def compute(self, X, y):
# build the column matrix
XC = as_column_matrix(X)
y = np.asarray(y)
# set a valid number of components
if self._num_components <= 0 or (self._num_components > XC.shape[1] - 1):
self._num_components = XC.shape[1] - 1
# center dataset
self._mean = XC.mean(axis=1).reshape(-1, 1)
XC = XC - self._mean
# perform an economy size decomposition (may still allocate too much memory for computation)
self._eigenvectors, self._eigenvalues, variances = np.linalg.svd(XC, full_matrices=False)
# sort eigenvectors by eigenvalues in descending order
idx = np.argsort(-self._eigenvalues)
self._eigenvalues, self._eigenvectors = self._eigenvalues[idx], self._eigenvectors[:, idx]
# use only num_components
self._eigenvectors = self._eigenvectors[0:, 0:self._num_components].copy()
self._eigenvalues = self._eigenvalues[0:self._num_components].copy()
# finally turn singular values into eigenvalues
self._eigenvalues = np.power(self._eigenvalues, 2) / XC.shape[1]
# get the features from the given data
features = []
for x in X:
xp = self.project(x.reshape(-1, 1))
features.append(xp)
return features
def compute(self, X, y):
# turn into numpy representation
Xc = as_column_matrix(X)
y = np.asarray(y)
# gather some statistics about the dataset
n = len(y)
c = len(np.unique(y))
# define features to be extracted
pca = PCA(num_components=(n - c))
lda = LDA(num_components=self._num_components)
# fisherfaces are a chained feature of PCA followed by LDA
model = ChainOperator(pca, lda)
# computing the chained model then calculates both decompositions
model.compute(X, y)
# store eigenvalues and number of components used
self._eigenvalues = lda.eigenvalues
self._num_components = lda.num_components
# compute the new eigenspace as pca.eigenvectors*lda.eigenvectors
self._eigenvectors = np.dot(pca.eigenvectors, lda.eigenvectors)
# finally compute the features (these are the Fisherfaces)
features = []
for x in X:
xp = self.project(x.reshape(-1, 1))
features.append(xp)
return features
def compute(self, X, y):
XC = as_column_matrix(X)
self._mean = XC.mean()
self._std = XC.std()
Xp = []
for xi in X:
Xp.append(self.extract(xi))
return Xp
def compute(self, X, y):
Xp = []
XC = as_column_matrix(X)
self._min = np.min(XC)
self._max = np.max(XC)
for xi in X:
Xp.append(self.extract(xi))
return Xp
def compute(self, X, y):
XC = as_column_matrix(X)
self._mean = XC.mean()
self._std = XC.std()
Xp = []
for xi in X:
Xp.append(self.extract(xi))
return Xp
def compute(self, X, y):
Xp = []
XC = as_column_matrix(X)
self._min = np.min(XC)
self._max = np.max(XC)
for xi in X:
Xp.append(self.extract(xi))
return Xp
def compute(self, X, y):
# build the column matrix
XC = as_column_matrix(X)
y = np.asarray(y)
# calculate dimensions
d = XC.shape[0]
c = len(np.unique(y))
# set a valid number of components
if self._num_components <= 0:
self._num_components = c - 1
elif self._num_components > (c - 1):
self._num_components = c - 1
# calculate total mean
meanTotal = XC.mean(axis=1).reshape(-1, 1)
# calculate the within and between scatter matrices
Sw = np.zeros((d, d), dtype=np.float32)
Sb = np.zeros((d, d), dtype=np.float32)
for i in range(0, c):
Xi = XC[:, np.where(y == i)[0]]
meanClass = np.mean(Xi, axis=1).reshape(-1, 1)
Sw = Sw + np.dot((Xi - meanClass), (Xi - meanClass).T)
Sb = Sb + Xi.shape[1] * np.dot((meanClass - meanTotal), (meanClass - meanTotal).T)
# solve eigenvalue problem for a general matrix
self._eigenvalues, self._eigenvectors = np.linalg.eig(np.linalg.inv(Sw) * Sb)
# sort eigenvectors by their eigenvalue in descending order
idx = np.argsort(-self._eigenvalues.real)
self._eigenvalues, self._eigenvectors = self._eigenvalues[idx], self._eigenvectors[:, idx]
# only store (c-1) non-zero eigenvalues
self._eigenvalues = np.array(self._eigenvalues[0:self._num_components].real, dtype=np.float32, copy=True)
self._eigenvectors = np.matrix(self._eigenvectors[0:, 0:self._num_components].real, dtype=np.float32, copy=True)
# get the features from the given data
features = []
for x in X:
xp = self.project(x.reshape(-1, 1))
features.append(xp)
return features
