')
ax_h[idx].set_xlabel('PCA dim.')
ax_h[idx].set_ylabel('Fraction of variance explained')
ax_h[idx].set_title('Fraction of variance explained')
# Subplots 2-4: 2D projections
# Iterate over dimensions and plot
plot_dim = [[0, 1], [0, 2], [1, 2]]
for ax, d in zip(ax_h[1:4], plot_dim):
ax.scatter(Z[:, d[0]], Z[:, d[1]], marker='.', c=color)
ax.set_xlabel('PC {}'.format(d[0] + 1))
ax.set_ylabel('PC {}'.format(d[1] + 1))
ax.set_title('Dim {} vs Dim {}'.format(d[0] + 1, d[1] + 1))
# Save figure
fh.savefig('results/FlipFlopRNN_{}.pdf'.format('PCA'))
# Figure 2: 3d representation
# Note that this needs to be done separately from the above plots
# because a separate argument is required when creating a subplot
# for a 3d plot
# This import registers the 3D projection, but is otherwise unused.
from mpl_toolkits.mplot3d import Axes3D # noqa: F401 unused import
# Create figure
fh = plt.figure()
ax = fh.add_subplot(111, projection='3d')
# Plot
ax.scatter(Z[:, 0], Z[:, 1], Z[:, 2], marker='o', c=color)
ax.set_xlabel('PC 1')
ax.set_ylabel('PC 2')
ax.set_zlabel('PC 3')
ax.set_title('Top 3 PCs')
# Save figure
fh.savefig('results/FlipFlopRNN_{}.pdf'.format('PCA_3D'))
return None
def pca_analysis(model, data):
"""Run PCA analysis on model to visualize hidden layer activity.
To get the values of the intermediate layer, a new model needs to be
created. This model takes the normal input from the RNN, and returns the
output of the rnn layer. The values of the hidden layer can then be found
using the 'predict()' method.
"""
# Unpack train data dict
X = data['X']
Y = data['Y']
# --- Get hidden layer activations and run PCA ---
# Create new model and predict input
inputs = model.input
outputs = [model.layers[0].output, model.layers[1].output]
act_model = tf.keras.Model(inputs=inputs, outputs=outputs)
activations = act_model.predict(X)
# Format activations into dimensions x observations
# Input dimensions: (obs x time x units)
n_inputs = X.shape[2]
n_obs = X.shape[0]
n_ts = X.shape[1]
n_rnn = activations[0].shape[2]
A = np.transpose(activations[0], (2, 0, 1)) # Now (units x obs x time)
Y = np.transpose(activations[1], (2, 0, 1))
A = A.reshape((n_rnn, -1), order='C') # Now (units x (obs*time))
Y = Y.reshape((n_inputs, -1), order='C')
# Run PCA (note that this is actually PPCA)
from sklearn.decomposition import PCA
n_pcs = 20
pca = PCA(n_components=n_pcs)
pca.fit(A.T)
# --- Figure 1: Variance explained ---
# Setup figure
fh, ax_h = pt.create_subplot(n_row=1, n_col=1)
# Plot fraction of variance explained
idx = 0
dims = np.arange(pca.n_components_) + 1
ax_h[idx].plot(dims, pca.explained_variance_ratio_, color='k', marker='.')
ax_h[idx].set_xlabel('PCA dim.')
ax_h[idx].set_ylabel('Fraction of variance explained')
ax_h[idx].set_title('Fraction of variance explained')
fig_name = 'FracVarExplained'
fh.savefig('./results/BCISimulation_PCAResults_{}.pdf'.format(fig_name))
# --- Figure 2: 2D projections of the PCA representation ---
# Setup figure. Define dimensions to plot
plot_dim = [[0, 1], [0, 2], [1, 2], [2, 3]]
n_row = 2
n_col = len(plot_dim)
fh, ax_h = pt.create_subplot(n_row=n_row, n_col=n_col)
# Find indices of specific trials to plot. Here we want to focus on a
# pair of diametrically-opposed targets (0 and 180 degrees)
start_pos = X[:, 0, :]
start_ang = np.rad2deg(np.arctan2(start_pos[:, 1], start_pos[:, 0]))
mask = start_ang < 0
start_ang[mask] = start_ang[mask] + 360
targ_ang = [0, 180]
targ_idx = [np.argmin(np.abs(start_ang - ang)) for ang in targ_ang]
# Iterate over trials
Z = np.zeros((n_obs, n_ts, n_pcs))
n_samp = np.zeros((n_obs), dtype=int)
for i in range(n_obs):
# Get data from current trial and find PCA representation
A_trial = activations[0][i, :, :]
Z_trial = pca.transform(A_trial)
Z[i, :, :] = Z_trial
# Limit to valid portion of the trajectory
Z_trial = Z_trial[data['onset'][i]:data['offset'][i]]
n_samp[i] = Z_trial.shape[0]
# Iterate over dimensions and plot
for ax, d in zip(ax_h[0:n_col], plot_dim):
plot_trajectory(Z_trial[:, d].T, X[i, 0, :], ax)
# If trial is to be highlighted, plot in a separate set of axes
if i in targ_idx:
for ax, d in zip(ax_h[n_col:], plot_dim):
plot_trajectory(Z_trial[:, d].T, X[i, 0, :], ax)
# Set axis labels
for ax, d in zip(ax_h, plot_dim * 2):
ax.set_xlabel('PC {}'.format(d[0] + 1))
ax.set_ylabel('PC {}'.format(d[1] + 1))
ax.set_title('Dim {} vs Dim {}'.format(d[0] + 1, d[1] + 1))
# Save figure
fig_name = '2DProj'
fh.savefig('./results/BCISimulation_PCAResults_{}.pdf'.format(fig_name))
# --- Figure 3: Linear mapping of PCA representation ---
# Get data to fit linear model
n_samp_all = np.sum(n_samp)
Z_mat = np.zeros((n_samp_all, n_pcs))
Y_mat = np.zeros((n_samp_all, n_inputs))
ctr = 0
for i in range(n_obs):
onset_idx = np.arange(data['onset'][i], data['offset'][i])
ctr_idx = np.arange(ctr, (ctr + len(onset_idx)))
Z_mat[ctr_idx, :] = Z[i, onset_idx, :]
Y_mat[ctr_idx, :] = data['Y'][i, onset_idx, :]
ctr = ctr_idx[-1] + 1
# Fit linear model -- do this independently for the X and Y dimensions
from sklearn import linear_model
reg_mdl = linear_model.LinearRegression(fit_intercept=False)
reg_mdl.fit(Z_mat, Y_mat)
r2 = reg_mdl.score(Z_mat, Y_mat)
print('Linear fit: r2 = {}'.format(r2))
W = reg_mdl.coef_
# Plot predicted trajectories
fh, ax_h = pt.create_subplot(n_row=1, n_col=1)
for i in range(n_obs):
# Predict cursor position from hidden unit activity
Z_temp = Z[i, data['onset'][i]:data['offset'][i], :]
y_pred = Z_temp @ W.T
y_pred = reg_mdl.predict(Z_temp)
plot_trajectory(y_pred.T, data['X'][i, 0, :], ax_h[0])
# Format plot axes
ax_h[0].set_title('Linear model - predicted trajectories')
ax_h[0].set_xlabel('X position')
ax_h[0].set_ylabel('Y position')
# Save figure
fig_name = 'LinearMapping'
fh.savefig('./results/BCISimulation_PCAResults_{}.pdf'.format(fig_name))
return None