class DiscriminantAnalysisModel(Classifier):
"""Model using LDA or GDA (linear discriminant analysis/ quadratic
discriminant analysis).
LDA is a classifier with a linear decision boundary, generated by
fitting class conditional densities to the data and using Bayes’ rule.
The model fits a Gaussian density to each class, assuming that all
classes share the same covariance matrix.
The fitted model can also be used to reduce the dimensionality of the input
by projecting it to the most discriminative directions.
Shrinkage is a tool to improve estimation of covariance matrices in
situations where the number of training samples is small compared to the
number of features. In this scenario, the empirical sample covariance is a poor estimator.
QDA is a classifier with a quadratic decision boundary, also generated by
fitting class conditional densities to the data and using Bayes’ rule.
"""
# WRITE DOCUMENTATION
def __init__(self,
type='lda',
solver='svd',
shrinkage=None,
reg_param=0.0,
ranking_size=30):
"""
"""
if type == 'lda':
self.solver = solver
self.shrinkage = shrinkage
self.clf = LinearDiscriminantAnalysis(solver=solver,
shrinkage=shrinkage)
elif type == 'qda':
self.reg_param = reg_param
self.clf = QuadraticDiscriminantAnalysis(reg_param=reg_param)
else:
raise Exception(f"Unknown type of discriminant analysis: '{type}'")
self.type = type
self.ranking_size = ranking_size
def transform(self, X):
"""Reduce the dimensionality of the input
by projecting it to the most discriminative directions.
"""
return self.clf.transform(X)
spikes.times, spikes.clusters, times)
trial_blocks = (trials.probabilityLeft[((
(trials.probabilityLeft > 0.55)
| (trials.probabilityLeft < 0.45)))] > 0.55).astype(int)
# Transform to LDA with leave-one-out cross validation
print(
'Projecting to LDA axis with leave-one-out cross-validation [%d of %d]'
% (i + 1, sessions.shape[0]))
resp = np.rot90(spike_counts)
loo = LeaveOneOut()
qda_transform = np.zeros(resp.shape[0])
for train_index, test_index in loo.split(resp):
qda = QDA()
qda.fit(resp[train_index], trial_blocks[train_index])
qda_transform[test_index] = np.rot90(qda.transform(
resp[test_index]))[0]
qda_convolve = np.convolve(qda_transform,
np.ones((10, )) / 10,
mode='same')
# Plot
fig, ax1 = plt.subplots(1, 1, figsize=(12, 8))
sns.set(style="ticks", context="paper", font_scale=2)
ax1.plot(np.arange(1, trial_times.shape[0] + 1),
qda_transform,
color=[0.6, 0.6, 0.6])
ax1.plot(np.arange(1, trial_times.shape[0] + 1), qda_convolve, 'k', lw=3)
ax1.set_ylabel('Position along LDA axis')
ax1.set(ylim=[-6, 6])
ax2 = ax1.twinx()
ax2.plot(np.arange(1, trial_times.shape[0] + 1),
