def _init_random_gaussians(self, X):
""" Initialize gaussian randomly """
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 _transform(self, X, dim):
covariance = calculate_covariance_matrix(X)
eigenvalues, eigenvectors = np.linalg.eig(covariance)
#sort eigenvalues and eiganvector 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 = np.dot(X, eigenvectors)
return X_transformed
def fit(self,X, y):
#separate data by class
X1 = X[y==0]
X2 = X[y==1]
#calcualte 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 its 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):
# 将数据集分两类
X1 = X[y == 0]
X2 = X[y == 1]
# 计算各分类的散列矩阵
X1_conv_mat = calculate_covariance_matrix(X1)
X2_conf_mat = calculate_covariance_matrix(X2)
# 散列矩阵
SW = X1_conv_mat + X2_conf_mat
# 均值
X1_mean = X1.mean(0)
X2_mean = X2.mean(0)
diff_mean = np.atleast_1d(X1_mean - X2_mean)
# 最佳方向w : w = SW的逆矩阵 * (diff_mean)
self.w = np.linalg.pinv(SW).dot(diff_mean).dot(diff_mean)
def transform(self, X, n_components):
""" Fit the dataset to the number of principal components specified in the
constructor and return the transformed dataset """
covariance_matrix = calculate_covariance_matrix(X)
# Where (eigenvector[:,0] corresponds to eigenvalue[0])
eigenvalues, eigenvectors = np.linalg.eig(covariance_matrix)
# 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 component
X_transformed = X.dot(eigenvectors)
return X_transformed
def init_random_gaussians(self, X):
"""
随机初始化高斯分布
Parameters
----------
X : np.array
"""
# 样本数量
n_samples = np.shape(X)[0]
# 先验概率
self.priors = (1 / self.k) * np.ones(self.k)
for i in range(self.k):
params = {}
# np.random.choice() 从给定的一维数据生成随机样本
params['mean'] = X[np.random.choice(range(n_samples))]
params['cov'] = calculate_covariance_matrix(X)
self.parameters.append(params)
def _calculate_scatter_matrix(self, X, y):
# 计算SW
n_features = np.shape(X)[1]
n_class = np.unique(y)
SW = np.empty((n_features, n_features))
for _class in n_class:
class_X = X[y == _class]
SW += calculate_covariance_matrix(class_X)
SB = np.empty(n_features, n_features)
tatol_mean = np.mean(X, axis=0)
for _class in n_class:
class_X = X[y == _class]
class_mean = np.mean(class_X, axis=0)
SB += len(class_X) * (class_mean - tatol_mean)
return SW, SB
def transform(self,X,n_components): """ fit dataset to principal_components and return transformed dataset """ ## get eigen vals and vectors from covar matrix covariance_matrix = calculate_covariance_matrix(X) eigenvalues , eigenvectors = np.linalg.eig(covariance_matrix) ## sort eigenvalues to get largest idx = eigenvalues.argsort()[::-1] eigenvalues = eigenvalues[idx][:n_components] eigenvectors = np.atleast_1d(eigenvectors[]:,idx)[:n_components] ## project data onto principal components X_transformed = X.dot(eigenvectors) return X_transformed