def _init_random_gaussians(self, X):
n_samples = np.shape(X)[0]
self.priors = (1/self.k) * np.ones(self.k)
for i in range(self.k):
params = {}
params["mean"] = X[np.random.choice(range(n_samples))]
params["cov"] = calculate_covariance_matrix(X)
self.parameters.append(params)
def _init_random_gaussians(self, X):
n_samples = np.shape(X)[0]
self.priors = (1 / self.k) * np.ones(self.k)
for i in range(self.k):
params = {}
params["mean"] = X[np.random.choice(range(n_samples))]
params["cov"] = calculate_covariance_matrix(X)
self.parameters.append(params)
def fit(self, X, y):
# Separate data by class
X1 = X[y == 0]
X2 = X[y == 1]
# Calculate the covariance matrices of the two datasets
cov1 = calculate_covariance_matrix(X1)
cov2 = calculate_covariance_matrix(X2)
cov_tot = cov1 + cov2
# Calculate the mean of the two datasets
mean1 = X1.mean(0)
mean2 = X2.mean(0)
mean_diff = np.atleast_1d(mean1 - mean2)
# Determine the vector which when X is projected onto it best separates the
# data by class. w = (mean1 - mean2) / (cov1 + cov2)
self.w = np.linalg.pinv(cov_tot).dot(mean_diff)
def fit(self, X, y):
# Separate data by class
X1 = X[y == 0]
X2 = X[y == 1]
# Calculate the covariance matrices of the two datasets
cov1 = calculate_covariance_matrix(X1)
cov2 = calculate_covariance_matrix(X2)
cov_tot = cov1 + cov2
# Calculate the mean of the two datasets
mean1 = X1.mean(0)
mean2 = X2.mean(0)
mean_diff = np.atleast_1d(mean1 - mean2)
# Determine the vector which when X is projected onto it best separates the
# data by class. w = (mean1 - mean2) / (cov1 + cov2)
self.w = np.linalg.pinv(cov_tot).dot(mean_diff)
def _transform(self, X, dim):
covariance = calculate_covariance_matrix(X)
eigenvalues, eigenvectors = np.linalg.eig(covariance)
# Sort eigenvalues and eigenvector by largest eigenvalues
idx = eigenvalues.argsort()[::-1]
eigenvalues = eigenvalues[idx][:dim]
eigenvectors = np.atleast_1d(eigenvectors[:, idx])[:, :dim]
# Project the data onto principal components
X_transformed = X.dot(eigenvectors)
return X_transformed
def transform(slef, X, n_components):
covariance = calculate_covariance_matrix(X)
eigenvalues, eigenvectors = np.linalg.eig(covariance)
print(np.diag(eigenvalues))
print(eigenvectors * covariance * eigenvectors.T)
idx = eigenvalues.argsort()[::-1]
# sort the eigenvalue, pick the the n_components latgest eigenvalues.
eigenvalues = eigenvalues[idx][:n_components]
eigenvectors = np.atleast_1d(eigenvectors[:, idx])[:, :n_components]
X_transformed = X.dot(eigenvectors)
return X_transformed
def transform(self, X, n_components):
covariance = calculate_covariance_matrix(X)
# Get the eigenvalues and eigenvectors.
# (eigenvector[:,0] corresponds to eigenvalue[0])
eigenvalues, eigenvectors = np.linalg.eig(covariance)
# Sort the eigenvalues and corresponding eigenvectors from largest
# to smallest eigenvalue and select the first n_components
idx = eigenvalues.argsort()[::-1]
eigenvalues = eigenvalues[idx][:n_components]
eigenvectors = np.atleast_1d(eigenvectors[:, idx])[:, :n_components]
# Project the data onto principal components
X_transformed = X.dot(eigenvectors)
return X_transformed
def transform(self, X, n_components):
covariance = calculate_covariance_matrix(X)
# Get the eigenvalues and eigenvectors.
# (eigenvector[:,0] corresponds to eigenvalue[0])
eigenvalues, eigenvectors = np.linalg.eig(covariance)
# Sort the eigenvalues and corresponding eigenvectors from largest
# to smallest eigenvalue and select the first n_components
idx = eigenvalues.argsort()[::-1]
eigenvalues = eigenvalues[idx][:n_components]
eigenvectors = np.atleast_1d(eigenvectors[:, idx])[:, :n_components]
# Project the data onto principal components
X_transformed = X.dot(eigenvectors)
return X_transformed
def _calculate_scatter_matrices(self, X, y):
n_features = np.shape(X)[1]
labels = np.unique(y)
# Within class scatter matrix:
# SW = sum{ (X_for_class - mean_of_X_for_class)^2 }
SW = np.empty((n_features, n_features))
for label in labels:
_X = X[y == label]
SW += (len(_X) - 1) * calculate_covariance_matrix(_X)
# Between class scatter:
# SB = sum{ n_samples_for_class * (mean_for_class - total_mean)^2 }
total_mean = np.mean(X, axis=0)
SB = np.empty((n_features, n_features))
for label in labels:
_X = X[y == label]
_mean = np.mean(_X, axis=0)
SB += len(_X) * (_mean - total_mean).dot((_mean - total_mean).T)
return SW, SB
def _calculate_scatter_matrices(self, X, y):
n_features = np.shape(X)[1]
labels = np.unique(y)
# Within class scatter matrix:
# SW = sum{ (X_for_class - mean_of_X_for_class)^2 }
SW = np.empty((n_features, n_features))
for label in labels:
_X = X[y == label]
SW += (len(_X) - 1) * calculate_covariance_matrix(_X)
# Between class scatter:
# SB = sum{ n_samples_for_class * (mean_for_class - total_mean)^2 }
total_mean = np.mean(X, axis=0)
SB = np.empty((n_features, n_features))
for label in labels:
_X = X[y == label]
_mean = np.mean(_X, axis=0)
SB += len(_X) * (_mean - total_mean).dot((_mean - total_mean).T)
return SW, SB
def get_covariance(self, X):
# Calculate the covariance matrix for the data
covariance = calculate_covariance_matrix(X)
return covariance
# Import helper functions dir_path = os.path.dirname(os.path.realpath(__file__)) sys.path.insert(0, dir_path + "/../utils") from data_operation import calculate_covariance_matrix, calculate_correlation_matrix from data_manipulation import normalize # Load dataset and only use the two first classes data = datasets.load_iris() X = normalize(data.data[data.target < 2]) y = data.target[data.target < 2] X1 = X[y == 0] X2 = X[y == 1] # Calculate the covariances of the two class distributions cov1 = calculate_covariance_matrix(X1) cov2 = calculate_covariance_matrix(X2) cov_tot = cov1 + cov2 # Get the means of the two class distributions mean1 = X1.mean(0) mean2 = X2.mean(0) mean_diff = np.atleast_1d(mean1 - mean2) # Calculate w as (x1_mean - x2_mean) / (cov1 + cov2) w = np.linalg.pinv(cov_tot).dot(mean_diff) # Project X onto w x1 = X.dot(w) x2 = X.dot(w)
def get_covariance(self, X):
# Calculate the covariance matrix for the data
covariance = calculate_covariance_matrix(X)
return covariance
# Import helper functions dir_path = os.path.dirname(os.path.realpath(__file__)) sys.path.insert(0, dir_path + "/../utils") from data_operation import calculate_covariance_matrix, calculate_correlation_matrix from data_manipulation import normalize # Load dataset and only use the two first classes data = datasets.load_iris() X = normalize(data.data[data.target < 2]) y = data.target[data.target < 2] X1 = X[y == 0] X2 = X[y == 1] # Calculate the covariances of the two class distributions cov1 = calculate_covariance_matrix(X1) cov2 = calculate_covariance_matrix(X2) cov_tot = cov1 + cov2 # Get the means of the two class distributions mean1 = X1.mean(0) mean2 = X2.mean(0) mean_diff = np.atleast_1d(mean1 - mean2) # Calculate w as (x1_mean - x2_mean) / (cov1 + cov2) w = np.linalg.pinv(cov_tot).dot(mean_diff) # Project X onto w x1 = X.dot(w) x2 = X.dot(w)
