def _initialize_with_pca(self,
datas,
inputs=None,
masks=None,
tags=None,
num_iters=20):
Keff = 1 if self.single_subspace else self.K
# First solve a linear regression for data given input
if self.M > 0:
from sklearn.linear_model import LinearRegression
lr = LinearRegression(fit_intercept=False)
lr.fit(np.vstack(inputs), np.vstack(datas))
self.Fs = np.tile(lr.coef_[None, :, :], (Keff, 1, 1))
# Compute residual after accounting for input
resids = [
data - np.dot(input, self.Fs[0].T)
for data, input in zip(datas, inputs)
]
# Run PCA to get a linear embedding of the data
pca, xs, ll = pca_with_imputation(self.D,
resids,
masks,
num_iters=num_iters)
self.Cs = np.tile(pca.components_.T[None, :, :], (Keff, 1, 1))
self.ds = np.tile(pca.mean_[None, :], (Keff, 1))
return pca
def _initialize_with_pca(self, datas, masks, num_iters=20):
pca, xs = pca_with_imputation(self.D, datas, masks, num_iters=num_iters)
Keff = 1 if self.single_subspace else self.K
self.Cs = np.tile(pca.components_.T[None, :, :], (Keff, 1, 1))
self.ds = np.tile(pca.mean_[None, :], (Keff, 1))
return pca
def _initialize_with_pca(self,
datas,
inputs=None,
masks=None,
tags=None,
num_iters=20):
Keff = 1 if self.single_subspace else self.K
# First solve a linear regression for data given input
if self.M > 0:
from sklearn.linear_model import LinearRegression
lr = LinearRegression(fit_intercept=False)
lr.fit(np.vstack(inputs), np.vstack(datas))
self.Fs = np.tile(lr.coef_[None, :, :], (Keff, 1, 1))
# Compute residual after accounting for input
resids = [
data - np.dot(input, self.Fs[0].T)
for data, input in zip(datas, inputs)
]
# Run PCA to get a linear embedding of the data with the maximum effective dimension
pca, xs, ll = pca_with_imputation(min(self.D * Keff, self.N),
resids,
masks,
num_iters=num_iters)
# Assign each state a random projection of these dimensions
Cs, ds = [], []
for k in range(Keff):
weights = npr.randn(self.D, self.D * Keff)
weights = np.linalg.svd(weights, full_matrices=False)[2]
Cs.append((weights @ pca.components_).T)
ds.append(pca.mean_)
# Find the components with the largest power
self.Cs = np.array(Cs)
self.ds = np.array(ds)
return pca
os.chdir("/Users/scott/Projects/zimmer")
ys, masks, z_trues, z_key, neuron_names = load_kato_data(include_unnamed=False,
signal="dff")
os.chdir(tmp)
# Preprocess the worm data
ys = [trend_filter(y) for y in ys]
K_true = len(z_key)
N = ys[0].shape[1]
W = len(ys)
Ts = [y.shape[0] for y in ys]
# Run factor analysis to get low dimensional continuous states
D = 10
pca, xs, lls = pca_with_imputation(D, ys, masks, num_iters=20)
# # Fit a MoG to one of the worms
# In[5]:
x = xs[-1]
# In[6]:
plt.plot(x[:, 0], x[:, 1])
# In[7]:
mog = MixtureOfGaussians(100, D)
mog.fit(x)