def inverse_transform(self, X):
"""
Perform an approximation of the input matrix of observations
to the original dimensionality space
:param X: The matrix of observations, where the training samples
populate the rows, and the features populate the columns
:return: Xhat, the dimensionality increased representation of the data
"""
return linalg.dot(X, self.principal) + self.mean
def transform(self, X):
"""
Perform dimensionality reduction of the input matrix X
:param X: The matrix of observations, where the training samples
populate the rows, and the features populate the columns
:return: Xtilde, the dimensionally reduced representation of the data
"""
# center the data by subtracting the mean
self.mean = T.mean(X, axis=0)
X -= self.mean
U, s, V = linalg.svd(X, full_matrices=False)
# Keep track of the 'M' principal directions
# The svd actually produces V^T, so the
# principal directions are stored in the rows of
# V as opposed to the columns
self.principal = V[:self.dim]
# Return the transformed data
return linalg.dot(X, T.transpose(self.principal))
