Methods for decoding neural population activity and analyzing latent dynamics. Covers dimensionality reduction, manifold analysis, and decoding algorithms. Activation: neural decoding, population coding, manifold, latent dynamics, dimensionality reduction.
Neural population decoding extracts information from collective activity of neuron ensembles. This skill covers dimensionality reduction, manifold identification, and decoding algorithms.
Information distributed across many neurons:
High-dimensional neural activity lives on low-dimensional manifolds.
import numpy as np
from scipy.stats import zscore
def preprocess_spikes(spike_times, bin_size=0.02):
"""Preprocess spike data for population analysis."""
all_spikes = np.concatenate(spike_times)
t_min, t_max = all_spikes.min(), all_spikes.max()
bins = np.arange(t_min, t_max + bin_size, bin_size)
n_neurons = len(spike_times)
n_bins = len(bins) - 1
rates = np.zeros((n_bins, n_neurons))
for i, spikes in enumerate(spike_times):
counts, _ = np.histogram(spikes, bins=bins)
rates[:, i] = counts / bin_size
rates = zscore(rates, axis=0, nan_policy='omit')
return rates
from sklearn.decomposition import PCA
def apply_pca(rates, n_components=10):
"""Apply PCA to neural population activity."""
pca = PCA(n_components=n_components)
projected = pca.fit_transform(rates)
return pca, projected, pca.explained_variance_ratio_
class KalmanFilterDecoder:
"""Kalman filter for neural decoding."""
def __init__(self):
self.A = None
self.C = None
def fit(self, rates, kinematics):
"""Fit Kalman filter parameters."""
self.C = np.linalg.lstsq(kinematics, rates, rcond=None)[0].T
x_prev = kinematics[:-1]
x_next = kinematics[1:]
self.A = np.linalg.lstsq(x_prev, x_next, rcond=None)[0]
def decode(self, rates):
"""Decode kinematics using Kalman filtering."""
n_time = rates.shape[0]
n_dims = self.A.shape[0]
states = np.zeros((n_time, n_dims))
for t in range(1, n_time):
x_pred = self.A @ states[t-1]
K = np.linalg.solve(self.C @ self.C.T, self.C)
states[t] = x_pred + K @ (rates[t] - self.C @ x_pred)
return states
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