wehub-resource-sync
157 lines
4.8 KiB
Python
Executable File
157 lines
4.8 KiB
Python
Executable File
import numpy as np
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class PCA(object):
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def __init__(self, n_components):
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"""
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construct principal component analysis
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Parameters
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----------
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n_components : int
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number of components
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"""
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assert isinstance(n_components, int)
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self.n_components = n_components
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def fit(self, X, method="eigen", iter_max=100):
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"""
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maximum likelihood estimate of pca parameters
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x ~ \int_z N(x|Wz+mu,sigma^2)N(z|0,I)dz
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Parameters
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----------
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X : (sample_size, n_features) ndarray
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input data
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method : str
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method to estimate the parameters
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["eigen", "em"]
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iter_max : int
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maximum number of iterations for em algorithm
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Attributes
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----------
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mean : (n_features,) ndarray
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sample mean of the data
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W : (n_features, n_components) ndarray
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projection matrix
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var : float
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variance of observation noise
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C : (n_features, n_features) ndarray
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variance of the marginal dist N(x|mean,C)
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Cinv : (n_features, n_features) ndarray
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precision of the marginal dist N(x|mean, C)
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"""
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method_list = ["eigen", "em"]
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if method not in method_list:
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print("availabel methods are {}".format(method_list))
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self.mean = np.mean(X, axis=0)
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getattr(self, method)(X - self.mean, iter_max)
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def eigen(self, X, *arg):
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sample_size, n_features = X.shape
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if sample_size >= n_features:
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cov = np.cov(X, rowvar=False)
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values, vectors = np.linalg.eigh(cov)
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index = n_features - self.n_components
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else:
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cov = np.cov(X)
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values, vectors = np.linalg.eigh(cov)
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vectors = (X.T @ vectors) / np.sqrt(sample_size * values)
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index = sample_size - self.n_components
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self.I = np.eye(self.n_components)
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if index == 0:
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self.var = 0
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else:
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self.var = np.mean(values[:index])
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self.W = vectors[:, index:].dot(np.sqrt(np.diag(values[index:]) - self.var * self.I))
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self.__M = self.W.T @ self.W + self.var * self.I
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self.C = self.W @ self.W.T + self.var * np.eye(n_features)
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if index == 0:
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self.Cinv = np.linalg.inv(self.C)
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else:
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self.Cinv = np.eye(n_features) / np.sqrt(self.var) - self.W @ np.linalg.inv(self.__M) @ self.W.T / self.var
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def em(self, X, iter_max):
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self.I = np.eye(self.n_components)
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self.W = np.eye(np.size(X, 1), self.n_components)
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self.var = 1.
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for i in range(iter_max):
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W = np.copy(self.W)
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stats = self._expectation(X)
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self._maximization(X, *stats)
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if np.allclose(W, self.W):
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break
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self.C = self.W @ self.W.T + self.var * np.eye(np.size(X, 1))
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self.Cinv = np.linalg.inv(self.C)
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def _expectation(self, X):
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self.__M = self.W.T @ self.W + self.var * self.I
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Minv = np.linalg.inv(self.__M)
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Ez = X @ self.W @ Minv
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Ezz = self.var * Minv + Ez[:, :, None] * Ez[:, None, :]
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return Ez, Ezz
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def _maximization(self, X, Ez, Ezz):
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self.W = X.T @ Ez @ np.linalg.inv(np.sum(Ezz, axis=0))
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self.var = np.mean(
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np.mean(X ** 2, axis=1)
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- 2 * np.mean(Ez @ self.W.T * X, axis=1)
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+ np.trace((Ezz @ self.W.T @ self.W).T) / np.size(X, 1))
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def transform(self, X):
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"""
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project input data into latent space
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p(Z|X) = N(Z|(X-mu)WMinv, sigma^-2M)
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Parameters
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----------
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X : (sample_size, n_features) ndarray
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input data
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Returns
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-------
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Z : (sample_size, n_components) ndarray
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projected input data
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"""
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return np.linalg.solve(self.__M, ((X - self.mean) @ self.W).T).T
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def fit_transform(self, X, method="eigen"):
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"""
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perform pca and whiten the input data
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Parameters
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----------
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X : (sample_size, n_features) ndarray
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input data
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Returns
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-------
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Z : (sample_size, n_components) ndarray
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projected input data
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"""
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self.fit(X, method)
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return self.transform(X)
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def proba(self, X):
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"""
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the marginal distribution of the observed variable
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Parameters
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----------
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X : (sample_size, n_features) ndarray
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input data
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Returns
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-------
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p : (sample_size,) ndarray
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value of the marginal distribution
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"""
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d = X - self.mean
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return (
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np.exp(-0.5 * np.sum(d @ self.Cinv * d, axis=-1))
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/ np.sqrt(np.linalg.det(self.C))
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/ np.power(2 * np.pi, 0.5 * np.size(X, 1)))
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